MBA CET 2025 Slot 4 question paper with solutions

Approach: Successive division — reconstruct the number from the last quotient.

Solution:
Let the last quotient be k. Work from the innermost division outwards.
Third division (by 7) leaves 4: the quotient before it = 7k + 4.
Second division (by 4) leaves 1: the quotient before it = 4(7k + 4) + 1 = 28k + 17.
First division (by 3) leaves 2: N = 3(28k + 17) + 2 = 84k + 53.
Note 3 × 4 × 7 = 84, so N = 84k + 53 ⇒ remainder on dividing by 84 = 53.
Check with k = 0: N = 53 → 53 ÷ 3 = 17 r 2; 17 ÷ 4 = 4 r 1; 4 ÷ 7 = 0 r 4. ✓

Cetking shortcut: Remainder by the product of divisors = r1 + d1·r2 + d1·d2·r3 = 2 + 3×1 + 12×4 = 53.

Answer: C

Approach: Assume a convenient total and convert each fraction to counts.

Solution:
Let total seats = 60 (LCM of 4, 5, 3).
Lower deck = 1/4 × 60 = 15 seats; sold = 4/5 × 15 = 12 → unsold on lower deck = 3.
Total sold = 2/3 × 60 = 40 → total unsold = 20.
Required fraction = 3/20.

Why the other options are wrong:
B (1/20): this is unsold lower-deck seats as a fraction of all seats, not of unsold seats.
C, D, E: do not follow from the counts 3 and 20.

Cetking shortcut: Take total = 60 (LCM of denominators) — all counts become integers instantly.

Answer: A

Approach: Perfect squares — estimate the root, then test which option leaves a square.

Solution:
553² = 305809 and 554² = 306916, so 306452 lies between them. Strictly, the smallest subtraction is 306452 − 305809 = 643, but 643 is not an option, so we test the options.
306452 − 1748 = 304704 = 552² (552² = 302500 + 2200 + 4 = 304704). ✓
Other options: 306452 − 1980 = 304472, − 1396 = 305056, − 1558 = 304894, − 1290 = 305162 — all lie strictly between 552² = 304704 and 553² = 305809, so none is a perfect square.
Hence the only choice that gives a perfect square is 1748.

Why the other options are wrong:
A, C, D, E: the results (304472, 305056, 304894, 305162) are not squares.

Cetking shortcut: Only the option giving 552² = 304704 works; the result must end in …04, which spots it fast.

Answer: B

Approach: LCM + common remainder, then the divisibility condition.

Solution:
LCM(6, 9, 15, 18) = 90, so the number = 90k + 4.
Test k = 1, 2, 3, 4: 94, 184, 274, 364.
Divisible by 7? 94 = 7×13 + 3 ✗; 184 = 7×26 + 2 ✗; 274 = 7×39 + 1 ✗; 364 = 7×52 ✓.
Least such multiple of 7 = 364.

Why the other options are wrong:
A (94), E (184): of the form 90k + 4 but not multiples of 7.
B (74): leaves remainder 2 on division by 6, so fails.
C (240): leaves remainder 0 on division by 6.

Cetking shortcut: 90k + 4 ≡ 6k + 4 (mod 7) = 0 ⇒ 6k ≡ 3 ⇒ k ≡ 4 → number = 364.

Answer: D

Approach: Biggest equal bag = HCF ⇒ fewest bags.

Solution:
Largest bag size = HCF(184, 230, 276).
184 = 2³ × 23, 230 = 2 × 5 × 23, 276 = 2² × 3 × 23 → HCF = 2 × 23 = 46 kg.
Bags = 184/46 + 230/46 + 276/46 = 4 + 5 + 6 = 15.

Cetking shortcut: Differences 46 and 46 hint the HCF directly: 230 − 184 = 46 and 46 divides all three.

Answer: B

Approach: Average shift — extra marks of the newcomers spread over the whole class.

Solution:
Total marks = 64n + 8 × 73 = 64n + 584.
New average = (64n + 584)/(n + 8) = 64 + 72/(n + 8).
For a whole number, (n + 8) must divide 72: possible n + 8 = 36, 72, 24, 18, …
With 25 < n < 60, n + 8 lies between 33 and 68 ⇒ n + 8 = 36, so n = 28.
The class (old + new students) therefore has 36 students; new average = 64 + 72/36 = 66.
Option B (36) is the strength of the entire class after the new students join.

Why the other options are wrong:
A (18), C (72): divisors of 72 but n + 8 = 18 or 72 gives n outside 25–60.
D (27), E (45): 72/(27) and 72/(45) are not whole numbers.

Cetking shortcut: Newcomers bring 8 × 9 = 72 extra marks; whole-class size must be a divisor of 72 between 33 and 68 → 36.

Answer: B

Approach: Split the team total into excluded + remaining.

Solution:
Let the team average = x ⇒ team total = 11x.
Captain = 25, wicket-keeper = 28 ⇒ their total = 53.
Remaining 9 players: average x − 1 ⇒ total 9(x − 1).
11x = 53 + 9x − 9 ⇒ 2x = 44 ⇒ x = 22.

Cetking shortcut: Removing two members lowers the average by 1 for 9 players: 53 − 2x = −9 ⇒ the two exceed the average by 9 in total ⇒ x = (53 − 9)/2 = 22.

Answer: B

Approach: Total = average × number.

Solution:
Total errors = 512 × 4 = 2048.
Errors in remaining pages = 2048 − 1208 = 840.
Remaining pages = 512 − 302 = 210.
Average = 840/210 = 4.

Cetking shortcut: First 302 pages average 1208/302 = 4, equal to the overall average ⇒ the rest must also average 4.

Answer: D

Approach: Reverse the operations from the end.

Solution:
After a sale: left = x/2 − ½ ⇒ before the sale x = 2(left + ½) = 2 × left + 1.
After 4th customer: 15 ⇒ before 4th = 31.
Before 3rd = 2 × 31 + 1 = 63.
Before 2nd = 2 × 63 + 1 = 127.
Before 1st = 2 × 127 + 1 = 255.

Cetking shortcut: Each step maps L → 2L + 1, i.e. (L + 1) doubles: 16 × 2⁴ = 256 ⇒ start = 255.

Answer: B

Approach: Form one linear equation in the price.

Solution:
Let price per book = p paise ⇒ money = 20p paise.
New price = (p − 25) paise; 22 books + 70 paise left: 22(p − 25) + 70 = 20p.
22p − 550 + 70 = 20p ⇒ 2p = 480 ⇒ p = 240 paise.
Money = 20 × 240 = 4800 paise = Rs. 48.
Check: 22 × 215 = 4730; 4800 − 4730 = 70 paise. ✓

Cetking shortcut: Options ÷ 20 give the price; only Rs. 48 → Rs. 2.40 per book works: Rs. 2.15 × 22 = 47.30, leaving 70 paise.

Answer: C

Approach: Place-value algebra.

Solution:
Original number = 10a + b.
Units digit +100% → 2b; tens digit +50% → 1.5a. New number = 10(1.5a) + 2b = 15a + 2b.
15a + 2b = 10a + b + 19 ⇒ 5a + b = 19.
a = 2 ⇒ b = 9 → 29; a = 3 ⇒ b = 4 → 34 (not an option).
Check 29: tens 2 → 3, units 9 → 18 ⇒ new value 30 + 18 = 48 = 29 + 19. ✓

Why the other options are wrong:
A (22): 5×2 + 2 = 12 ≠ 19.
B (25): 15 ≠ 19.
C (27): 17 ≠ 19.
E (21): 11 ≠ 19.

Cetking shortcut: Just test 5 × (tens) + (units) = 19 on the options — only 29 gives 10 + 9 = 19.

Answer: D

Approach: Expenditure = Price × Consumption.

Solution:
Let original price = P; original expenditure = 10P.
New price = 1.32P; new expenditure = 1.10 × 10P = 11P.
New consumption = 11P/1.32P = 11/1.32 = 8.33 kg.

Why the other options are wrong:
A, B, D, E: none equals 11/1.32 = 8.33.

Cetking shortcut: Consumption factor = 1.10/1.32 = 5/6 ⇒ 10 × 5/6 = 8.33 kg.

Answer: C

Approach: Complement percentage gives the count.

Solution:
Adults = 30% + 40% = 70% ⇒ children = 30%.
30% of total = 24 ⇒ total = 24 × 100/30 = 80.

Cetking shortcut: 10% = 8 ⇒ 100% = 80.

Answer: B

Approach: Successive percentage change.

Solution:
Value factor = 1.10 × 0.80 = 0.88.
Change = 0.88 − 1 = −12% ⇒ 12% decrease.
Formula check: 10 − 20 + (10 × −20)/100 = −10 − 2 = −12%.

Why the other options are wrong:
D (10% decrease): simple addition, ignores the cross term.
C, E, B: do not match 1.1 × 0.8.

Cetking shortcut: a + b + ab/100 = 10 − 20 − 2 = −12.

Answer: A

Approach: Same SP ⇒ CP ratio = inverse of multiplying factors.

Solution:
Let the costs be x (profit 40%) and y (loss 40%).
Same SP: 1.4x = 0.6y ⇒ x : y = 0.6 : 1.4 = 3 : 7.
x + y = 8000 ⇒ x = 3/10 × 8000 = 2400, y = 5600.
Cheaper instrument = Rs. 2400.

Cetking shortcut: CP ratio = 60 : 140 = 3 : 7 ⇒ 8000 × 3/10 = 2400.

Answer: B

Approach: Total SP from overall loss, then per-unit price.

Solution:
Cost = Rs. 300; overall loss 10% ⇒ total SP = 0.9 × 300 = Rs. 270.
Saleable butter = 5 − 1 = 4 kg.
SP per kg = 270/4 = Rs. 67.50.

Why the other options are wrong:
E (55) / B (52.5): dividing over 5 kg or wrong loss base.
D (60): that is the cost price per kg.

Answer: A

Approach: Compute both cost prices from the same SP.

Solution:
CP₁ = 500/1.20 = 416.67.
CP₂ = 500/0.88 = 568.18.
Total CP = 984.85; total SP = 1000.
Gain = 15.15 ⇒ gain% = 15.15/984.85 × 100 ≈ 1.54% ≈ 1.5% gain.

Why the other options are wrong:
B, D, E: give a loss, but total CP is below total SP.
C (2% gain): over-estimates; exact value ≈ 1.54%.

Cetking shortcut: Take SP = 1320 (LCM-friendly): CP₁ = 1100, CP₂ = 1500 ⇒ CP total 2600, SP 2640 ⇒ gain 40/2600 ≈ 1.54%.

Answer: A

Approach: Successive multiplying factors, reversed.

Solution:
Customer price = CP × 1.18 × 1.20 × 1.25.
1.18 × 1.20 = 1.416; × 1.25 = 1.77.
CP = 30.09/1.77 = Rs. 17.

Cetking shortcut: Test the options: 17 × 1.77 = 30.09 ✓.

Answer: C

Approach: Two linear equations from the folded halves.

Solution:
Let the sheet be l × b.
Fold across the length: half is (l/2) × b ⇒ perimeter = l + 2b = 34.
Fold across the breadth: half is l × (b/2) ⇒ perimeter = 2l + b = 38.
Adding: 3(l + b) = 72 ⇒ l + b = 24. Subtracting: l − b = 4 ⇒ l = 14, b = 10.
Area = 14 × 10 = 140 sq. cm.

Cetking shortcut: Add the two perimeters: 3(l + b) = 72 ⇒ l + b = 24, then subtract for l − b = 4.

Answer: B

Approach: Absolute quantities of each component, then add.

Solution:
Volumes 3 : 4 : 5.
Milk = 3 × 4/5 + 4 × 3/4 + 5 × 5/7 = 12/5 + 3 + 25/7.
Water = 3 × 1/5 + 4 × 1/4 + 5 × 2/7 = 3/5 + 1 + 10/7.
Multiply by 35: milk = 84 + 105 + 125 = 314; water = 21 + 35 + 50 = 106.
Ratio = 314 : 106 = 157 : 53.

Why the other options are wrong:
A (4:1), E (5:2): just one container's ratio.
C, D: arithmetic slips in the LCM step.

Cetking shortcut: Total = 12 parts; water total ≈ 106/35 ≈ 3.03 ⇒ milk : water ≈ 2.96 : 1 — only 157:53 (≈ 2.96) fits.

Answer: B

Approach: Partnership — time-weighted capital.

Solution:
Let P, Q invest 5x and 6x for 12 months; R invests 6x for 6 months.
Capital employed over the year (in year-equivalents) = 5x + 6x + 6x × 6/12 = 14x.
Profit = 20% of capital employed = 0.2 × 14x = 2.8x = 98000.
x = 98000/2.8 = 35000.
R's investment = 6x = 6 × 35000 = Rs. 2,10,000.
Check: R's capital-months 210000 × 6 = 12.6 lakh out of 58.8 lakh total ⇒ R's profit share = 98000 × 3/14 = 21000 (10% of his amount for half a year at 20% p.a.). ✓

Why the other options are wrong:
A, B, D, E: do not give 6x with 2.8x = 98000.

Cetking shortcut: Year-equivalent capital = 14 units; 20% of 14 = 2.8 units = 98000 ⇒ 1 unit = 35000 ⇒ R = 6 units.

Answer: C

Approach: Replacement — component removed in proportion.

Solution:
Let A = 7k, B = 5k (total 12k).
9 L drawn: A removed = 9 × 7/12 = 21/4, B removed = 9 × 5/12 = 15/4.
After refilling with 9 L of B: A = 7k − 21/4, B = 5k − 15/4 + 9 = 5k + 21/4.
(7k − 21/4) : (5k + 21/4) = 7 : 9 ⇒ 63k − 189/4 = 35k + 147/4 ⇒ 28k = 84 ⇒ k = 3.
Initial A = 7 × 3 = 21 litres.

Why the other options are wrong:
A, B, D, E: the equation fixes k = 3 uniquely, so A must be 7 × 3 = 21; e.g. A = 18 gives final ratio 12.75 : 18.11, not 7 : 9.

Cetking shortcut: A is unchanged except for the proportional removal: total after = 12k and A share falls from 7/12 to 7/16 ⇒ A after = 7k − 21/4 = 7/16 × 12k ⇒ k = 3.

Answer: C

Approach: Distance = speed × time, then rectangle with ratio sides.

Solution:
12 km/hr = 12000 m/60 min = 200 m/min.
Perimeter = 200 × 8 = 1600 m.
Sides 3x and 2x ⇒ 2(3x + 2x) = 10x = 1600 ⇒ x = 160.
Length = 480 m, breadth = 320 m.
Area = 480 × 320 = 153600 sq. m.

Why the other options are wrong:
A, B, D, E: near-miss values; 480 × 320 is exactly 153600.

Cetking shortcut: Area = 6x² with x = 160 ⇒ 6 × 25600 = 153600.

Answer: C

Approach: Capital × months for each partner.

Solution:
A: 2000 × 12 = 24000.
B: 3000 × 4 + 4000 × 8 = 12000 + 32000 = 44000.
C: 4000 × 9 + 3000 × 3 = 36000 + 9000 = 45000.
Ratio = 24 : 44 : 45, total 113.
A's share = 24/113 × 8475 = 24 × 75 = Rs. 1800.

Why the other options are wrong:
A, C, D, E: none equals 24/113 × 8475 = 1800 (ignoring the changes in B's and C's capital gives a different ratio).

Cetking shortcut: 8475 = 113 × 75 — once you see that, A's share = 24 × 75 = 1800.

Answer: B

Approach: Mid-point theorem — medial triangle has 1/4 area.

Solution:
By the mid-point theorem, PQ, QR, RP are each half of the opposite side and parallel to it.
So triangle PQR is similar to ABC with ratio 1 : 2 ⇒ area ratio 1 : 4.
The four small triangles APR, PBQ, RQC and PQR are congruent.
Area of PQR = 20/4 = 5 sq. units.

Why the other options are wrong:
A (10): half, not a quarter.
B, D, E: not 20/4.

Answer: C

Approach: Relative speed, same direction.

Solution:
Relative speed = 125/10 = 12.5 m/s = 12.5 × 18/5 = 45 km/hr.
Same direction ⇒ train speed − 5 = 45 ⇒ train speed = 50 km/hr.

Why the other options are wrong:
A (45): relative speed, forgot to add the man's 5 km/hr.
C, D, E: arithmetic slips.

Answer: B

Approach: Train length + bridge length = speed × time.

Solution:
45 km/hr = 45 × 5/18 = 12.5 m/s.
Distance in 30 s = 12.5 × 30 = 375 m.
Bridge = 375 − 130 = 245 m.

Why the other options are wrong:
D (250), B (230), A (200), E (220): miscalculated distance or wrong subtraction.

Answer: C

Approach: Relative speed — opposite direction trains.

Solution:
Let speeds be x and y; lengths = 27x and 17y.
Opposite directions: (27x + 17y)/(x + y) = 23.
27x + 17y = 23x + 23y ⇒ 4x = 6y ⇒ x : y = 3 : 2.

Why the other options are wrong:
A, C, D, E: do not satisfy 4x = 6y.

Cetking shortcut: Ratio = (t₂ − t)/(t − t₁) = (23 − 17)/(27 − 23) = 6/4 = 3 : 2.

Answer: B

Approach: Equal train length in both cases.

Solution:
4.5 km/hr = 1.25 m/s; 5.4 km/hr = 1.5 m/s. Let the train speed = v m/s.
Length = 8.4(v − 1.25) = 8.5(v − 1.5).
8.4v − 10.5 = 8.5v − 12.75 ⇒ 0.1v = 2.25 ⇒ v = 22.5 m/s.
v = 22.5 × 18/5 = 81 km/hr.
Check: length = 8.4 × 21.25 = 178.5 m = 8.5 × 21 ✓.

Why the other options are wrong:
A, B, C, E: substituting gives unequal train lengths.

Cetking shortcut: Test options in m/s: 81 km/hr = 22.5 m/s ⇒ 8.4 × 21.25 = 8.5 × 21 = 178.5 ✓.

Answer: D

Approach: LCM / units method with cycles.

Solution:
Total work = LCM(20, 30, 60) = 60 units.
Efficiencies: A = 3, B = 2, C = 1 units/day.
3-day cycle: day 1 = 3, day 2 = 3, day 3 = 3 + 2 + 1 = 6 ⇒ 12 units per 3 days.
60/12 = 5 cycles ⇒ 5 × 3 = 15 days (work ends exactly on a cycle boundary).

Why the other options are wrong:
A (12), C (16), D (18), E (13): wrong cycle count or wrong cycle output.

Answer: B

Approach: Mandays — convert everyone to boy-units.

Solution:
Let a man do M and a boy B units/day.
10(6M + 8B) = 2(26M + 48B) ⇒ 60M + 80B = 52M + 96B ⇒ 8M = 16B ⇒ M = 2B.
Work = 10(6 × 2B + 8B) = 10 × 20B = 200B.
15 men + 20 boys = 30B + 20B = 50B per day.
Days = 200B/50B = 4.

Why the other options are wrong:
B, C, D, E: do not equal 200/50.

Cetking shortcut: 1 man = 2 boys ⇒ first group = 20 boy-units × 10 days = 200; new group = 50 boy-units ⇒ 4 days.

Answer: A

Approach: Rate method with a machine switched off.

Solution:
Take work = 120 units (LCM of 8, 10, 12): P = 15, Q = 12, R = 10 units/hr.
9 A.M.–11 A.M. (2 hr), all three: 2 × 37 = 74 units.
Remaining = 120 − 74 = 46 units; Q + R = 22 units/hr.
Time = 46/22 ≈ 2.09 hr ≈ 2 hr 5 min.
Finish ≈ 11 A.M. + 2 hr 5 min ≈ 1:05 P.M. ≈ 1:00 P.M.

Why the other options are wrong:
A, C: before 11 A.M. the work is only 74/120 done.
B (12:30 P.M.): only 33 more units by then.
E (1:30 P.M.): overshoots by ~25 min.

Answer: D

Approach: Units method with pair rates.

Solution:
Work = 24 units. A+B = 3, B+C = 2, A+B+C = 4 units/day.
C = 4 − 3 = 1; A = 4 − 2 = 2.
A + C = 3 units/day ⇒ 24/3 = 8 days.

Why the other options are wrong:
B (6): that is the trio's time.
D (12): that is B + C's time.
A, E: not 24/3.

Cetking shortcut: C = 1/6 − 1/8 = 1/24 and A = 1/6 − 1/12 = 2/24 ⇒ A + C = 3/24 = 1/8 ⇒ 8 days.

Answer: C

Approach: AP sum of ages.

Solution:
Ages: x, x + 3, x + 6, x + 9, x + 12.
Sum = 5x + 30 = 50 ⇒ x = 4.
Youngest = 4 years.

Why the other options are wrong:
C (10): the middle child's age.
B, D, E: do not give sum 50.

Cetking shortcut: Middle child = 50/5 = 10 ⇒ youngest = 10 − 6 = 4.

Answer: A

Approach: Ratio of ages with time shift.

Solution:
Sameer = 5x, Anand = 4x.
(5x + 3)/(4x + 3) = 11/9 ⇒ 45x + 27 = 44x + 33 ⇒ x = 6.
Anand = 4 × 6 = 24 years.

Why the other options are wrong:
E (30): Sameer's age.
B, C, D: not multiples of 4 that fit.

Cetking shortcut: Anand's age must be a multiple of 4: test 24 ⇒ Sameer 30 ⇒ 33 : 27 = 11 : 9 ✓.

Answer: A

Approach: Ratio ages with a past-sum condition.

Solution:
Present ages 4x, 7x, 9x ⇒ sum 20x.
Eight years ago: 20x − 24 = 56 ⇒ 20x = 80 ⇒ x = 4.
Ages = 16, 28, 36 years.

Why the other options are wrong:
A, D, E: not in ratio 4 : 7 : 9.
C (20, 35, 45): right ratio, but sum 8 years ago = 76, not 56.

Cetking shortcut: Only options in ratio 4:7:9 are B and C; B's sum 80 − 24 = 56 ✓.

Answer: B

Approach: Combinations — case-wise addition.

Solution:
3 men + 2 women: 7C3 × 6C2 = 35 × 15 = 525.
4 men + 1 woman: 7C4 × 6C1 = 35 × 6 = 210.
5 men: 7C5 = 21.
Total = 525 + 210 + 21 = 756.

Why the other options are wrong:
A, B, D, E: miss a case or miscount 6C2 = 15.

Answer: C

Approach: Permutations with identical letters.

Solution:
LEADER: 6 letters with E repeated twice (L, A, D, R once).
Arrangements = 6!/2! = 720/2 = 360.

Why the other options are wrong:
B, C, D, E: not 720/2.

Answer: A

Approach: nPr for ordered selections.

Solution:
LOGARITHMS has 10 distinct letters (L, O, G, A, R, I, T, H, M, S).
4-letter words without repetition = 10P4 = 10 × 9 × 8 × 7 = 5040.

Why the other options are wrong:
A, B, D, E: not 10 × 9 × 8 × 7.

Answer: C

Approach: Cube root via powers of 10.

Solution:
0.000216 = 216 × 10⁻⁶.
∛216 = 6 and ∛10⁻⁶ = 10⁻².
∛0.000216 = 6 × 10⁻² = 0.06.
Check: 0.06³ = 0.000216 ✓.

Why the other options are wrong:
A (0.6): cube = 0.216.
C (0.006): cube = 0.000000216.
D, E: 16 is not a cube root of 216.

Answer: B

Approach: Fixed distance — speed down, time up.

Solution:
Let the usual speed = s km/hr; scheduled time = 600/s.
600/(s − 200) − 600/s = 1/2.
600 × 200 = ½ × s(s − 200) ⇒ s² − 200s − 240000 = 0 ⇒ (s − 600)(s + 400) = 0 ⇒ s = 600 km/hr.
Scheduled duration of the flight = 600/600 = 1 hr (the slowed flight took 1 hr + 30 min = 1.5 hr).
The duration asked (scheduled flight time) = 1 hr.

Why the other options are wrong:
B (2 hrs): s = 300 ⇒ 600/100 − 2 = 4 hr extra, not 0.5.
C, D, E: likewise give extra time ≠ 30 min.

Cetking shortcut: Test options as the scheduled time t: 600/t − 600/(t + 0.5) must be 200 ⇒ t = 1: 600 − 400 = 200 ✓.

Answer: A

Approach: tan θ = height / base.

Solution:
Ship at 30°: distance = 100 × cot 30° = 100√3 ≈ 173.2 m.
Ship at 45°: distance = 100 × cot 45° = 100 m.
Opposite sides ⇒ distance between ships = 173.2 + 100 = 273.2 ≈ 273 m.

Why the other options are wrong:
C (173 m): only one ship's distance.
A, D, E: rounding or arithmetic slips; 100(√3 + 1) = 273.2.

Answer: B

Approach: Hollow cylinder volume × density.

Solution:
External radius R = 8/2 = 4 cm; internal radius r = 4 − 1 = 3 cm.
Volume = 22/7 × (16 − 9) × 21 = 22/7 × 7 × 21 = 462 cm³.
Weight = 462 × 8 = 3696 g = 3.696 kg.

Why the other options are wrong:
A, B, D, E: rounding variants; exact value is 3.696 kg.

Answer: C

Approach: Speed ∝ 1/time for a fixed distance.

Solution:
Upstream time = 8 h 48 min = 8.8 hr; downstream time = 4 hr.
Downstream : upstream speed = 8.8 : 4 = 11 : 5.
b + c = 11k, b − c = 5k ⇒ b = 8k, c = 3k.
Boat : current = 8 : 3.

Why the other options are wrong:
A, B, D, E: do not give (b + c)/(b − c) = 11/5.

Cetking shortcut: b : c = (11 + 5)/2 : (11 − 5)/2 = 8 : 3.

Answer: C

Approach: Boats and streams — time difference equation.

Solution:
36/(10 − s) − 36/(10 + s) = 1.5.
36 × 2s = 1.5(100 − s²) ⇒ 72s = 150 − 1.5s² ⇒ s² + 48s − 100 = 0.
(s + 50)(s − 2) = 0 ⇒ s = 2 mph.
Check: 36/8 − 36/12 = 4.5 − 3 = 1.5 hr = 90 min ✓.

Why the other options are wrong:
B (2.5): 36/7.5 − 36/12.5 = 1.92 hr.
C (3): 36/7 − 36/13 ≈ 2.37 hr.
D, E: even larger gaps.

Cetking shortcut: Option test is fastest: s = 2 gives 4.5 − 3 = 1.5 hr ✓.

Answer: A

Approach: Average of downstream and upstream speeds.

Solution:
Upstream: 0.75 km in 11 min 15 s = 11.25 min ⇒ speed = 0.75 × 60/11.25 = 4 km/hr.
Downstream: 0.75 km in 7.5 min ⇒ speed = 0.75 × 60/7.5 = 6 km/hr.
Still water speed = (6 + 4)/2 = 5 km/hr.

Why the other options are wrong:
A (1 km/hr): that is the stream speed.
B, C, D: not (6 + 4)/2.

Answer: E

Approach: Fill fraction by the full-time pipe first.

Solution:
A fills 1/37.5 = 2/75 per min; in 30 min A fills 30 × 2/75 = 4/5.
B fills the remaining 1/5 of the cistern.
B's time = (1/5) × 45 = 9 min.
So B was turned off after 9 minutes.

Why the other options are wrong:
A, C, D, E: give B's share ≠ 1/5.

Cetking shortcut: A alone in 30 min = 30/37.5 = 80% ⇒ B did 20% of 45 min = 9 min.

Answer: B

Approach: LCM units, two phases.

Solution:
Tank = 60 units; A = 4, B = 3 units/min.
First 4 min together: 4 × 7 = 28 units.
Remaining 32 units by B alone: 32/3 = 10 2/3 min = 10 min 40 s.
Total = 4 min + 10 min 40 s = 14 min 40 s.

Why the other options are wrong:
E (10 min 40 s): time for B alone after A stops.
A, B, D: arithmetic slips in 32/3.

Answer: C

Approach: Clock angle formula.

Solution:
At 4:20, H = 4, M = 20.
Angle = |30 × 4 − 5.5 × 20| = |120 − 110| = 10°.

Why the other options are wrong:
A, B, C, E: not |120 − 110|.

Cetking shortcut: Minute hand at 4 exactly (120°); hour hand has moved 20 × 0.5 = 10° past 4 ⇒ 10°.

Answer: D

Approach: Races — head start and time margin.

Solution:
A's speed = 5 km/hr = 25/18 m/s ⇒ A's time for 100 m = 100 × 18/25 = 72 s.
B starts 8 m ahead ⇒ runs 92 m, and finishes 8 s after A ⇒ B's time = 80 s.
B's speed = 92/80 = 1.15 m/s = 1.15 × 18/5 = 4.14 km/hr.

Why the other options are wrong:
B, C, D, E: use 100 m or 72/80 s wrongly.

Cetking shortcut: B's speed = 5 × (92/100) × (72/80) = 5 × 0.92 × 0.9 = 4.14 km/hr.

Answer: A

Approach: Logical chain — fact, consequence, reason, contrast, example, conclusion.

Solution: A states the fact (branded diapers are sold everywhere). D draws the consequence with "So": demand at any one store is price sensitive. B explains why: a customer can simply buy the brand elsewhere. C begins the contrast ("By contrast") with private labels, available only at one chain. E gives the example of that private label (SavOn). F concludes with "Then": stores should keep a higher margin on private labels. Order: A-D-B-C-E-F.

Why the other options are wrong:
A (ABCDEF) / B (ABCEDF): put B before D, so the "So" in D no longer follows the availability fact it depends on.
D (AEDBCF): E is an example of a private label and cannot come before C introduces private labels.
E (AEDCFB): same E-misplacement, and B (branded-diaper reasoning) cannot come after the conclusion F.

Cetking shortcut: Link words decide it: "So" (D) right after the fact, "By contrast" (C) opens the second half, "For instance" (E) must follow what it exemplifies, "Then" (F) closes.

Answer: C

Approach: Pronoun pairing + two idea blocks (discipline, then configuration).

Solution: Block 1 — discipline: A introduces "having a strategy is a matter of discipline"; C ("It requires... trade-offs") explains that discipline; E continues it (stay the course during upheaval). Block 2 — beyond best practices: D opens the new idea; B ("It involves the configuration of a tailored value chain") explains D; F ends with the system-fit consequence. Order: A-C-E-D-B-F.

Why the other options are wrong:
B (ACBDEF): B's "It involves configuration" explains D, so B cannot precede D.
C (DCBEFA) / E (DABCEF): A is the natural opener of the discipline block; ending with A or splitting A-C-E breaks it.
D (ABCEDF): B (value chain) is not about discipline and does not follow A.

Cetking shortcut: Each "It" (B, C) must sit right after the sentence it refers to: C after A (discipline), B after D (strategy beyond best practices).

Answer: A

Approach: General statement, reasons, conclusion with "So", then explanation of the conclusion.

Solution: B opens (ambassadors must choose their words). E explains their position (specialized job, ceremonial lives). A adds the constraint "As officials..." (their vision must stay close to the local people's). D concludes with "So" — there is an ambivalence at a first meeting. C explains that ambivalence: to say what they must, they appear to deny part of what they know. Order: B-E-A-D-C.

Why the other options are wrong:
A (BCEDA) / D (BCDEA): C explains the ambivalence and cannot come before D introduces it.
B (BEDAC): "So" in D needs both reasons (E and A) before it.
E (BACDE): E (specialized job) describes ambassadors generally and belongs right after B, not at the end.

Cetking shortcut: All options start with B; locate the "So" conclusion (D) and its explanation (C) as the final pair.

Answer: C

Approach: Chronology + "the two" reference + "on the other hand" pair.

Solution: E sets the background: both the Centre and the states had sounded the alarm. C — rains revived and a divide emerged "between the two" (Centre and states, named in E). B gives the Centre's side; D ("on the other hand") gives the states' side. A quotes an official on this face-off. Order: E-C-B-D-A.

Why the other options are wrong:
A (EBCDA): C's divide must be introduced before the two sides are described.
B (DBACE) / C (BDCAE): "the two" in C needs E first; D's "on the other hand" needs B before it.
E (ECBAD): A comments on the face-off and must come after both sides (B and D).

Cetking shortcut: "The two" (C) points straight back to E, and "on the other hand" (D) must follow B — only ECBDA keeps both.

Answer: D

Approach: Question, refinement, method, expected result, confirmation.

Solution: B poses the question (exact shape of the earth). E narrows it: it was known to be an oblate spheroid, but "how much more" was open. D gives the method ("One way of doing that" = establishing how much more). C states what the method predicts (arc shorter near the equator). A confirms "This fact" with the 1730s expeditions. Order: B-E-D-C-A.

Why the other options are wrong:
A (BECAD): D's "doing that" must directly follow the open question in E, not come last.
C (EDACB) / D (EBDCA): B is the clear opener introducing the topic.
E (BEDAC): "This fact" in A refers to C, so C must precede A.

Cetking shortcut: "This fact" (A) needs a stated fact (C) just before it; "doing that" (D) needs a task (E) just before it — BEDCA.

Answer: B

Approach: Sentence-opening adverb that fits the author's tone.

Solution: The paragraph before describes an idealised model (all options considered, utility of every outcome computed). The blank opens the comment "___ such a model reflects major simplifications of the way divisions [sic: decisions] are made in the real world" — the author treats this as self-evident, so "Obviously" fits.

Why the other options are wrong:
A Regrettably: adds a sense of regret the author does not express.
B Firstly: no list of points follows.
D Apparently: suggests doubt, but the author is certain.
E Important: an adjective, ungrammatical as a sentence opener here.

Answer: C

Approach: Collocation with the model being described.

Solution: The model assigns "a numerical value" to each outcome. Humans "tend not to think ___ as easily as the model calls for", i.e. they do not think in numbers — "quantitatively".

Why the other options are wrong:
B Systematically / C Scientifically / D Analytically: humans do think this way to some extent; the model's special demand is numerical valuation.
E Interestingly: unrelated to manner of thinking in the model.

Cetking shortcut: Look back for a matching clue: "numerical value derived for the utility" = quantitative.

Answer: A

Approach: Parallel structure within the sentence.

Solution: The sentence reads: "they often deal with a particular option without really assessing its ___ and when they do assess alternatives..." The second half repeats the idea with "alternatives", so the first half must be "alternatives" — people consider one option without comparing it with the others.

Why the other options are wrong:
A Implication / C Utility: fit "assessing" but the follow-up "when they do assess alternatives" shows the missing word is alternatives.
B Disadvantages / E Assets: too narrow; the model compares options, not pros or cons of one.

Cetking shortcut: "...when they DO assess alternatives" repeats the blank word — the echo gives the answer.

Answer: D

Approach: Verb collocation with "argument".

Solution: Firing people is as rare in a large company as using "a gun or a switch-blade to ___ an argument". One "resolves" (settles) an argument; the violent tool is used to end the dispute.

Why the other options are wrong:
B Thwart / C Defeat: one defeats an opponent, not an argument in this sense.
D Close: "close an argument" is not the natural idiom.
E Assume: makes no sense.

Answer: A

Approach: Meaning in context — process that let a failure happen.

Solution: The fired employee is a "failed product", and the question is how the process "___ such a phenomenon in the first place" — i.e. how the hiring/managing process let it happen: "allowed".

Why the other options are wrong:
A Derived: one derives something from a source, not a phenomenon from a process.
B Engineered / C Produced: imply deliberate creation, too strong.
E Delivered: used for products, not for letting a failure occur.

Cetking shortcut: "In the first place" signals asking how it was permitted to happen — allowed.

Answer: D

Approach: Word meaning — find the synonym.

Solution: Taciturnity means the habit of saying very little — reserve, quietness. The synonym is Calmness.

Why the other options are wrong:
B Strength, D Courage: qualities of character unrelated to speech.
C Precious: an adjective (valuable), wrong part of speech too.
E Beauty: unrelated.

Cetking shortcut: Taciturn = silent/reserved; of the options only "calmness" carries the quiet, composed sense.

Answer: A

Approach: Word meaning — find the synonym.

Solution: Attenuate means to make thin or weak, to reduce in force. The synonym is Make Thin.

Why the other options are wrong:
A Repent: to feel regret.
C Force: the opposite idea (strength).
D Divide: to split.
E Rule: to govern.

Cetking shortcut: Root "tenuis" (Latin) = thin, as in tenuous.

Answer: B

Approach: Word meaning — find the synonym.

Solution: Haughty means arrogantly proud, looking down on others. The synonym is Imperious.

Why the other options are wrong:
A Cemetery: a burial ground (noun).
B Adamant: refusing to change one's mind — stubborn, not proud.
D Recover: a verb, get back.
E Deadly: causing death.

Answer: C

Approach: Word meaning — find the synonym.

Solution: Reprisal means an act of retaliation, paying back an injury. The synonym is Retribution.

Why the other options are wrong:
A Indulgence: allowing oneself pleasure.
C Expanse: a wide area.
D Reluctance: unwillingness.
E Cautious: careful (adjective).

Answer: B

Approach: Word meaning — find the synonym.

Solution: Condescend means to behave as if one is superior; to look down on someone. The synonym is Disdain.

Why the other options are wrong:
A Mystery / C Joy / E Comprehend: unrelated meanings.
B Deride: to mock or ridicule openly — an act of scorn, while condescension is a superior attitude; "disdain" (to regard as beneath oneself) is the closer match.

Answer: D

Approach: Word meaning — find the antonym.

Solution: Axiom means a self-evident truth, an accepted principle. The antonym is Absurdity.

Why the other options are wrong:
A Scenic: having beautiful views.
B Flashy: showy.
D Subtle: delicate, hard to notice.
E Dark: lacking light.

Cetking shortcut: Only C is a noun about truth/sense — a self-evident truth vs. something plainly unreasonable.

Answer: C

Approach: Word meaning — find the antonym.

Solution: Repudiate means to reject, disown or refuse to accept. The antonym is Emphasize.

Why the other options are wrong:
B Abandon / C Decline: close to the meaning of repudiate (synonym-type distractors).
D Modest: an adjective, humble.
E Orient: to position or align.

Cetking shortcut: Strike out the synonyms first (abandon, decline); "emphasize" — to stress and affirm — is the only opposite-direction verb left.

Answer: A

Approach: Word meaning — find the antonym.

Solution: Remonstrate means to protest or object forcefully. The antonym is Endorse.

Why the other options are wrong:
A Dictate: to order.
B Neglect / E Abandon: to ignore or leave — not the opposite of protesting.
D Strengthen: to make stronger.

Answer: C

Approach: One-word substitution for a stage of life.

Solution: Dotage = extreme old age marked by weakness of mind, when a person behaves foolishly.

Why the other options are wrong:
A Nostalgia: longing for the past.
B Serendipity: a happy chance discovery.
D Superannuation: retirement because of age / pension scheme — no foolish behaviour implied.
E Ethnicity: belonging to a cultural group.

Cetking shortcut: In one's dotage = senile; "dote" also means to be foolishly fond.

Answer: C

Approach: One-word substitution for a belief.

Solution: A fatalist believes that all events are predetermined (fate) and cannot be changed.

Why the other options are wrong:
A Extremist: holds extreme political/religious views.
C Tyrant: a cruel ruler.
D Puritan: one with very strict moral/religious standards.
E Egalitarian: believes all people are equal.

Answer: B

Approach: Third conditional (past unreal condition): if + had + V3, would have + V3.

Solution: The main clause "would have died" is a past unreal result, so the if-clause must be in the past perfect: "if the villagers had not got him admitted". "Did not get" (simple past) is wrong. The error is in part C.

Why the other options are wrong:
A "He fell from a running train": correct simple past.
B "and would have died": correct third-conditional result.
D "to a nearby hospital immediately": correct.
E No error: there is a tense error in C.

Cetking shortcut: "Would have + V3" in one clause → "had + V3" in the if-clause.

Answer: C

Approach: Phrasal idiom: "go down to one's doom".

Solution: The idiom is "to go (down) to one's doom" — the preposition "to" is missing. Correct: "and then went down to his doom very quickly". The error is in part D.

Why the other options are wrong:
A "He deserted the path of honor": correct.
B "in order to": correct purpose phrase.
C "satisfy his ambition": correct.
E No error: the preposition is missing in D.

Cetking shortcut: When a verb of motion is followed by a destination noun (doom, death, ruin), check for "to".

Answer: D

Approach: "One of the + superlative + plural noun".

Solution: "One of the ..." picks one item from a group, so the noun must be plural: "one of the most interesting books". The error is in part B.

Why the other options are wrong:
A "This is one of the": correct.
C "I have": correct present perfect.
D "ever read": correct.
E No error: "book" must be plural.

Cetking shortcut: "One of the" is always followed by a plural noun.

Answer: B

Approach: Narrative chronology.

Solution: 3 sets the scene (Mintu wants a day off). 5 follows with "Therefore" (he pretends to be sick). 2: his father believes it and calls the doctor. 1: the doctor examines him and takes out a syringe. 4: "Immediately" Mintu jumps up and says he is fine. Order: 3-5-2-1-4.

Why the other options are wrong:
B (35241): 4 (reaction) cannot come before 1 (the syringe that causes it).
C (15234): the doctor cannot appear before he is summoned.
D (34215): Mintu cannot jump up "immediately" before anything happens.
E (35412): same problem — 4 before the doctor is called.

Cetking shortcut: Find the trigger-reaction pair: syringe (1) → jumps up (4) must be the last two.

Answer: A

Approach: General statement → two parallel examples → shift → closing question.

Solution: 5 introduces the topic: both the industry and the government have acted. 2 ("The industry, on its part") and 4 ("The Government, on the other hand") give the two actions in that order. 3 shifts from legality to morality. 1 ends with the moral question to the reader. Order: 5-2-4-3-1.

Why the other options are wrong:
A (15243) / E (51243): the rhetorical question 1 fits after the morality point, not as the opener here.
B (53241): 3 ("more than the legality") must come after the legal actions 2 and 4.
C (52413): puts the moral question 1 before 3, which first introduces the morality angle.

Cetking shortcut: "Both the industry and the government" (5) names the order: industry (2), then government (4).

Answer: D

Approach: Idiom meaning.

Solution: To make a clean breast of something = to confess it fully and frankly — "to confess without reserve" (option C).

Why the other options are wrong:
A To gain prominence / B To praise oneself / D To destroy before it blooms / E To appreciate someone: none relate to confessing.

Answer: C

Approach: Idiom meaning.

Solution: To catch a tartar = to tackle someone who turns out to be far too strong for you; to meet more than your match. That is option D, "To deal with a person who is more than one's match".

Why the other options are wrong:
A To trap wanted criminal with great difficulty / B To catch a dangerous person: literal readings of "catch"; the idiom is about the catcher being overpowered.
C To meet with disaster: too general.
E To meet an old friend: unrelated.

Cetking shortcut: Story behind it: a soldier shouts he has caught a Tartar, but the Tartar will not let him go — the captor is the one trapped.

Answer: D

Approach: Idiom meaning.

Solution: To have an axe to grind = to have a private, selfish motive behind what one does — "a private end to serve" (option D).

Why the other options are wrong:
A To fail to arouse interest / B To have no result: unrelated.
C To work for both sides: that is double-dealing.
E To be unbiased: the opposite — an axe to grind means bias.

Answer: D

Approach: Idiom meaning.

Solution: To pick holes (in something) = to find faults, to criticise — "to criticise someone" (option C).

Why the other options are wrong:
A To find some reason to quarrel: "pick a quarrel", a different idiom.
B To destroy something / D To cut some part of an item: literal readings.
E To find escape routes: unrelated.

Answer: C

Approach: Idiom meaning.

Solution: To look a gift horse in the mouth = to find fault with or be ungrateful about something received as a gift (from checking a gifted horse's teeth to judge its age). Option B.

Why the other options are wrong:
A Welcome a gift: the opposite.
C Be fastidious: too general.
D To be kind: unrelated.
E Examine a gift carefully: the literal action; the idiom stresses ungrateful fault-finding.

Answer: B

Approach: Specific detail — locate the line on gradual emancipation.

Solution: Para 2: Lincoln proposed compensation and "colonization", "But fate was to deem otherwise. The haste with which the South wanted to break away from the Union with the North, compelled him to move faster than he expected." So the South's haste to secede blocked the gradual process — option D.

Why the other options are wrong:
A His proposition of a grant for rehabilitation: part of his gradual plan, not the obstacle.
B His own over-enthusiasm: the text says he was compelled, not eager.
C Inadequate compensation: never mentioned.
E His ownership mindset: not in the passage.

Cetking shortcut: Signal phrase "But fate was to deem otherwise" — the answer is the very next sentence.

Answer: D

Approach: Inference — meaning of a quoted line from its context.

Solution: Lincoln said "We must free the slaves, or be ourselves subdued" and then "In giving freedom to the slaves, we assure freedom to the free." Freeing the slaves protects the freedom of those already free — i.e. it safeguards our own interests (option D).

Why the other options are wrong:
A "they will serve us better": the passage never talks of slaves serving anyone after freedom.
B "they will free themselves": not suggested.
C "honouring the concept of freedom": an abstract idea; the line is about securing the freedom of the free, as "or be ourselves subdued" shows.
E "we are helping them": only the slaves' side; the line is about "the free".

Cetking shortcut: Read the sentence just before the quote — "or be ourselves subdued" points to self-protection.

Answer: D

Approach: Vocabulary in context.

Solution: The passage: "grants for the rehabilitation of blacks — 'colonization' as he called it." So colonization means settling the freed slaves in a separate place of their own — a colony of (freed) slaves, option E.

Why the other options are wrong:
A Handing over slaves to slave-owners: the opposite of emancipation.
B Efforts by blacks to free themselves: not what the word refers to.
C Separate dwellings for slave-owners / D Rehabilitation for slave-owners: the rehabilitation was for blacks, not owners (owners got compensation).

Cetking shortcut: The dash defines the term: "rehabilitation of blacks — colonization" → resettling the freed slaves.

Answer: E

Approach: Inference — what shows his compassion.

Solution: Para 1: Lincoln "did not fancy himself a liberator. He thought it would be better for all if emancipation was a gradual process", with compensation for owners and rehabilitation grants for blacks. A slow plan that took care of every party is what the passage presents as his compassionate approach — option E.

Why the other options are wrong:
A His hesitation: not presented as a virtue.
B "His efforts to force the American blacks from slavery": "force" distorts the idea of freeing; the passage stresses gradual, not forced, change.
C His care and compassion: restates the question (circular) instead of naming what made him compassionate.
D Indifference in conducting the war: the passage praises his dignity in the war.

Cetking shortcut: Reject the circular option that repeats the question's own word ("compassion").

Answer: E

Approach: Preposition with "hell-bent".

Solution: "Hell-bent" (determined at any cost) takes "on/upon" + -ing: "hell-bent upon getting". "At" is wrong. "Upon" is the formal form of "on", so option C "hell bent upon getting" corrects the sentence.

Why the other options are wrong:
A hell bent on getting: also an acceptable form; the key takes the formal "upon".
B for / D in: wrong prepositions with "bent".
E No improvement: "bent at" is incorrect.

Cetking shortcut: "Bent on/upon" = determined — never "bent at" or "bent for".

Answer: C

Approach: Third conditional — inverted form.

Solution: The result "I would have been able to read" is a past unreal result, so the condition is past perfect. "Had the room been brighter" is the inverted (if-less) third conditional and is the improvement the question expects; note that option D repeats the original text, so the setter treats C as the preferred form.

Why the other options are wrong:
A If the room was brighter: simple past — second conditional, wrong with "would have been".
B If the room are brighter: subject-verb error.
D If the room had been brighter: identical to the given part, so it is not a replacement.
E No improvement: rejected because D already reproduces the original.

Cetking shortcut: Third conditional: "If + had + V3" = "Had + subject + V3".

Answer: C

Approach: Direct to indirect — imperative with "Please".

Solution: A request beginning with "Please" becomes "requested + object + to-infinitive"; "my" changes to "his". So: "He requested his father to increase his pocket-money."

Why the other options are wrong:
A keeps the direct speech with quotes.
B "pleaded his father ... please ... my": keeps "please" and "my" — not converted.
D "asked his father to": loses the polite request sense of "Please".
E "asked ... if he could": turns a request into a question.

Cetking shortcut: "Please" in direct speech → "requested" in indirect speech.

Answer: C

Approach: Analogy — antonym pair.

Solution: Indigent (very poor) : Wealthy (rich) are opposites. The only pair built as an opposite is C, gauche (awkward, lacking grace) : graceful: the paper prints "disgraceful", clearly a slip for "graceful" (the antonym of gauche).

Why the other options are wrong:
A angry : rich / B native : affluent: unrelated words.
D scholarly : erudite: synonyms (both learned), not opposites.
E bushel : corn: unit : thing measured.

Cetking shortcut: Classify the stem pair first (antonyms), then delete every synonym or unrelated pair.

Answer: C

Approach: Analogy — antonym pair.

Solution: Corporeal (bodily, physical) : Spiritual (of the soul) are opposites. Moron (very foolish person) : Savant (very learned person) are also opposites — option B.

Why the other options are wrong:
A mesa : plateau: near-synonyms (flat-topped landforms).
C foreigner : immigrant: related, not opposite.
D pedagogue : teacher: synonyms.
E colours : pallet: things on a palette — part/holder relation.

Answer: B

Approach: Conjunction "that" vs. relative "what".

Solution: "Know" needs a noun clause: "they know that it requires a long time". "What it requires a long time" is ungrammatical because "what" would need a missing object, but "a long time" already fills it. Error in part C.

Why the other options are wrong:
A "Those who want to do good are": correct.
B "neither selfish nor in a hurry because": correct neither-nor pair.
D "time to impregnate people with good": correct.
E No error: C is wrong.

Cetking shortcut: If the clause after "what" is already complete, "what" must become "that".

Answer: C

Approach: Main idea — the statement that covers every paragraph.

Solution: The passage moves from the history of robots (1921 play, 1961 first robot) to industrial uses, scientific/space uses, home robots (Roomba) and robot cars, ending with "Robots have come a long way... Now, robots help people at home, in factories, and in scientific research." The idea that runs through all of it is that robots now perform many complex tasks — option C.

Why the other options are wrong:
A The word robot was invented in 1921: a single detail from para 1.
B Robots in industry and scientific research: covers only part of the passage (misses home use and cars).
D People won't drive cars in future: only the last paragraph's prediction.
E Loss of some jobs: one point from para 3.

Cetking shortcut: For thesis questions, test each option against the first AND last paragraph — only C fits both ("latest robots... complex tasks" / "robots have come a long way").

Answer: C

Approach: Specific detail.

Solution: Para 1: Engelberger and Devol "produced the first real robot in 1961. Robots of this type were installed at automobile plants." Option A.

Why the other options are wrong:
B A machine that thinks like a person: the robot in Capek's play, which was fiction.
C Invented by a science fiction writer: Asimov coined "robotics", he did not build a robot.
D Looked and behaved like a human: para 2 says industrial robots were nothing like fiction's creatures.
E Invented in 1921: that was the word, not the real robot (1961).

Cetking shortcut: The word "real" in the question separates the 1961 robot from the 1921 fictional one.

Answer: A

Approach: Specific detail.

Solution: Para 2: "they could perform certain jobs that were difficult or dangerous for humans, particularly jobs that involve high heat." Option B.

Why the other options are wrong:
A They saved money for companies: a result, not a kind of job.
C All kinds of jobs: overstated.
D Jobs that involve fewer humans / E Jobs needing less strength: not stated.

Answer: B

Approach: Specific detail — sentence completion.

Solution: Para 3: "Though the use of robots has meant the loss of some jobs, at the same time other jobs have been created in the design, development, and production of the robots." So in industry robots have taken away some jobs and created others — option A.

Why the other options are wrong:
B Caused factories to close: not stated.
C Look and behave like humans: para 2 says the opposite.
D Replace programmers and engineers: they create such jobs.
E "work only": incomplete and unsupported.

Answer: A

Approach: Indirect to direct — order (imperative).

Solution: "Ordered him to go to his room and study" → a command in direct speech: His father said, "Go to your room and study." The pronoun "his" becomes "your", the order of actions (go, then study) is kept, and no added tone word is needed.

Why the other options are wrong:
B "Go and study in your room": changes the structure of the order.
C "shouted ... right now ... study room": adds words not in the original.
D "said firmly" / E "said politely": add a tone adverb and reorder the actions.

Cetking shortcut: Keep exactly the content of the order; reject options that add adverbs (firmly, politely, right now).

Answer: A

Approach: Specific detail.

Solution: Last paragraph: "What is fascinating, however, is the intense yearning of this class for a clean, corruption-less politics and society." Option C (clean honest society).

Why the other options are wrong:
A Better material resources: their ambitions soared, but the "intense yearning" is for clean politics.
B Extensive practice of corruption: a fact about them, not a yearning.
D Law of increasing returns: misreads "not subjected to the law of diminishing returns".
E Freedom of speech: not mentioned.

Cetking shortcut: Match the question's word "intensely yearns" to "intense yearning" in the passage.

Answer: C

Approach: Specific detail.

Solution: "If teachers do not figure high on this priority list, it is not for lack of trying, but for lack of opportunities." Option B.

Why the other options are wrong:
A Courage / D Ambition / E Willingness: the passage says they are "trying", so lack of will is ruled out.
C Support: not mentioned.

Answer: B

Approach: Vocabulary in context / description of the middle class.

Solution: Para 1: "The Indian middle class consists of so many strata that it defies categorization under a single term class, which would imply a considerable degree of homogeneity." Many strata = stratified (divided into layers). Option D.

Why the other options are wrong:
A Defiant: "defies categorization" is about the term, not the class's attitude.
B Mysterious / E Unique: not stated.
C Homogeneous: the passage says the class is NOT homogeneous.

Cetking shortcut: "Strata" → stratified; "homogeneity" is denied, so C is the trap.

Answer: D

Approach: Inference — meaning of a phrase.

Solution: The author says salvation lies not in politics or trade but "in a deeper transformation of life, in the liberation of consciousness in love, in the realization of God in man." "God in man" = the divine qualities present within human beings, to be realised by inner growth — option D.

Why the other options are wrong:
A God assuming the shape of man: an incarnation idea, not the author's point.
B Neither fully godly nor fully human: not suggested.
C Man transformed into God: overstates; the author speaks of realizing the divine within, not becoming God.
E The divine qualities of God: refers to God, not to man.

Answer: D

Approach: Inference — author's likely view.

Solution: The author credits the decline in illiteracy to "specific campaigns designed to increase educational opportunities for girls" and notes that two-thirds of the 771 million illiterate adults are still women. This shows the author values giving women the same access to education as men — option A.

Why the other options are wrong:
B Men need higher education more: contradicts the passage's focus on women's education.
C Women need medical care more than reading: medical care is never mentioned.
D Educated women have fewer children: a claim not made in the passage.
E Women have all opportunities: contradicted — most illiterate adults are women.

Cetking shortcut: In "author would agree" questions, reject any option that brings in a new topic (medical care, family size).

Answer: A

Approach: Interleaved series — a repeating constant plus a main series with alternating differences.

Solution:
28, 25, 5, 21, 18, 5, 14, ...
The number 5 appears after every two terms.
Remove the 5s: 28, 25, 21, 18, 14 → differences −3, −4, −3, −4.
Next difference is −3: 14 − 3 = 11.
After 14 and 11 comes the pair-breaker 5 again.
So the next two terms are 11, 5.

Why the other options are wrong:
B (10,7), C (11,8): 7 and 8 break the repeating 5.
D (5,10): 5 cannot come before 11; 10 also breaks −3/−4.
E (10,5): 14 − 4 = 10 uses the wrong difference (−3 is due).

Cetking shortcut: When a number repeats at fixed gaps, strike it out first — the rest is usually a simple difference series.

Answer: A

Approach: Two alternating series.

Solution:
Odd positions: 13, 15, 17, 19 → +2 each time.
Even positions: 29, 26, 23 → −3 each time.
The last given term 19 is an odd-position term, so the next term belongs to the even series: 23 − 3 = 20.
Then the odd series continues: 19 + 2 = 21.
Next pair = 20, 21.

Why the other options are wrong:
A (21,23): puts the odd-series term first and repeats 23.
C (20,17): 17 already used; odd series is increasing.
D, E: neither number fits either series in order.

Cetking shortcut: Note which series the last given term belongs to — the very next term comes from the other series.

Answer: B

Approach: Selection-criteria check — test each of the 4 conditions; if exactly one fails, look for the matching exception clause; if data is missing, it is Data inadequate.

Solution:
(i) MBBS ≥ 50%: Gauri has 47% → fails.
(ii) 4 yrs rural practice: 5½ yrs in a remote village → OK.
(iii) 3-year bond: ready → OK.
(iv) Local language: good command → OK.
Only (i) fails, so check exception (C): MBBS ≥ 45% (47% ✓) and M.S./M.D. with ≥ 50% (M.D. 56% ✓).
Exception (C) applies → refer to the Chief Medical Officer.

Why the other options are wrong:
A: she does not meet (i) directly, so she cannot be selected outright.
B: exception (C) rescues her, so not rejected.
C: Assistant Secretary is for the language exception (B); her language is fine.
D: all required data is given.

Cetking shortcut: Scan the case for numbers below the cut-off first — the failed condition tells you which exception to read.

Answer: E

Approach: Selection-criteria check — test each of the 4 conditions; if exactly one fails, look for the matching exception clause; if data is missing, it is Data inadequate.

Solution:
(i) MBBS ≥ 50%: more than 60% in every exam → OK.
(ii) 4 yrs rural practice: 5 years in her native village → OK.
(iii) 3-year bond: ready → OK (she plans to go abroad only after 4 more years, which is beyond the bond).
(iv) Local language: knows it very well → OK.
All four conditions are met → select.

Why the other options are wrong:
B: no condition fails.
C, E: referrals apply only when a condition fails.
D: every condition can be checked from the case.

Cetking shortcut: Extra details (plans to go abroad, popularity of her dispensary) are distractors — test only the four listed conditions.

Answer: A

Approach: Selection-criteria check — test each of the 4 conditions; if exactly one fails, look for the matching exception clause; if data is missing, it is Data inadequate.

Solution:
(i) MBBS ≥ 50%: his MBBS percentage is not given (only M.S. 53% is stated) → cannot be checked.
(ii) 4 yrs rural practice: 6 years in a big city → fails; exception (A) could cover him (urban practice ≥ 4 yrs and schooling in rural areas), which would mean referral to the Secretary, not selection.
(iii) Bond: ready → OK.
(iv) Local language: good → OK.
Because the MBBS marks are missing, we cannot decide whether he satisfies (i), or whether exception (A) is the only one needed. Hence the data is inadequate.

Why the other options are wrong:
A: he fails (ii) directly, so he can never be selected outright.
B: he may qualify through exception (A), so rejection cannot be concluded.
C: Assistant Secretary is for the language exception; his language is fine.
E: CMO is for the MBBS-marks exception, and his MBBS marks are unknown.

Cetking shortcut: Tick each condition against the case; the moment a required figure (here MBBS %) is missing, Data inadequate is the answer.

Answer: D

Approach: Syllogism — draw Venn diagrams; a conclusion follows only if it is true in every possible diagram.

Solution:
No women teacher (W) can play (P) → W and P are separate circles.
Some W are athletes (A) → A overlaps W.
Conclusion 1 — 'Male athletes can play': the statements say nothing about males → does not follow.
Conclusion 2 — 'Some athletes can play': A and P may or may not overlap (a case with no overlap is possible) → does not follow.
What does follow is 'Some athletes cannot play' — not given here.

Why the other options are wrong:
A, E: Conclusion 1 brings in 'males', an outside term.
B: A–P overlap is only a possibility.
C: the two conclusions are not a complementary pair, so 'either-or' does not apply.

Cetking shortcut: Some + No → 'Some ... not' conclusion only. Any positive 'some' between the outer terms fails.

Answer: D

Approach: Syllogism — draw Venn diagrams; a conclusion follows only if it is true in every possible diagram.

Solution:
All mangoes (M) are golden (G) → M inside G.
No golden thing is cheap (C) → G and C separate, so M and C are separate too.
Conclusion 1 — 'All mangoes are cheap': opposite of the definite 'No mango is cheap' → false.
Conclusion 2 — 'Golden-coloured mangoes are not cheap': all mangoes are golden and nothing golden is cheap → follows.

Why the other options are wrong:
A, E: Conclusion 1 contradicts the statements.
C: either-or needs a complementary pair where neither is definite; here 2 is definite.
D: Conclusion 2 does follow.

Cetking shortcut: All + No → No (All A are B, No B is C ⇒ No A is C).

Answer: B

Approach: Syllogism — draw Venn diagrams; a conclusion follows only if it is true in every possible diagram.

Solution:
All flowers (Fl) are trees (T) → Fl inside T.
No fruit (Fr) is a tree → Fr outside T, so Fr is outside Fl as well.
Conclusion 1 — 'No fruit is flower': follows (Fr is completely outside T, which contains Fl).
Conclusion 2 — 'Some trees are flowers': conversion of 'All flowers are trees' → follows.

Why the other options are wrong:
A, B: each leaves out a conclusion that does follow.
C: either-or is only for a complementary pair where neither follows definitely.
D: both follow.

Cetking shortcut: 'All A are B' always converts to 'Some B are A'; No + All (reversed) → No.

Answer: E

Approach: Syllogism — draw Venn diagrams; a conclusion follows only if it is true in every possible diagram.

Solution:
All swords (S) are rusty (R) → S inside R.
Some swords are sharp (Sh) → Sh overlaps S, hence overlaps R.
Conclusion 1 — 'Some rusty things are sharp': the sharp swords are rusty → follows.
Conclusion 2 — 'Some rusty things are not sharp': all rusty things could be sharp (R inside Sh is possible) → does not follow.

Why the other options are wrong:
B, E: Conclusion 2 is only a possibility.
C: Conclusion 1 is definite, so 'either-or' does not apply.
D: Conclusion 1 does follow.

Cetking shortcut: With only positive statements, a negative conclusion can never be definite.

Answer: A

Approach: Two alternating arithmetic series.

Solution:
Odd positions: 8, 11, __, 17 → +3 each time, so blank = 11 + 3 = 14 (check: 14 + 3 = 17).
Even positions: 43, 41, 39 → −2 each time.
Missing number = 14.

Why the other options are wrong:
A (13), B (15), D (16): do not keep the +3 step from 11 to 17.
E (40): belongs to the pattern of the even series, but the blank is an odd-position term.

Cetking shortcut: The blank sits between 11 and 17 in its own series — just take the midpoint: (11 + 17)/2 = 14.

Answer: C

Approach: Statement–Assumption — an assumption is implicit only if the speaker must take it for granted for the statement to make sense.

Solution:
The statement links India's glorious past to the growing popularity of ayurvedic medicines in the world.
A: 'Popular in India' — the claim is about worldwide popularity; the speaker need not assume anything about popularity within India → not implicit.
B: 'Not popular in India' — equally unnecessary; nothing in the statement depends on it → not implicit.
Neither assumption is required.

Why the other options are wrong:
A, B, D: each needs at least one assumption to be required, but the statement is silent on India.
E: C is a valid choice, so 'None of these' does not apply.

Cetking shortcut: When two assumptions are exact opposites about something the statement does not talk about, usually neither is implicit.

Answer: C

Approach: Statement–Assumption — an assumption is implicit only if the speaker must take it for granted for the statement to make sense.

Solution:
The in-charge says: to bring punctuality (discipline), give a conveyance allowance (reward/benefit).
A: 'Conveyance allowance will not help in bringing punctuality' — this contradicts the speaker, who believes it will help → not implicit.
B: 'Discipline and reward should go hand in hand' — the proposal ties a discipline goal to a benefit; the speaker takes this link for granted → implicit.

Why the other options are wrong:
A, D: A is the opposite of the speaker's belief.
C: B is needed for the suggestion to make sense.
E: B is a valid choice.

Cetking shortcut: An assumption that contradicts the speaker's own recommendation is never implicit — strike it out first.

Answer: B

Approach: Statement–Assumption — an assumption is implicit only if the speaker must take it for granted for the statement to make sense.

Solution:
Decision: appoint four thousand primary school teachers next year.
A: 'Enough schools exist to accommodate them' — a government would not plan 4,000 appointments without places to post them → implicit.
B: 'Candidates may not apply because the government may not appoint so many' — this doubts the decision itself; the government cannot be assuming its own decision will not be carried out → not implicit.

Why the other options are wrong:
B, D: B works against the decision.
C: A is necessary for the decision.
E: A is a valid choice.

Cetking shortcut: For a decision statement, the feasibility assumption (resources/places exist) is usually implicit; doubts about the decision are not.

Answer: A

Approach: Order & ranking — total = position from left + position from right − 1.

Solution:
A is 7th from left; B is 9th from right.
After interchange, A stands at B's old place and is 11th from left.
So B's old place = 11th from left and 9th from right.
Total = 11 + 9 − 1 = 19.

Why the other options are wrong:
A, B, C: use A's original 7th position or forget to subtract/add correctly (e.g. 7 + 9 = 16).
E (21): adds 11 + 9 + 1.

Cetking shortcut: After a swap, the new position of one person + the old position of the other from the opposite end gives the total (minus 1).

Answer: D

Approach: Letter series — each letter moves by a fixed step.

Solution:
First letters: C, E, G, __, K → +2 each → I.
Second & third letters (same in each term): M, O, Q, __, U → +2 each → S.
Missing term = ISS.

Why the other options are wrong:
A (GRR), B (GSS): first letter G repeats instead of moving to I.
D (ITT): T is +3 from Q.
E (HSS): H is +1 from G.

Cetking shortcut: Check the first letter only: C→E→G→I→K. Only C and D start with I; the Q→S step then picks C.

Answer: C

Approach: Alternating operations series (+2, ×2).

Solution:
4 + 2 = 6
6 × 2 = 12
12 + 2 = 14
14 × 2 = 28
28 + 2 = 30
30 × 2 = 60

Why the other options are wrong:
D (32): applies +2 again instead of ×2.
A, C, E: fit no consistent operation.

Cetking shortcut: Differences 2, 6, 2, 14, 2 — every alternate difference is 2, so the other step must be a multiplication.

Answer: B

Approach: Alternating multipliers ×1.1 and ×0.9.

Solution:
10000 × 1.1 = 11000
11000 × 0.9 = 9900
9900 × 1.1 = 10890
10890 × 0.9 = 9801
9801 × 1.1 = 10781.1 → written as 10781
Check with alternate terms: 11000 → 10890 → 10781 is a fall of 1% each time (110, then 109), and 10000 → 9900 → 9801 also falls 1% each time.

Why the other options are wrong:
B (10241), C (10423), D (10929): none is about 1% below 10890.
E (10900): rises from 10890 instead of falling.

Cetking shortcut: Alternate terms 10000 → 9900 → 9801 drop by 1%, so 10890 − 1% ≈ 10890 − 109 = 10781.

Answer: A

Approach: Odd one out — find the ratio common to most pairs.

Solution:
70 : 80 = 7 : 8
28 : 32 = 7 : 8
21 : 24 = 7 : 8
14 : 16 = 7 : 8
54 : 62 = 27 : 31 → not 7 : 8.
So 54–62 is the odd pair. (For 7 : 8, 54 should pair with 54 × 8/7, which is not a whole number.)

Why the other options are wrong:
A, C, D, E: all are in the ratio 7 : 8 (multiples 10, 4, 3, 2 of 7–8).

Cetking shortcut: Check if the first numbers are multiples of 7 (70, 28, 21, 14) — 54 is not.

Answer: B

Approach: Odd one out — property shared by all numbers in a group (primes).

Solution:
A: 71, 7, 3, 17 → all prime.
B: 67, 71, 3, 5 → all prime.
C: 41, 5, 3, 47 → all prime.
D: 37, 14, 19, 7 → 14 = 2 × 7 is not prime.
E: 11, 3, 5, 17 → all prime.

Why the other options are wrong:
A, B, C, E: every number is prime.

Cetking shortcut: Look for the only even number greater than 2 — it cannot be prime.

Answer: D

Approach: Letter-shift coding with alternating −2 / +2.

Solution:
ROAST → PQYUR: R−2=P, O+2=Q, A−2=Y, S+2=U, T−2=R.
Pattern: −2, +2, −2, +2, ...
SLOPPY: S−2=Q, L+2=N, O−2=M, P+2=R, P−2=N, Y+2=A (Y→Z→A).
Code = QNMRNA.

Why the other options are wrong:
A, B, D, E: correct letters in the wrong order, or wrong shifts (e.g. start with M/N/R).

Cetking shortcut: Only the first letter is needed: S − 2 = Q, and only option C starts with Q.

Answer: C

Approach: Reverse the word, then shift each letter −1.

Solution:
health reversed = H T L A E H.
Each −1: H→G, T→S, L→K, A→Z, E→D, H→G = GSKZDG ✓.
north reversed = H T R O N.
Each −1: H→G, T→S, R→Q, O→N, N→M = GSQNM.

Why the other options are wrong:
B (GSQMN): last two letters swapped.
C, D: first letter F is −2 from H.
E (GSRNM): R is not shifted.

Cetking shortcut: Decode one letter: in GSKZDG the last letter G is H−1 and matches the first letter of 'health' reversed — so reverse first, then shift −1.

Answer: A

Approach: Opposite-letter coding (A↔Z, B↔Y ...; position p ↔ 27 − p).

Solution:
BEAT → YVZG: B(2)↔Y(25), E(5)↔V(22), A(1)↔Z(26), T(20)↔G(7) ✓.
MILD: M(13)↔N(14), I(9)↔R(18), L(12)↔O(15), D(4)↔W(23).
Code = NROW.

Why the other options are wrong:
A, B, C, E: same letters in the wrong order.

Cetking shortcut: Remember the pair sum 27; M's opposite is N, so only D and E qualify, and I → R picks D.

Answer: D

Approach: Matrix puzzle — fix the direct clues, then use the 'same colour' links and exclusions.

Solution:
Direct: B shirt red; D shirt green, trousers indigo; G shirt blue; E trousers blue.
Shirts left for A, C, E, F: white, black, yellow, violet. Trousers left for A, B, C, F, G: red, white, black, cream, yellow.
A's shirt = F's trousers → must be white, black or yellow. A is not white; F wears no yellow → black. So A shirt black, F trousers black.
B: not red (same as shirt), not cream/yellow, not black (taken) → white.
E's shirt = C's trousers → from white/yellow/violet ∩ red/cream/yellow → yellow. E shirt yellow, C trousers yellow.
A and G get red and cream; G (blue shirt) cannot wear red (no red–blue combo) → G cream, A red.
C and F shirts: white/violet (not fixed).

G's trousers = Cream.

Why the other options are wrong:
A (White): worn by B.
C (Green): not a trouser colour.
D (Indigo): worn by D.
E (Red): red–blue combination is not allowed for G.

Answer: B

Approach: Matrix puzzle — fix the direct clues, then use the 'same colour' links and exclusions.

Solution:
Direct: B shirt red; D shirt green, trousers indigo; G shirt blue; E trousers blue.
Shirts left for A, C, E, F: white, black, yellow, violet. Trousers left for A, B, C, F, G: red, white, black, cream, yellow.
A's shirt = F's trousers → must be white, black or yellow. A is not white; F wears no yellow → black. So A shirt black, F trousers black.
B: not red (same as shirt), not cream/yellow, not black (taken) → white.
E's shirt = C's trousers → from white/yellow/violet ∩ red/cream/yellow → yellow. E shirt yellow, C trousers yellow.
A and G get red and cream; G (blue shirt) cannot wear red (no red–blue combo) → G cream, A red.
C and F shirts: white/violet (not fixed).

The violet shirt is worn by C or F — the clues do not fix which.

Why the other options are wrong:
A, B: each alone is not certain.
D, E: G wears a blue shirt.

Answer: C

Approach: Matrix puzzle — fix the direct clues, then use the 'same colour' links and exclusions.

Solution:
Direct: B shirt red; D shirt green, trousers indigo; G shirt blue; E trousers blue.
Shirts left for A, C, E, F: white, black, yellow, violet. Trousers left for A, B, C, F, G: red, white, black, cream, yellow.
A's shirt = F's trousers → must be white, black or yellow. A is not white; F wears no yellow → black. So A shirt black, F trousers black.
B: not red (same as shirt), not cream/yellow, not black (taken) → white.
E's shirt = C's trousers → from white/yellow/violet ∩ red/cream/yellow → yellow. E shirt yellow, C trousers yellow.
A and G get red and cream; G (blue shirt) cannot wear red (no red–blue combo) → G cream, A red.
C and F shirts: white/violet (not fixed).

B's trousers = White.

Why the other options are wrong:
A (Black): F wears black trousers.
C (Indigo): D's.
D (Blue): E's; also red–blue not allowed.
E (Yellow): excluded for B directly.

Answer: B

Approach: Artificial-language coding — isolate common parts and note the word order.

Solution:
agnos-crenia = poisonous spider; agnos-deery = brown spider → agnos = spider, crenia = poisonous, deery = brown.
delano-crenia = poisonous snake → delano = snake.
Order rule: the noun comes first, then the describing word (agnos-crenia = spider-poisonous).
'Black widow spider' = agnos + two new words (for black and widow) → agnos-vitri-blunin.

Why the other options are wrong:
A: contains deery (= brown).
B: contains delano (= snake).
D: 'agnos' is placed last, breaking the noun-first order.
E: brown snake.

Cetking shortcut: Eliminate any option using a known word for something else (deery, delano), then check where the noun sits.

Answer: C

Approach: Three-way matrix (player–town–role) using first-letter exclusions.

Solution:
Rule (i): no name, town or role starts with the same letter as another in the same row (e.g. Sumeet ≠ Surat/Spinner, Philips ≠ Pune/Pace, Wasim ≠ Warangal/Wicket keeper, Bishan ≠ Bangalore/Batsman, Chetan ≠ Chandigarh/Captain; Pune ≠ Pace, Warangal ≠ Wicket keeper, Chandigarh ≠ Captain, Bangalore ≠ Batsman).
Philips and Wasim are not from Surat/Bangalore. Captain is from Pune and neither of them is captain → neither is from Pune.
Wasim ≠ Warangal → Wasim = Chandigarh; Philips = Warangal.
Captain (Pune) from Sumeet/Bishan/Chetan: Bishan ≠ Pune, Chetan ≠ Captain → Sumeet = Captain, Pune.
Bishan ≠ Bangalore → Bishan = Surat, Chetan = Bangalore = Wicket keeper.
Roles left (spinner, pace, batsman) for Philips, Wasim, Bishan: Bishan ≠ batsman, batsman not from Warangal (Philips) → Wasim = Batsman. Philips ≠ Pace → Philips = Spinner, Bishan = Pace bowler.

Spinner = Philips.

Why the other options are wrong:
B Chetan: wicket keeper. C Bishan: pace bowler. D Wasim: batsman. E Sumeet: captain (and cannot be spinner by the first-letter rule).

Cetking shortcut: Start from the person with the most exclusions (Wasim: not Surat, Bangalore, Warangal, Pune) — he gets fixed first.

Answer: A

Approach: Three-way matrix (player–town–role) using first-letter exclusions.

Solution:
Rule (i): no name, town or role starts with the same letter as another in the same row (e.g. Sumeet ≠ Surat/Spinner, Philips ≠ Pune/Pace, Wasim ≠ Warangal/Wicket keeper, Bishan ≠ Bangalore/Batsman, Chetan ≠ Chandigarh/Captain; Pune ≠ Pace, Warangal ≠ Wicket keeper, Chandigarh ≠ Captain, Bangalore ≠ Batsman).
Philips and Wasim are not from Surat/Bangalore. Captain is from Pune and neither of them is captain → neither is from Pune.
Wasim ≠ Warangal → Wasim = Chandigarh; Philips = Warangal.
Captain (Pune) from Sumeet/Bishan/Chetan: Bishan ≠ Pune, Chetan ≠ Captain → Sumeet = Captain, Pune.
Bishan ≠ Bangalore → Bishan = Surat, Chetan = Bangalore = Wicket keeper.
Roles left (spinner, pace, batsman) for Philips, Wasim, Bishan: Bishan ≠ batsman, batsman not from Warangal (Philips) → Wasim = Batsman. Philips ≠ Pace → Philips = Spinner, Bishan = Pace bowler.

Spinner (Philips) is from Warangal.

Why the other options are wrong:
A Chandigarh: Wasim (batsman). B Pune: captain. D Surat: Bishan (pace). E Bangalore: wicket keeper.

Answer: C

Approach: Three-way matrix (player–town–role) using first-letter exclusions.

Solution:
Rule (i): no name, town or role starts with the same letter as another in the same row (e.g. Sumeet ≠ Surat/Spinner, Philips ≠ Pune/Pace, Wasim ≠ Warangal/Wicket keeper, Bishan ≠ Bangalore/Batsman, Chetan ≠ Chandigarh/Captain; Pune ≠ Pace, Warangal ≠ Wicket keeper, Chandigarh ≠ Captain, Bangalore ≠ Batsman).
Philips and Wasim are not from Surat/Bangalore. Captain is from Pune and neither of them is captain → neither is from Pune.
Wasim ≠ Warangal → Wasim = Chandigarh; Philips = Warangal.
Captain (Pune) from Sumeet/Bishan/Chetan: Bishan ≠ Pune, Chetan ≠ Captain → Sumeet = Captain, Pune.
Bishan ≠ Bangalore → Bishan = Surat, Chetan = Bangalore = Wicket keeper.
Roles left (spinner, pace, batsman) for Philips, Wasim, Bishan: Bishan ≠ batsman, batsman not from Warangal (Philips) → Wasim = Batsman. Philips ≠ Pace → Philips = Spinner, Bishan = Pace bowler.

Chandigarh = Wasim.

Why the other options are wrong:
A Sumeet: Pune. C Philips: Warangal. D Bishan: Surat. E Chetan: cannot be from Chandigarh (same first letter); he is from Bangalore.

Answer: B

Approach: Three-way matrix (player–town–role) using first-letter exclusions.

Solution:
Rule (i): no name, town or role starts with the same letter as another in the same row (e.g. Sumeet ≠ Surat/Spinner, Philips ≠ Pune/Pace, Wasim ≠ Warangal/Wicket keeper, Bishan ≠ Bangalore/Batsman, Chetan ≠ Chandigarh/Captain; Pune ≠ Pace, Warangal ≠ Wicket keeper, Chandigarh ≠ Captain, Bangalore ≠ Batsman).
Philips and Wasim are not from Surat/Bangalore. Captain is from Pune and neither of them is captain → neither is from Pune.
Wasim ≠ Warangal → Wasim = Chandigarh; Philips = Warangal.
Captain (Pune) from Sumeet/Bishan/Chetan: Bishan ≠ Pune, Chetan ≠ Captain → Sumeet = Captain, Pune.
Bishan ≠ Bangalore → Bishan = Surat, Chetan = Bangalore = Wicket keeper.
Roles left (spinner, pace, batsman) for Philips, Wasim, Bishan: Bishan ≠ batsman, batsman not from Warangal (Philips) → Wasim = Batsman. Philips ≠ Pace → Philips = Spinner, Bishan = Pace bowler.

Pace bowler = Bishan.

Why the other options are wrong:
A Chetan: wicket keeper. B Wasim: batsman. C Sumeet: captain. E Philips: cannot be pace (same first letter); he is the spinner.

Answer: D

Approach: Artificial-language coding — split compound words into parts.

Solution:
migen-lasan = cup-board; lasan-poen = board-walk → lasan = board, migen = cup, poen = walk.
cuop-dansa = pull-man (no common part with walkway).
Word order matches English (cup-board = migen-lasan).
'walkway' = poen + (new word for 'way') → poen-forc.

Why the other options are wrong:
A (poenmigen): migen = cup → 'walkcup'.
B (cuopeisel): no 'poen'.
C (lasandansa): board + man.
E (lasanforc): lasan = board → 'boardway'.

Cetking shortcut: Find 'walk' (poen) first, it must come first; then reject any second part that is already a known word.

Answer: D

Approach: Convert all weights into one variable and rank.

Solution:
Let C = x.
D = 2x (C is half of D).
E = 2D = 4x.
B = 4.5C = 4.5x.
A = 2B = 9x.
Check (5): E (4x) is less than A (9x) and more than C (x) ✓.
Order: A (9x) > B (4.5x) > E (4x) > D (2x) > C (x).

Lightest = C.

Why the other options are wrong:
A, B, D, E are 9x, 4.5x, 2x and 4x — all heavier than x.

Cetking shortcut: C is 'half of D' and B is a multiple of C — C is the base of every chain, so it is the lightest.

Answer: C

Approach: Convert all weights into one variable and rank.

Solution:
Let C = x.
D = 2x (C is half of D).
E = 2D = 4x.
B = 4.5C = 4.5x.
A = 2B = 9x.
Check (5): E (4x) is less than A (9x) and more than C (x) ✓.
Order: A (9x) > B (4.5x) > E (4x) > D (2x) > C (x).

E (4x) is lighter than A (9x) and B (4.5x).

Why the other options are wrong:
B, D: E is heavier than C.
C, E: E is heavier than D.

Answer: A

Approach: Convert all weights into one variable and rank.

Solution:
Let C = x.
D = 2x (C is half of D).
E = 2D = 4x.
B = 4.5C = 4.5x.
A = 2B = 9x.
Check (5): E (4x) is less than A (9x) and more than C (x) ✓.
Order: A (9x) > B (4.5x) > E (4x) > D (2x) > C (x).

E (4x) is heavier than D (2x) and C (x).

Why the other options are wrong:
A, E (A, C): E is lighter than A.
C (B, C): E is lighter than B.
D (A, B): E is lighter than both.

Answer: B

Approach: Word formation from selected letter positions.

Solution:
N O M I N A T I O N → positions 1 N, 2 O, 3 M, 4 I, 5 N, 6 A, 7 T, 8 I, 9 O, 10 N.
1st = N, 3rd = M, 6th = A, 8th = I → letters N, M, A, I.
Meaningful word: MAIN (only one).
3rd letter of MAIN = I.

Why the other options are wrong:
A (N), C (M): not the 3rd letter of MAIN.
D (X): a word can be formed.
E (Y): only one common English word (MAIN) can be formed.

Answer: B

Approach: Grouping + ranking with gender and couple clues.

Solution:
Administration: F and his only colleague G → exactly {F, G}; G earns the most.
Accounts: C (least earner) and A.
Remaining: B, E, H. B and E are in different departments → one in Accounts, one in Operations.
Operations needs at least 2 people → H must be in Operations.
Departments: Admin {F, G}; Accounts {A, C, B/E}; Operations {H, E/B}.
Females: one per department. F is male ('his'), A is a husband, B and E are brothers → females are G (Admin), C (Accounts), H (Operations).
Earnings: G highest; wife H > husband A; A > F, B, E; C lowest → G > H > A > {F, B, E} > C.

Three people (A, C and B/E) work in Accounts.

Why the other options are wrong:
A: Operations has 2 (H and one brother).
C: Administration has exactly 2 (F, G).
D, E: only Accounts has three.

Cetking shortcut: 'Only other colleague' closes Administration at 2 — then the 'at least two' rule forces H into Operations.

Answer: B

Approach: Grouping + ranking with gender and couple clues.

Solution:
Administration: F and his only colleague G → exactly {F, G}; G earns the most.
Accounts: C (least earner) and A.
Remaining: B, E, H. B and E are in different departments → one in Accounts, one in Operations.
Operations needs at least 2 people → H must be in Operations.
Departments: Admin {F, G}; Accounts {A, C, B/E}; Operations {H, E/B}.
Females: one per department. F is male ('his'), A is a husband, B and E are brothers → females are G (Admin), C (Accounts), H (Operations).
Earnings: G highest; wife H > husband A; A > F, B, E; C lowest → G > H > A > {F, B, E} > C.

Females = G, C, H.

Why the other options are wrong:
A, C: E is a brother (male).
D: B is a brother.
E: F is male ('his').

Answer: B

Approach: Grouping + ranking with gender and couple clues.

Solution:
Administration: F and his only colleague G → exactly {F, G}; G earns the most.
Accounts: C (least earner) and A.
Remaining: B, E, H. B and E are in different departments → one in Accounts, one in Operations.
Operations needs at least 2 people → H must be in Operations.
Departments: Admin {F, G}; Accounts {A, C, B/E}; Operations {H, E/B}.
Females: one per department. F is male ('his'), A is a husband, B and E are brothers → females are G (Admin), C (Accounts), H (Operations).
Earnings: G highest; wife H > husband A; A > F, B, E; C lowest → G > H > A > {F, B, E} > C.

A is 3rd from the top (after G and H).

Why the other options are wrong:
A: G earns the maximum.
B: H (wife) earns more than A.
D, E: A earns more than F, B, E and C.

Answer: C