MBA CET 2026 Slot 4 question paper with solutions

Approach: Chain two ratios by making the common term (B) equal.

Solution:
A : B = 2 : 3 and B : C = 4 : 5.
Make B equal: LCM of 3 and 4 = 12.
A : B = 8 : 12 and B : C = 12 : 15.
So A : B : C = 8 : 12 : 15 ⇒ A : C = 8 : 15.

Why the other options are wrong:
A (2:5) – simply multiplies the outer terms, ignoring B.
C (3:5) – uses B's term from the second ratio wrongly.
D (8:12) – this is A : B, not A : C.
E (6:15) – multiplies 2 × 3 instead of 2 × 4.

Cetking shortcut: A : C = (2 × 4) : (3 × 5) = 8 : 15 — multiply the 'A-side' numerators and the 'C-side' denominators directly.

Answer: B

Approach: Ages in ratio — form one equation from the past ratio.

Solution:
Present ages: mother = 7x, daughter = x.
4 years ago: (7x − 4)/(x − 4) = 19/1.
7x − 4 = 19x − 76 ⇒ 12x = 72 ⇒ x = 6.
Mother now = 42 years (daughter 6; 4 years ago 38 : 2 = 19 : 1 ✓).
Mother 4 years from now = 42 + 4 = 46 years.

Why the other options are wrong:
A (42) – mother's present age; the question asks 4 years later.
B (38) – mother's age 4 years ago.
D, E (36, 40) – do not satisfy both ratios.

Cetking shortcut: Options test: the present age must be a multiple of 7 and (age − 4) : (age/7 − 4) = 19 : 1; 42 → 38 : 2 = 19 : 1 instantly.

Answer: C

Approach: Place value = digit × its positional value; face value = the digit itself.

Solution:
In 4782, 7 is in the hundreds place.
Place value = 7 × 100 = 700.
Face value = 7.
Difference = 700 − 7 = 693.

Why the other options are wrong:
A (700) – place value only.
B (7) – face value only.
D (782) – the number after the 4, not a place value.
E (707) – adds instead of subtracts.

Cetking shortcut: Difference = digit × (place − 1) = 7 × 99 = 693.

Answer: C

Approach: Units digit of a product depends only on the units digits of the factors.

Solution:
Units digits: 5, 2, 7, 4.
5 × 2 = 10 → units digit 0.
Anything × (number ending in 0) ends in 0.
Units digit of 15 × 22 × 37 × 44 = 0.

Why the other options are wrong:
A, D, E (2, 4, 8) – come from ignoring the 5 × 2 pair.
B (5) – 5 × odd ends in 5, but here 5 meets an even number.

Cetking shortcut: A factor ending in 5 together with any even factor always gives units digit 0.

Answer: C

Approach: Bells toll together at multiples of the LCM of their intervals; count the start too.

Solution:
LCM(2, 4, 6, 8, 10, 12) = 2³ × 3 × 5 = 120 s = 2 min.
In 30 min they toll together every 2 min: 30 / 2 = 15 times after the start.
Add the toll at the start (time 0): 15 + 1 = 16.

Why the other options are wrong:
A (15) – forgets the toll at the beginning.
C, D (30, 31) – assume they meet every minute.
E (12) – wrong LCM (150 s).

Cetking shortcut: 'Commence together' = add 1 to (total time ÷ LCM).

Answer: B

Approach: For numbers in ratio a:b:c with a, b, c co-prime, numbers = ax, bx, cx; HCF = x and LCM = x × LCM(a, b, c).

Solution:
Numbers = 3x, 4x, 5x (3, 4, 5 pairwise co-prime).
LCM = x × LCM(3, 4, 5) = 60x.
60x = 2400 ⇒ x = 40.
HCF = x = 40 (numbers 120, 160, 200).

Why the other options are wrong:
B (80), C (120), D (200) – 120 and 200 are actual numbers, not the HCF; 80 is 2x.
E (15) – no basis.

Cetking shortcut: HCF = LCM ÷ (3 × 4 × 5) = 2400 ÷ 60 = 40.

Answer: A

Approach: Direct percentage of a number.

Solution:
15% of 200 = 0.15 × 200 = 30.
20% of 150 = 0.20 × 150 = 30.
Sum = 30 + 30 = 60.

Cetking shortcut: x% of y = y% of x: 15% of 200 = 200% of 15 = 30.

Answer: C

Approach: Recognise the identity a² + b² + 2ab = (a + b)².

Solution:
a = 0.2, b = 0.3.
0.2 × 0.2 + 0.3 × 0.3 + 2 × 0.2 × 0.3 = (0.2 + 0.3)².
= (0.5)² = 0.25.
Check: 0.04 + 0.09 + 0.12 = 0.25.

Why the other options are wrong:
A (0.025) – decimal placed wrongly.
C (0.5) – forgets to square a + b.
D (0.05), E (0.6) – arithmetic slips.

Cetking shortcut: Spot a² + b² + 2ab at a glance → (a + b)²; no multiplication needed.

Answer: B

Approach: Prime-factorise; every prime's power must be a multiple of 3 for a perfect cube.

Solution:
675 = 25 × 27 = 3³ × 5².
3³ is already a cube; 5² needs one more 5.
Multiply by 5: 675 × 5 = 3375 = 15³.

Why the other options are wrong:
A (2), D (6) – introduce a new prime 2.
B (3) – 3⁴ would spoil the cube.
E (9) – makes 3⁵.

Cetking shortcut: Group primes in triples; the missing members form the multiplier.

Answer: C

Approach: Perfect squares end in 0, 1, 4, 5, 6, 9 and have a matching square root near √N.

Solution:
2362 (ends in 2), 5688 (ends in 8), 1253 (ends in 3) – squares never end in 2, 3, 8 → rejected.
4410 – ends in a single 0; a square ending in 0 must end in 00 → rejected.
7921: 89² = (90 − 1)² = 8100 − 180 + 1 = 7921 ✓.

Why the other options are wrong:
A (4410) – odd number of trailing zeros.
B, D, E – last digits 2, 8, 3 are impossible for squares.

Cetking shortcut: Last-digit test removes four options in seconds; verify the survivor with (90 − 1)².

Answer: C

Approach: Average of the first n natural numbers = (n + 1)/2.

Solution:
Sum of 1 to 50 = 50 × 51 / 2 = 1275.
Average = 1275 / 50 = 25.5.
Or directly (50 + 1)/2 = 25.5.

Why the other options are wrong:
A (25) – uses n/2.
C (26) – rounding up.
D (50.5), E (51) – use n + 1 or (n + 1) without halving.

Cetking shortcut: In any AP the average = (first + last)/2 = (1 + 50)/2.

Answer: B

Approach: Total runs after 12 innings = 12 × new average; set it equal to old total + 90.

Solution:
Let the old average (11 innings) = x.
New average = x + 5 over 12 innings.
12(x + 5) = 11x + 90 ⇒ 12x + 60 = 11x + 90 ⇒ x = 30.
New average = 30 + 5 = 35.

Why the other options are wrong:
A (30) – the old average.
B, C, D (40, 45, 50) – do not balance the totals.

Cetking shortcut: New average = score − (old innings × increase) = 90 − 11 × 5 = 35.

Answer: E

Approach: Remainders multiply: rem(N²) = rem(r²).

Solution:
N = 5k + 3, so N leaves remainder 3.
N² leaves the same remainder as 3² = 9 when divided by 5.
9 = 5 × 1 + 4 ⇒ remainder 4.
Check: N = 8, N² = 64 = 5 × 12 + 4 ✓.

Why the other options are wrong:
C (3) – assumes the remainder stays the same.
A, B, E – arithmetic slips.

Cetking shortcut: Pick the smallest such number (3): 3² = 9 → remainder 4.

Answer: D

Approach: Compare fractions by decimals or by 'gap from 1'.

Solution:
7/6 = 1.17 (greater than 1).
7/9 = 0.778, 4/5 = 0.800, 5/7 = 0.714, 9/11 = 0.818.
Smallest = 5/7 = 0.714.

Why the other options are wrong:
A (7/6) – more than 1, the largest.
B (7/9 = 0.778), C (4/5 = 0.8), E (9/11 = 0.818) – all above 0.714.

Cetking shortcut: For fractions of the form (n − k)/n, compare the gap k/n: 5/7 is short by 2/7 ≈ 0.29, the biggest gap → smallest fraction.

Answer: D

Approach: Ages in ratio — the future ratio gives one equation.

Solution:
Present ages: A = 3x, B = 4x.
(3x + 10)/(4x + 10) = 4/5.
15x + 50 = 16x + 40 ⇒ x = 10.
Ages 30 and 40 (after 10 years 40 : 50 = 4 : 5 ✓). Sum = 70.

Why the other options are wrong:
A (60), C (80), D (50), E (90) – sum must be 7x and satisfy the future ratio; only 70 does.

Cetking shortcut: Sum must be a multiple of 7 (3x + 4x) → only 70 among options.

Answer: B

Approach: Sum = average × count; new person's value = new sum − old sum.

Solution:
Sum of 15 students = 15 × 18 = 270.
With teacher: 16 people, average 19 ⇒ sum = 16 × 19 = 304.
Teacher's age = 304 − 270 = 34 years.

Why the other options are wrong:
E (30), A (32), D (33) – D adds 15 to the old average 18; others are arithmetic slips.
C (35) – uses 16 × 1 added to the new average (16 + 19).

Cetking shortcut: Teacher = new average + (old count × increase) = 19 + 15 × 1 = 34.

Answer: B

Approach: Expenditure = price × consumption; keep the product constant.

Solution:
New price = 1.2 × old.
Consumption must become 1/1.2 = 5/6 of old.
Reduction = 1 − 5/6 = 1/6 = 16.66%.
Formula: r/(100 + r) × 100 = 20/120 × 100 = 16.66%.

Why the other options are wrong:
A (20.33%) – assumes the cut equals the rise.
C, D, E – arithmetic slips.

Cetking shortcut: 20% = 1/5 rise ⇒ cut = 1/(5 + 1) = 1/6 = 16.66%.

Answer: B

Approach: Successive spending — apply the 80% to the remaining income only.

Solution:
Food + education = 35% + 25% = 60% ⇒ remaining = 40%.
Rent = 80% of 40% = 32%.
Left = 40% − 32% = 8% of income.

Why the other options are wrong:
E (6%), B (10%), C (12%), D (15%) – come from taking 80% of the whole income or mixing bases.

Cetking shortcut: Left = 40% × 20% = 8%.

Answer: A

Approach: Fix the cost of one orange from the loss case, then price it for the gain.

Solution:
SP of 1 orange = Re 1/12 at 20% loss ⇒ CP = (1/12)/0.8 = 5/48.
For 20% gain: SP = 1.2 × 5/48 = 1/8.
So he must sell 8 oranges for a rupee.

Why the other options are wrong:
C (15), D (16) – sell more per rupee, i.e. a bigger loss.
B (10), E (9) – do not reach 20% gain.

Cetking shortcut: Count × (1 + profit%) is constant: 12 × 0.8 = n × 1.2 ⇒ n = 8.

Answer: A

Approach: Set CP = 100x and compare the two scenarios.

Solution:
Original: CP = 100x, SP = 105x.
New: CP = 95x, SP = 105x − 1, profit 10% ⇒ SP = 1.1 × 95x = 104.5x.
105x − 1 = 104.5x ⇒ 0.5x = 1 ⇒ x = 2.
CP = Rs. 200. Check: 190 → 209 = 10% profit ✓.

Why the other options are wrong:
A, B, D, E – on testing, the two SPs do not differ by Rs. 1.

Cetking shortcut: Difference in the two SPs = 105% − (110% of 95%) = 105% − 104.5% = 0.5% of CP = Rs. 1 ⇒ CP = 200.

Answer: C

Approach: Same time period ⇒ profit ratio = capital ratio.

Solution:
C's profit = 1000 − 500 − 300 = Rs. 200.
Profit ratio A : B : C = 500 : 300 : 200 = 5 : 3 : 2.
A's 5 parts = Rs. 10,000 ⇒ 1 part = Rs. 2,000.
C's capital = 2 × 2,000 = Rs. 4,000.

Why the other options are wrong:
C (6000) – this is B's capital.
B (5000) – A's half, not C's.
D, E – no basis in the ratio.

Cetking shortcut: C's capital = 10,000 × 200/500 = Rs. 4,000.

Answer: A

Approach: Profit ratio = capital × time.

Solution:
Capitals: A = 3k, B = 5k, C = 5k (equal to B).
Time: A and B 12 months, C 6 months.
A : B : C = 3 × 12 : 5 × 12 : 5 × 6 = 36 : 60 : 30 = 6 : 10 : 5.

Why the other options are wrong:
A (3:5:2), B (3:5:5) – ignore that C invested only for 6 months or scale wrongly.
D (3:7:8), E (6:10:3) – wrong time/amount for C.

Cetking shortcut: Halve C's capital for half the time: 3 : 5 : 2.5 = 6 : 10 : 5.

Answer: C

Approach: Work ∝ men × days × hours: M₁D₁H₁/W₁ = M₂D₂H₂/W₂.

Solution:
Case 1: 12 × 24 × 6 = 1728 man-hours for 460 chairs.
Case 2: 18 × 36 × 8 = 5184 man-hours.
5184/1728 = 3 ⇒ chairs = 460 × 3 = 1380.

Why the other options are wrong:
A (1260), B (1320), C (1400), E (1200) – miss one of the factors (e.g. 18/12 × 36/24 = 2.25 alone).

Cetking shortcut: Multiply the factor changes: (18/12) × (36/24) × (8/6) = 1.5 × 1.5 × 4/3 = 3.

Answer: D

Approach: Total man-days of work stay constant.

Solution:
Let x men be employed: work = 9x man-days.
Actually (x − 6) men took 15 days: work = 15(x − 6).
9x = 15x − 90 ⇒ 6x = 90 ⇒ x = 15.

Why the other options are wrong:
A (12) – with 6 present, 6 × 15 = 90 ≠ 108.
C (18), D (20), E (24) – 9x ≠ 15(x − 6).

Cetking shortcut: Absent men × 15 days = extra days (15 − 9) × x ⇒ 6 × 15 = 6x ⇒ x = 15.

Answer: B

Approach: Net rate = leak rate − inlet rate; find the tap's rate as a fraction of the tank.

Solution:
Leak alone empties in 8 h ⇒ −1/8 per hour.
With tap on, it empties in 12 h ⇒ net −1/12 per hour.
Tap rate = 1/8 − 1/12 = 1/24 tank per hour ⇒ tap fills the tank in 24 h.
Tap gives 6 L/min = 360 L/h ⇒ capacity = 24 × 360 = 8640 L.

Why the other options are wrong:
A, B, D, E – result from wrong time (e.g. 20 h or 25 h) or not converting minutes to hours.

Cetking shortcut: Tap time = (8 × 12)/(12 − 8) = 24 h; capacity = 24 × 60 × 6 = 8640.

Answer: C

Approach: Use efficiencies: total work = combined efficiency × time.

Solution:
Let A = 1 unit/h ⇒ B = 2, C = 4 (C twice B, B twice A).
Combined = 7 units/h; tank filled in 5 h ⇒ capacity = 35 units.
A alone = 35/1 = 35 hours.

Why the other options are wrong:
A (20), B (25), C (30), E (40) – wrong efficiency ratios (e.g. 1 : 2 : 3).

Cetking shortcut: A alone time = 5 × (1 + 2 + 4)/1 = 35 h.

Answer: D

Approach: Work in 3-day cycles using LCM units.

Solution:
Total work = LCM(20, 30, 60) = 60 units. Efficiencies: A = 3, B = 2, C = 1 per day.
Days 1 and 2: A alone = 3 + 3 = 6 units.
Day 3: A + B + C = 3 + 2 + 1 = 6 units.
One 3-day cycle = 12 units ⇒ 60/12 = 5 cycles = 15 days (finishes exactly at the end of a cycle).

Why the other options are wrong:
A (10), B (12) – assume help every day or every second day.
D (16), E (18) – add extra days after the work is already done.

Cetking shortcut: Cycle work = 1/5 of the job ⇒ 5 cycles × 3 days = 15.

Answer: C

Approach: Equate total work from both groups to find the man : boy efficiency.

Solution:
10(6M + 8B) = 2(26M + 48B) ⇒ 60M + 80B = 52M + 96B ⇒ 8M = 16B ⇒ 1M = 2B.
Work = 10 × (6 × 2 + 8)B = 10 × 20B = 200 boy-days.
15 men + 20 boys = 30B + 20B = 50B.
Time = 200/50 = 4 days.

Why the other options are wrong:
B (5) – uses 1M = 1.5B or similar slip.
C, D, E – wrong efficiency relation.

Cetking shortcut: Convert everyone into boys (1M = 2B) and divide total boy-days by the new strength.

Answer: A

Approach: Opposite directions ⇒ relative speed = sum; distance = sum of lengths.

Solution:
Distance = 108 + 112 = 220 m; time = 6 s.
Relative speed = 220/6 = 110/3 m/s = 110/3 × 18/5 = 132 km/h.
Speed of second train = 132 − 50 = 82 km/h.

Why the other options are wrong:
A (48), B (54), C (66) – use relative speed as a difference or forget the conversion.
E (90) – arithmetic slip.

Cetking shortcut: 220 m in 6 s ⇒ 220 × 3.6/6 = 132 km/h; subtract 50.

Answer: D

Approach: Same direction ⇒ relative speed = difference; train length is the same in both cases.

Solution:
Let train speed = v km/h. Relative speeds: (v − 2) and (v − 4) km/h.
L = (v − 2) × 5/18 × 9 = (v − 4) × 5/18 × 10.
9v − 18 = 10v − 40 ⇒ v = 22 km/h.
L = 20 × 5/18 × 9 = 50 m (check: 18 × 5/18 × 10 = 50 m ✓).

Why the other options are wrong:
A (45), C (54), D (72), E (60) – do not give the same length from both persons.

Cetking shortcut: Test options: 50 m in 9 s = 20 km/h relative and in 10 s = 18 km/h relative — the 2 km/h gap matches the walkers' 4 − 2.

Answer: B

Approach: Alligation on profit percentages.

Solution:
Profits: 8% and 18%; mean 14%.
Quantity at 8% : quantity at 18% = (18 − 14) : (14 − 8) = 4 : 6 = 2 : 3.
Quantity at 18% = 3/5 × 1000 = 600 kg.

Why the other options are wrong:
A (400 kg) – this is the part sold at 8%.
B (500 kg) – would give an average of 13%.
D, E – average would exceed 14%.

Cetking shortcut: 14% is closer to 18% than to 8% ⇒ more than half (600) is at 18%.

Answer: C

Approach: Replacement: only syrup is removed-and-not-replaced; track the syrup fraction.

Solution:
Syrup = 5/8 of the vessel. Draw off fraction f and replace with water.
Syrup left = 5/8 × (1 − f). Need it = 1/2.
1 − f = (1/2)/(5/8) = 4/5 ⇒ f = 1/5.

Why the other options are wrong:
A (1/3), B (1/4), C (2/7), D (1/7) – leave syrup at 5/12, 15/32, 25/56, 15/28 of the vessel, not 1/2.

Cetking shortcut: Fraction to replace = 1 − (target syrup / present syrup) = 1 − (4/8 ÷ 5/8) = 1/5.

Answer: E

Approach: Simple interest: I = PRT/100.

Solution:
Doubles ⇒ interest = principal ⇒ I = P.
P = P × R × 8/100 ⇒ R = 100/8 = 12.5%.

Why the other options are wrong:
A, B, D, E – give interest ≠ P in 8 years (e.g. 12% → 96%).

Cetking shortcut: SI doubling: R × T = 100 ⇒ R = 100/8.

Answer: C

Approach: Half-yearly compounding: halve the rate, double the periods.

Solution:
Rate per half-year = 5%; periods = 2.
Amount = 1000 × 1.05² = 1000 × 1.1025 = 1102.50.
CI = 1102.50 − 1000 = Rs. 102.50.

Why the other options are wrong:
A (100) – simple interest / annual compounding.
B, C, E – arithmetic slips.

Cetking shortcut: CI for 2 periods at r% = 2r + r²/100 = 10 + 0.25 = 10.25% of 1000.

Answer: D

Approach: Diagonals of a rhombus bisect each other at right angles.

Solution:
Half-diagonals = 12 cm and 5 cm.
Side = √(12² + 5²) = √169 = 13 cm.
Perimeter = 4 × 13 = 52 cm.

Why the other options are wrong:
B, C, D, E – use full diagonals or add them instead of using Pythagoras.

Cetking shortcut: 5–12–13 triplet: half-diagonals 5 and 12 ⇒ side 13.

Answer: A

Approach: Melting conserves volume.

Solution:
Total volume = 3³ + 4³ + 5³ = 27 + 64 + 125 = 216 cm³.
New side = ∛216 = 6 cm.

Why the other options are wrong:
B, C, D, E – add sides (12) or cube-roots incorrectly.

Cetking shortcut: Remember 3³ + 4³ + 5³ = 6³.

Answer: A

Approach: Races with a head start — compare the times to finish.

Solution:
A runs 500 − 140 = 360 m at speed 3 ⇒ time = 120 units.
In 120 units B runs 4 × 120 = 480 m.
When A finishes, B is 500 − 480 = 20 m short ⇒ A wins by 20 m.

Why the other options are wrong:
A (10), C (30), D (40), E (60) – wrong time base (e.g. using 500 m for A).

Cetking shortcut: Distance ratio = speed ratio: B covers 360 × 4/3 = 480 m while A covers 360 m.

Answer: B

Approach: Constant speeds ⇒ speed ratios chain: (A/B) × (B/C) = (A/C).

Solution:
Let the race length = L. When A finishes, B has run L − 12 and C has run L − 18.
When B finishes, C has run L − 8 ⇒ C/B = (L − 8)/L.
Also C/B = (L − 18)/(L − 12).
(L − 8)/L = (L − 18)/(L − 12) ⇒ L² − 20L + 96 = L² − 18L ⇒ 2L = 96 ⇒ L = 48 m.
Check: A : B : C = 48 : 36 : 30; B/C = 36/30 = 48/40 ✓.

Why the other options are wrong:
A (36), B (24), C (60), D (72) – fail the chained ratio check.

Cetking shortcut: B beats C by 6 m over the last L − 12 m and by 8 m over L m: 6/(L − 12) = 8/L ⇒ L = 48.

Answer: E

Approach: Classical probability with two dice: 36 outcomes.

Solution:
Sum 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) = 6 ways.
Sum 11: (5,6), (6,5) = 2 ways.
Mutually exclusive ⇒ favourable = 8; P = 8/36 = 2/9.

Why the other options are wrong:
A (1/6) – sum 7 only.
B (1/9) – 4/36, undercounts.
C (7/36), D (5/36) – miscounted pairs.

Cetking shortcut: Remember: P(sum 7) = 6/36 and P(sum 11) = 2/36.

Answer: E

Approach: Divisible by 5 ⇒ units digit is 0 or 5; only 5 is available.

Solution:
Units digit fixed = 5 (1 way).
Hundreds digit: any of the remaining 5 digits.
Tens digit: any of the remaining 4 digits.
Total = 5 × 4 × 1 = 20.

Why the other options are wrong:
A (5) – fills only one free place.
C (15), E (25) – allow repetition or wrong count.
B (10) – uses combinations (5C2).

Cetking shortcut: Fix the restricted place first, then fill the rest: 5P2 = 20.

Answer: D

Approach: Average = sum of the four quarterly values ÷ 4.

Solution:
Product B: Q1 = 30, Q2 = 50, Q3 = 65, Q4 = 75 (in '000s).
Sum = 30 + 50 + 65 + 75 = 220.
Average = 220/4 = 55.

Why the other options are wrong:
A (50) – Q2 value only.
C (60), D (65) – read another product or a single quarter.
E (52.5) – arithmetic slip.

Cetking shortcut: Pair the ends: (30 + 75) + (50 + 65) = 105 + 115 = 220.

Answer: B

Approach: Add the three bars of each quarter and compare.

Solution:
Q1 = 45 + 30 + 55 = 130.
Q2 = 60 + 50 + 40 = 150.
Q3 = 55 + 65 + 70 = 190.
Q4 = 80 + 75 + 60 = 215 → highest.

Why the other options are wrong:
A, B – clearly lower totals.
C (Q3) – 190 < 215.
E – Q3 and Q4 are not equal (190 vs 215).

Cetking shortcut: Q4 has the two tallest bars (80, 75) and its third bar (60) is only 10 below Q3's 70 — Q4 wins by inspection.

Answer: D

Approach: Percentage increase = (new − old)/old × 100.

Solution:
Product A: Q1 = 45, Q4 = 80.
Increase = 80 − 45 = 35.
% increase = 35/45 × 100 = 7/9 × 100 = 77.78%.

Why the other options are wrong:
D (43.75%) – divides by the new value 80 (35/80).
A (75%), B (80%) – rounding or wrong base.
E (56.25%) – wrong values.

Cetking shortcut: 35/45 = 7/9 = 77.78% (memorise ninths: 1/9 = 11.11%).

Answer: C

Approach: Find each product's annual total, then simplify the ratio.

Solution:
Product C total = 55 + 40 + 70 + 60 = 225.
Product A total = 45 + 60 + 55 + 80 = 240.
C : A = 225 : 240 = 15 : 16 (divide by 15).

Why the other options are wrong:
C (16:15) – ratio reversed (A : C).
A, D, E – not supported by the totals.

Cetking shortcut: Both totals are multiples of 15: 225 = 15 × 15, 240 = 15 × 16.

Answer: B

Approach: Share = Product B ÷ quarter total; compare fractions.

Solution:
Q1: 30/130 = 23.1%.
Q2: 50/150 = 33.3%.
Q3: 65/190 = 34.2%.
Q4: 75/215 = 34.9%.
Lowest share = Q1.

Why the other options are wrong:
B, C, D – each above 33%.
E – Q1 and Q2 shares differ (23.1% vs 33.3%).

Cetking shortcut: In Q1, B (30) is less than a quarter of 130; in every other quarter B is about one-third of the total.

Answer: A

Approach: Convert the percentage difference into an amount.

Solution:
Salaries = 35%, Infrastructure = 15%.
Difference = 20% of the budget.
20% of Rs. 20 crore = Rs. 4 crore.

Why the other options are wrong:
A (3 Cr) – uses 15% difference.
C (5 Cr) – uses Marketing 25%.
D, E – arithmetic slips.

Cetking shortcut: Subtract percentages first, then convert once: 20% × 20 = 4.

Answer: B

Approach: 'Percent less than' uses the compared-to value (Marketing) as base.

Solution:
Marketing = 25%, R&D = 15%.
Difference = 10.
% less = 10/25 × 100 = 40%.

Why the other options are wrong:
A (10%) – the percentage-point difference, not percent.
E (33.33%) – uses a wrong base (10/30).
C (60%) – R&D as % of Marketing.
D (25%) – Marketing's share.

Cetking shortcut: R&D/Marketing = 15/25 = 60% ⇒ 40% less.

Answer: B

Approach: Central angle = share % × 360°.

Solution:
Salaries = 35%.
Angle = 0.35 × 360° = 126°.

Why the other options are wrong:
A (108°) – 30%.
B (120°) – one-third.
C (135°) – 37.5%.
E (144°) – 40%.

Cetking shortcut: 1% = 3.6° ⇒ 35 × 3.6 = 126°.

Answer: D

Approach: Budget total is unchanged — just move share from one sector to another.

Solution:
Miscellaneous = 10%; half of it = 5%.
This 5% is moved to R&D: 15% + 5% = 20%.
Total stays 100%, so the new R&D share = 20%.

Why the other options are wrong:
E (17.5%) – adds half of half.
A (18%), D (22.5%) – wrong amount moved.
B (25%) – adds the whole 10%.

Cetking shortcut: Transfers inside the same total don't change the base, so add percentages directly.

Answer: C

Approach: Add the two shares and compare with Salaries.

Solution:
Marketing + Miscellaneous = 25% + 10% = 35%.
Salaries = 35%.
Ratio = 35 : 35 = 1 : 1.

Why the other options are wrong:
C (5:7) – Marketing alone to Salaries.
E (7:5) – Salaries to Marketing.
A, D – not supported by the data.

Cetking shortcut: Ratios of amounts = ratios of percentages; no need for the total budget.

Answer: B

Approach: Synonym: find the word with the same meaning as DERIDE.

Solution: DERIDE = to laugh at, mock or ridicule with contempt (e.g. 'critics derided the plan as naive').
JEER = to shout rude, mocking remarks at someone. Both describe mocking someone, so Jeer is the synonym.

Why the other options are wrong:
A Stimulate: to excite or encourage, unrelated.
B Comfort: to console, the opposite in spirit.
D Inspire: to motivate, unrelated.
E Praise: the antonym of deride.

Cetking shortcut: Positive words (Stimulate, Comfort, Inspire, Praise) all cluster together; deride is negative, so the lone negative word wins.

Answer: C

Approach: Synonym: find the word with the same meaning as GARRULOUS.

Solution: GARRULOUS = talking too much, usually about unimportant things (from Latin garrire, to chatter). TALKATIVE is the direct synonym.

Why the other options are wrong:
A Guttural / B Throaty: describe a harsh sound produced in the throat, not the amount of talking.
C Concise: brief and to the point, opposite in spirit.
E Taciturn: reserved and silent, the antonym.

Cetking shortcut: When an option pair is exact opposites (Talkative vs Taciturn), the answer is usually one of them.

Answer: D

Approach: Synonym: find the word with the same meaning as BEMOAN.

Solution: BEMOAN = to complain about or express grief over something ('he bemoaned the lack of facilities').
LAMENT = to express sorrow or regret. Same meaning.

Why the other options are wrong:
B Soothe: to calm, opposite in tone.
C Denounce: to publicly condemn; that is criticism, not sorrow.
D Loathe: to hate intensely; a feeling, not an expression of grief.
E Ghoul: a noun (an evil spirit), not even the same part of speech.

Cetking shortcut: 'Moan' sits inside bemoan; a moan is a sound of grief, and lament is grief expressed.

Answer: A

Approach: Antonym: find the word nearest to the opposite of VAGRANT.

Solution: VAGRANT = a person without a settled home or job who wanders from place to place. The opposite idea is someone with a fixed home, i.e. SETTLED.

Why the other options are wrong:
A Vagabond, D Tramp, E Wayfarer: all are synonyms (wanderers), not opposites.
B Biased: means prejudiced, unrelated.

Cetking shortcut: Three options are synonyms of the word, so they cancel out; only one option is about 'staying in one place'.

Answer: C

Approach: Antonym: find the word nearest to the opposite of HAUGHTY.

Solution: HAUGHTY = arrogant, looking down on others. The opposite is HUMBLE = modest, not thinking oneself superior.

Why the other options are wrong:
A Pitiable: deserving pity, not the opposite of pride.
B Scared / D Cowardly: about fear, not about pride.
E Insolent: rude and disrespectful, close to haughty, so a synonym trap.

Answer: C

Approach: One-word substitution using Latin number roots.

Solution: A person aged 90 to 99 is in their nineties. The Latin root nonageni = ninety, so the word is NONAGENARIAN.

Why the other options are wrong:
A Octogenarian: 80 to 89 years.
B Centenarian: 100 years or more.
C Septuagenarian: 70 to 79 years.
E Puerile: childishly silly; not an age word.

Cetking shortcut: Remember the ladder: sexagenarian 60, septuagenarian 70, octogenarian 80, nonagenarian 90, centenarian 100.

Answer: D

Approach: One-word substitution using Greek roots.

Solution: Greek kleptes = thief. KLEPTOMANIA = a compulsive urge to steal things, usually things one does not need.

Why the other options are wrong:
A Logomania: abnormal talkativeness (logos = word).
B Melomania: excessive love of music (melos = song).
D Hypomania: a mild form of mania (mood state).
E Mythomania: compulsive lying or exaggeration.

Cetking shortcut: Link the root to a known word: klepto = thief (as in 'kleptocracy', rule by thieves).

Answer: C

Approach: Idiom meaning: picture the literal image.

Solution: A hornet's nest is full of angry, stinging insects; disturbing it brings trouble. Figuratively, 'a hornet's nest' = an unpleasant, troublesome situation full of hostility.

Why the other options are wrong:
A A comfortable position / C Among roses / E Keeping the peace: all pleasant, opposite meaning.
D A dilemma: a choice between two bad options; the idiom is about trouble and anger, not choosing.

Answer: B

Approach: Idiom meaning from its origin.

Solution: A will-o'-the-wisp is a flickering light seen over marshes at night; travellers who followed it got lost. Figuratively it means anything that deludes, deceives or keeps escaping one's grasp, i.e. 'anything which eludes or deceives'.

Why the other options are wrong:
B / C: acting childishly or foolishly is not the meaning.
D Desires unbacked by efforts: that is 'wishful thinking', a different idea.
E Verity: means truth, the opposite of deception.

Answer: A

Approach: Idiom meaning: the first man had only one drink.

Solution: Adam, the first man, had nothing to drink but water. So 'Adam's ale' (also 'Adam's wine') = WATER.

Why the other options are wrong:
A Grace / B Pleasure: abstract qualities, not drinks.
D Juice / E Brew: real drinks, but the word 'ale' is a trap; the phrase means plain water.

Answer: C

Approach: Article rule: 'a' before a consonant sound, 'an' before a vowel sound.

Solution: 'Unique' is pronounced 'yoo-neek'; it begins with the consonant sound /j/. So it takes 'a', not 'an'.
Correct part B: 'I am reminded of a unique incident'.

Why the other options are wrong:
A 'Even now when I see the spot' is correct.
C 'that took place' correctly uses past tense for a past event.
D 'several years ago' correctly pairs with simple past.
E There is an error in B.

Cetking shortcut: Same trap words: a university, a European, a one-day match, a useful tip; but an hour, an honest man, an MBA.

Answer: B

Approach: Preposition in a fixed expression: something you are concerned about is 'on your mind'.

Solution: The sentence says a need 'has been in the minds of people for some time now', i.e. it has been a concern people kept thinking about. The standard idiom for that is 'on the minds of people' / 'on people's minds'.
Correct part C: 'has been on the minds of people'.
Subject-verb ('The need ... has been') and the present perfect with 'for some time now' are both correct.

Why the other options are wrong:
A 'The need to set up' is correct.
B 'a good library in the locality' is correct.
D 'for some time now' correctly pairs with present perfect 'has been'.
E 'No error' is wrong because the preposition in C is idiomatically incorrect.

Cetking shortcut: When grammar (tense, agreement, articles) is clean, check the prepositions in fixed phrases: on one's mind, in one's opinion, at one's wits' end.

Answer: C

Approach: Articles: a singular countable noun cannot stand alone.

Solution: 'Day' is a singular countable noun; with an adjective before it, it still needs 'a'.
Correct part A: 'It being a rainy day,'.
The rest ('we decided not to go out but to stay at home and watch a movie') is parallel and correct.

Why the other options are wrong:
B 'we decided not to go out' is correct.
C 'but to stay at home' is parallel with 'not to go out'.
D 'and watch a movie' correctly continues 'to stay ... and (to) watch'.
E There is an error in A.

Answer: A

Approach: Verb pattern: verb + object + to-infinitive must suit the meaning (request vs command).

Solution: 'Told his teacher to explain' sounds like an order, which does not fit a boy speaking to his teacher. A request is expressed by 'asked + object + to-infinitive'.
Correct: 'The boy asked his teacher to explain the passage.'

Why the other options are wrong:
A 'called his teacher to explain': means summoned, wrong sense.
B 'said to his teacher to explain': 'say' does not take object + to-infinitive.
D 'spoke his teacher': 'speak' needs 'to'; ungrammatical.
E The original is inappropriate in tone, so it needs improvement.

Answer: C

Approach: Check the part of speech and meaning of the highlighted word.

Solution: After 'efforts to' we need a verb (to-infinitive). 'Rehabilitate' is a verb meaning to restore to a normal, useful life after illness or disability, which is exactly what Helen Keller did despite her triple handicap. So no improvement is needed.

Why the other options are wrong:
A 'manage herself': vague, loses the idea of restoring.
B 'reinstate herself': means restore to a post or position, wrong sense.
C 'readapt herself': weaker and not the standard term for overcoming a disability.
D 'rehabilitation': a noun, cannot follow 'to' here.

Answer: E

Approach: Collocation: which verb the exam expects with 'the truth'.

Solution: Traditional grammar books pair 'truth' with SPEAK: 'He never speaks the truth' (and 'tell' with lies, stories, jokes). So 'speaks' replaces 'tells'.

Why the other options are wrong:
A 'says the truth': 'say' does not collocate with 'the truth'.
B 'utters the truth': unidiomatic.
D 'lives the truth': changes the meaning.
E 'No improvement': 'tells the truth' is common in everyday English, but CET follows the textbook collocation 'speak the truth', so an improvement is expected.

Cetking shortcut: In CET-style sentence improvement, the textbook pairings win: speak the truth, tell a lie, make a mistake, do one's duty.

Answer: C

Approach: Active to passive, simple present: is/am/are + V3.

Solution: Active: He (subject) teaches (simple present) us (indirect object) Grammar (direct object).
Make the personal object the subject: us → We; teaches → are taught; He → by him.
Passive: 'We are taught Grammar by him.'

Why the other options are wrong:
A 'Grammar is taught to us by him': a valid but less standard passive; the textbook answer keeps the personal object as subject.
B 'We are being taught': present continuous, tense changed.
C 'Grammar is being taught us': wrong tense and missing 'to'.
E 'We taught him Grammar': active, past tense, and meaning reversed.

Cetking shortcut: First kill every option whose tense changed (being = continuous, taught = past active); then pick the person-first passive.

Answer: D

Approach: Passive of a 'Who' question in present continuous.

Solution: 'Who is creating this mess?' → Who → By whom; is creating (present continuous) → is being created; object 'this mess' becomes subject.
Question order: By whom + is + this mess + being created?
Passive: 'By whom is this mess being created?'

Why the other options are wrong:
A 'Who has created': still active, tense changed to present perfect.
B 'has this mess been created': present perfect, tense changed.
C 'By whom this mess is being created?': statement order, not a question.
E 'Who is being created this mess?': ungrammatical.

Answer: D

Approach: Passive infinitive: to + be + V3, with the object introduced by 'for'.

Solution: Active infinitive: 'to ring the bell' (the bell is the object).
Passive: object comes forward with 'for', and the infinitive becomes 'to be rung' (ring–rang–rung).
Passive: 'It is time for the bell to be rung.'

Why the other options are wrong:
A 'It is time the bell rings': changes the structure and is not passive.
B 'It is being time': ungrammatical.
C 'for the bell to ring': still active (the bell rings by itself).
E 'It is bell ring time': not standard English.

Answer: D

Approach: Indirect speech: habitual facts / still-true statements may keep the present tense.

Solution: Direct: He said, "I clean my teeth twice a day." This is a daily habit that remains true.
I → he; 'my' → his; reporting verb 'said' → 'said that'.
Since it is a habitual action, the present tense is retained: 'He said that he cleans his teeth twice a day.'

Why the other options are wrong:
A 'cleaned': strict back-shift; it ignores the habitual-action rule, under which a habit that is still true keeps the present tense.
C 'used to clean': suggests a past habit that has stopped, wrong meaning.
D 'is used to cleaning': means 'is accustomed to', different meaning.
E 'is cleaning': continuous tense, wrong for a habit.

Answer: B

Approach: Indirect speech: tense back-shift plus change of place words.

Solution: Reporting verb 'said' is past, so: saw (simple past) → had seen (past perfect).
I → he; here → there (the speaker is no longer at that place).
Result: 'He said that he had seen a book there.'

Why the other options are wrong:
A 'saw a book here': no back-shift, no change of 'here'.
B 'saw a book there': place word changed but tense not back-shifted.
C 'had seen a book here': tense right, 'here' not changed.
E 'he see a book here': ungrammatical.

Cetking shortcut: Two changes are needed (tense + place), so pick the only option with both.

Answer: D

Approach: Imperative sentences: said → requested/begged/ordered + object + (not) to + verb; drop 'please'.

Solution: 'Please' shows a plea, so the reporting verb becomes 'begged'. Negative imperative 'don't go' → 'not to go'. The listener (me) is the object.
Result: 'She begged me not to go away.'

Why the other options are wrong:
A 'said to please her': misreads 'please' as a verb; ungrammatical.
B 'told me not to go away': grammatical but loses the request tone.
C 'begged that I not go away': awkward; the standard pattern is begged + object + to-infinitive.
E 'said me not to': 'say' cannot take a personal object without 'to'.

Answer: D

Approach: Single blank: the clue is 'coating ... on the unwashed sink'.

Solution: We need a noun for a dirty, slippery layer on an unwashed sink. SLIME = a thick, slippery, unpleasant substance. 'A coating of slime on the unwashed sink' fits perfectly.

Why the other options are wrong:
B Slew: a large number of something; also a verb (to turn).
C Slink: a verb, to move stealthily.
D Sledge: a vehicle on runners or a heavy hammer.
E Coat: 'a coating of coat' is redundant and meaningless.

Cetking shortcut: The options are sound-alikes (sli-, sle-); only one is a substance.

Answer: A

Approach: Single blank with confusable adjectives; clue word 'injury' and 'worried'.

Solution: NIGGLING = slight but persistent and troubling. A 'niggling injury' is a standard sports phrase for a minor injury that will not go away, which naturally worries team management.

Why the other options are wrong:
B Niggardly: miserly, used for people and money.
C Stingy: also miserly, same problem.
D Nifty: clever or stylish, positive and illogical with injury.
E Important: an injury is 'serious', not 'important'; poor collocation.

Cetking shortcut: Niggardly and stingy are synonyms of each other, so both can be eliminated together.

Answer: A

Approach: Single blank; the article 'an' and the clue 'plea for mercy' guide the choice.

Solution: A victim begging for mercy would plead with strong feeling. IMPASSIONED = filled with intense emotion. 'An impassioned plea for mercy' is a standard collocation.

Why the other options are wrong:
A Impassive: expressionless, unemotional; opposite of what fits.
B Impassable: cannot be crossed (a road), not for a plea.
D Imperial: relating to an empire; also 'an imperial' fails the article.
E Letter: 'an letter' is ungrammatical and 'letter plea' meaningless.

Answer: C

Approach: Collocation: which verb goes with 'pain and suffering ... on people'.

Solution: INFLICT = to cause something unpleasant (pain, damage, suffering) to be suffered by someone. The pattern 'inflict pain and suffering on' is a fixed collocation.

Why the other options are wrong:
A Deplored: means condemned; 'deplored pain on people' makes no sense.
B Eliminated: means removed, opposite meaning and wrong preposition.
C Affected: takes a direct object (affected people), not 'pain on'.
E Imposed: used with rules, taxes, restrictions or one's will, not pain and suffering.

Answer: D

Approach: Single blank: the father's natural reaction to good news.

Solution: His son was selected for the college team, which is happy news. ELATED = very happy and proud. 'He felt elated' fits.

Why the other options are wrong:
A Enamoured: in love with someone or something; wrong sense.
C Exasperated: intensely irritated, negative.
D Embittered: resentful, negative.
E Effervescent: bubbly and lively by nature; one 'is' effervescent rather than 'feels' it at news.

Answer: B

Approach: Question tags: repeat the same auxiliary/modal; flip negative to positive.

Solution: The statement 'You daren't come here' uses the semi-modal 'dare' in the negative (daren't = dare not).
Rule: negative statement → positive tag with the same auxiliary and the subject pronoun.
Tag: 'dare you?'

Why the other options are wrong:
B 'will you': 'will' is not the auxiliary used in the statement.
C 'daren't you': negative + negative is wrong.
D 'won't you': wrong auxiliary and wrong polarity.
E 'can you': wrong modal.

Cetking shortcut: Tag = same helping verb, opposite polarity, same subject pronoun.

Answer: A

Approach: Idiom meaning.

Solution: 'French leave' comes from the 18th-century custom of leaving a party without saying goodbye to the host. It now means being absent from work or duty WITHOUT PERMISSION.

Why the other options are wrong:
A Long absence: length is not the point; lack of permission is.
B Leave on the pretext of illness: that is a false excuse, but permission is still sought.
C Casual leave: an official, sanctioned leave.
E Holiday: an approved break.

Answer: D

Approach: Idiom meaning: picture a storm inside a tiny cup.

Solution: A storm is huge, a teacup is tiny. So 'a storm in a teacup' = a big fuss or much excitement over something trivial.

Why the other options are wrong:
A Unexpected event / E Expected event: the idiom is not about timing.
B A danger signal: no warning meaning.
D A great noise: captures the fuss but not the triviality of the cause.

Answer: C

Approach: Check each option against the four tenets of a 'true' newspaper listed in paragraph 3.

Solution: The passage lists the tenets: accessible to the public; published at a regular interval (daily, weekly, monthly etc.); information is current; covers a variety of topics.
Option B, a newspaper published once a month, directly satisfies the 'regular interval' tenet, which the passage itself illustrates with 'monthly'.

Why the other options are wrong:
A Accessible only to Asian readers: restricts access, violating 'accessibility by the public'.
C Printed in quarto, not folio: size is a debate point, not one of the four tenets.
D Covers historic developments: violates 'information is current'.
E Handwritten: the passage says handwritten copies could not be mass distributed.

Cetking shortcut: Underline the bracket '(daily, weekly, monthly etc.)'; the option that echoes it is the one the passage itself certifies.

Answer: B

Approach: Locate the line on how 'true newspapers' began (paragraph 2).

Solution: 'The first true newspapers arrived after Johannes Gutenberg introduced his movable type printing press to the European world around 1440.' So the printing press paved the way.

Why the other options are wrong:
A The folio broadsheet (1618) came much later, after true newspapers already existed.
C Printing in multiple languages is never mentioned.
D Government's larger role made sharing information a necessity; it did not make mass distribution possible.
E Says the press 'blocked' the way, the opposite of the passage.

Answer: B

Approach: Verify every detail (year, place, size) against paragraph 3.

Solution: Passage: 'The first English newspaper was published in 1665 in Oxford, England. Known as the Oxford Gazette, the newspaper moved to London in 1666 and was renamed the London Gazette.' Option E states exactly this.

Why the other options are wrong:
A Johann Carolus published in 1604, not 1904.
B The Relation is debated because it was printed in quarto; the option twists the logic into a reason it qualifies.
C The first English newspaper was in 1665, not 1965.
D The 1618 Amsterdam broadsheet was printed in folio size, not quarto.

Cetking shortcut: In 'which is true' detail questions, examiners change one number or one word; scan dates and size words first.

Answer: E

Approach: Vocabulary in context: read the sentence around the word.

Solution: 'Disseminating news and information on paper presented significant challenges. When each copy had to be handwritten, mass distribution was impossible.' The context is about distribution, so disseminating = SPREADING widely.

Why the other options are wrong:
A Agree: unrelated.
B Taunt, C Barb, D Sneer: all mean mocking or insulting remarks; none fits distributing news.

Cetking shortcut: Three options are synonyms of one another (taunt/barb/sneer), so all three are out at once.

Answer: E

Approach: Locate the challenge in paragraph 1.

Solution: 'When each copy had to be handwritten, mass distribution was impossible.' Option B paraphrases this exactly ('next to impossible').

Why the other options are wrong:
A Pigeons are never mentioned.
C / E Government affirmation for printing is not discussed.
D Says copies were 'printed', which contradicts the passage; printing was the solution, not the problem.

Cetking shortcut: B and D differ by one word; when two options are near-twins, the answer is usually one of them, so check that word.

Answer: B

Approach: Locate the last sentence of the passage.

Solution: 'As renewable energy prices continue to fall, however, Professor Moslener said government subsidies are likely to become less and less important.' Option B ('price of clean energy technology continues to plummet') says the same.

Why the other options are wrong:
A China's investment is not given as the reason.
C The passage never calls fossil fuels the better alternative.
D Wind and solar potential in the Nile areas is unrelated to subsidies.
E Rising prices would make subsidies more, not less, important.

Answer: B

Approach: Locate the keyword 'desalination' (paragraph 2).

Solution: 'Egypt is also considering financing options to conduct feasibility studies for building the world's largest solar power plant for both electricity generation and water desalination.'

Why the other options are wrong:
A China: the largest investor in 2017, not this project.
B Sweden, C Mexico, D Australia: mentioned only as countries that more than doubled clean-energy investment.

Cetking shortcut: Scan for the rare keyword in the question ('desalination'); it appears only once.

Answer: E

Approach: Vocabulary in context: read the sentence.

Solution: 'China was by far the world's largest investor ... accounting for nearly half of the new infrastructure commissioned.' Here 'accounting for' = forming or contributing that share. CONTRIBUTE fits.

Why the other options are wrong:
A Contradict: to deny; unrelated.
C Devious: dishonest; an adjective.
D Retrieve: to get back.
E Categorical: absolute; an adjective.

Answer: B

Approach: Vocabulary in context.

Solution: 'As the price of clean energy technology plummets, it has become an increasingly attractive prospect.' Falling prices make it attractive, so plummets = falls sharply. SLUMP = a sudden fall.

Why the other options are wrong:
A Intensify / B Escalate: mean increase, the opposite.
C Callous: insensitive; unrelated.
E Reminiscent: suggestive of the past; unrelated.

Answer: D

Approach: Locate the sentence with '2017' and 'largest investor' (paragraph 1).

Solution: 'China was by far the world's largest investor in renewable energy in 2017, accounting for nearly half of the new infrastructure commissioned.'

Why the other options are wrong:
B Egypt: only considering a solar plant feasibility study.
C Sweden, D Mexico, E Australia: they more than doubled investment but were not the largest.

Answer: A

Approach: 'NOT true' question: find the option that contradicts the passage's central claim.

Solution: Wilde's line: 'Most people are other people. Their thoughts are someone else's opinions, their lives a mimicry, their passions a quotation.' The author adds that 'the vast majority of us are not who we have been pretending to be'. So people's feelings are borrowed, not genuine. Option B ('People are genuine in expressing their feelings') is therefore NOT true.

Why the other options are wrong:
A True: our thoughts are 'someone else's opinions', so we speak in others' voices.
C True: 'their lives a mimicry'; we imitate others.
D Consistent: people stay 'content with admiring the wrapping' and would rather conform than break free.
E True: it is the direct restatement of 'their passions a quotation'.

Cetking shortcut: In NOT-true questions, look for the pair of opposites (B vs E); one is the passage's view and the other is the answer.

Answer: B

Approach: Vocabulary in context: what was Wilde's attitude in the quote?

Solution: 'As he so wryly observed, the vast majority of us are not who we have been pretending to be.' Wilde is mocking people's lack of originality with dry, ironic humour; the attitude underneath is critical. Of the options, DISAPPROVINGLY captures this critical, mocking sense.

Why the other options are wrong:
B Unwillingly / D Hesitatingly: Wilde's remark is confident, not reluctant.
C Repulsively: means in a disgusting way; far too strong and wrong sense.
E Willingly: describes readiness, not tone.

Answer: A

Approach: Decode the metaphor from the sentence before it.

Solution: The previous line says our lives 'are molded according to rules and values that are not our own'. The 'discarded chewing gum' is those borrowed views. Humanity gets stuck by giving preference to others' views over its own, which is option A.

Why the other options are wrong:
B Sponsored products: not discussed.
C 'Using discarded things': a literal reading of the metaphor.
D Appreciating others' ideas is not being trapped by them; the passage criticises surrender, not appreciation.
E Criticising others' ideas is the opposite of conformity.

Answer: A

Approach: Translate both halves of the expression.

Solution: Mimicry = imitation of others. A quotation = words borrowed from someone else. So: lives are imitations, feelings are borrowed. Option C ('Lives an imitation, feelings a borrowing') matches both halves.

Why the other options are wrong:
A Parody implies mockery or humour; 'repetition' misses the idea of borrowing.
B Recitation is reciting aloud, narrower than borrowing.
D Sham and deception suggest deliberate fraud; the passage describes unconscious conformity.
E Says lives are original, the opposite.

Answer: C

Approach: Read 'brave enough to forsake this trap' with the trap identified earlier.

Solution: The 'trap' is living by others' opinions. 'Brave enough to forsake' it = daring enough to break free from it. Option B says exactly this; later the passage repeats that 'very few summon the courage ... to walk alone'.

Why the other options are wrong:
A 'Quite serious to give up the old values': courage, not seriousness, is the key quality.
C 'Pretentious to discard one's convictions': the wrong attitude and the wrong target.
D 'Coaxed': being persuaded by others is the opposite of bravery.
E 'Hold up others' views': the opposite of forsaking the trap.

Cetking shortcut: Match the key word: 'brave' = 'daring'. Only one option carries a courage word.

Answer: B

Approach: Read the sentence just before 'Leonard calls it tacit knowledge' and see what 'it' refers to.

Solution: 'It is critical that long time workers transfer the knowledge they've gained from decades of experience ... Leonard calls it "tacit knowledge."' 'It' = the knowledge held by long-time workers. Option A uses the passage's own noun.

Why the other options are wrong:
B A checklist or binder of procedures is what tacit knowledge is contrasted with.
C 'Experience held by long-time workers': experience is the source; what is called tacit knowledge is the knowledge gained from it.
D 'Procedures': procedures can be written in manuals; tacit knowledge has never been written down.
E 'Can't be passed down': the passage says it is hard, not impossible, to pass on.

Cetking shortcut: In definition questions, trace the pronoun ('it') back to its noun and pick the option that repeats that noun.

Answer: A

Approach: Tone: look at the emotionally loaded words.

Solution: Signals of worry: 'they'll be sunk', 'such anxious departures happen 10,000 times a day', 'imminent loss of detailed know-how', 'haemorrhaging its veteran employees', 'companies often fail to retain it'. The author is uneasy about a looming problem: APPREHENSIVE.

Why the other options are wrong:
A Light-hearted: the farewell lunch detail is brief; the concern is serious.
B Mournful: no grief; the author proposes solutions.
C Nostalgic: no longing for the past.
E Descriptive: the passage does describe, but 'anxious', 'sunk' and 'haemorrhaging' show a clear attitude of concern.

Cetking shortcut: If the passage names a looming risk and urges action, the tone is concerned/apprehensive, not neutral.

Answer: D

Approach: Locate the phrase 'knowledge transfer plans' (paragraph 6).

Solution: 'Melissa Moran, the nuclear group's manager of strategic workforce planning, asked nuclear managers to develop and submit knowledge transfer plans for team members nearing retirement.'

Why the other options are wrong:
A / D Dorothy Leonard (Harvard Business School professor) distinguished information from knowledge.
C The University of North Carolina study gave the 40 percent figure.
E The Pew Research Centre gave the 10,000-a-day figure.

Answer: B

Approach: Vocabulary in context: haemorrhage = heavy loss of blood, used figuratively for a heavy loss.

Solution: The passage is about senior workers retiring and taking know-how with them ('Such anxious departures happen 10,000 times a day'). So a company 'haemorrhaging its veteran employees' is losing its most experienced employees to retirement: option E.

Why the other options are wrong:
A Healthcare after retirement: a literal 'medical' misreading.
B Pressuring them to return: not discussed.
C Severing ties: colleagues even keep her number to call her.
D Laying off: the employees retire; they are not fired.

Answer: E

Approach: Locate 'information and knowledge' (paragraph 3).

Solution: 'Dorothy Leonard, a professor of business administration at Harvard Business School, says there is a big difference between information and knowledge.'

Why the other options are wrong:
A Melissa Moran asked for knowledge-transfer plans.
B Pew Research Centre is cited only for the 10,000-a-day figure.
C The University of North Carolina study gave the 40 percent figure.
E Duke is the utility that launched transfer initiatives.

Answer: D

Approach: Multiplicative series: next term = previous × 2 + 2.

Solution:
2 × 2 + 2 = 6
6 × 2 + 2 = 14
14 × 2 + 2 = 30
30 × 2 + 2 = 62
62 × 2 + 2 = 126

Cetking shortcut: Differences 4, 8, 16, 32 double each time, so the next difference is 64: 62 + 64 = 126. Also every term = 2ⁿ⁺¹ − 2.

Answer: B

Approach: Multiplicative series: next term = previous × 3 − 1.

Solution:
5 × 3 − 1 = 14
14 × 3 − 1 = 41
41 × 3 − 1 = 122
122 × 3 − 1 = 365

Cetking shortcut: Differences 9, 27, 81 are powers of 3, so the next difference is 243: 122 + 243 = 365.

Answer: B

Approach: Difference table — second differences in AP.

Solution:
Terms: 7, 20, 47, 94, 167
1st differences: 13, 27, 47, 73
2nd differences: 14, 20, 26 (rising by 6)
Next 2nd difference = 26 + 6 = 32
Next 1st difference = 73 + 32 = 105
Next term = 167 + 105 = 272

Answer: A

Approach: Power-based series: term = n³ − n² = n²(n − 1), n = 2, 3, 4…

Solution:
2³ − 2² = 4
3³ − 3² = 18
4³ − 4² = 48
5³ − 5² = 100
6³ − 6² = 216 − 36 = 180
Check: 7³ − 7² = 343 − 49 = 294 ✓

Cetking shortcut: Factor each term: 4 = 2²×1, 18 = 3²×2, 48 = 4²×3, 100 = 5²×4 → 6²×5 = 180.

Answer: C

Approach: Power-based series: term = n³ − n = (n − 1) × n × (n + 1).

Solution:
6 = 1×2×3, 24 = 2×3×4, 60 = 3×4×5
120 = 4×5×6, 210 = 5×6×7
Next = 6×7×8 = 336

Cetking shortcut: Second differences 18, 24, 30 rise by 6 → next 36; differences 18, 36, 60, 90 → next 126; 210 + 126 = 336.

Answer: A

Approach: Part-to-whole analogy: the formal opening section of a text.

Solution:
A prologue is the introductory section of a novel/play.
A preamble is the introductory statement of a law, statute or constitution (e.g. the Preamble to the Constitution).

Why the other options are wrong:
A Speech – has an opening, not formally a preamble.
C Poem – an introduction to a poem is a proem/prelude.
D Drama – the introduction to a drama is itself a prologue.
E Action – not a text at all.

Answer: B

Approach: Antonym analogy.

Solution:
Obstinate (stubborn, unyielding) ↔ Yielding — opposites.
Optimistic (expecting the best) ↔ Pessimistic — opposites.

Why the other options are wrong:
A Cheerful, B Hopeful, D Confident, E Positive – all synonyms or near-synonyms of optimistic.

Answer: C

Approach: Field of work : its product.

Solution:
Cartography → makes maps.
Lexicography → compiles dictionaries.

Why the other options are wrong:
A Book – too general.
B Language – subject of linguistics.
D Grammar – studied by grammarians.
E Alphabet – not the output of lexicography.

Answer: C

Approach: Object : defining scope.

Solution:
Panacea = a remedy for all ills → its defining quality is universal.
Antidote = a remedy against a particular poison → its defining quality is specific.

Why the other options are wrong:
A Rare – not a defining feature.
C Curative / D Medicinal – true of both, so not the parallel quality.
E Preventive – an antidote counteracts after exposure; it does not prevent.

Answer: B

Approach: Antonym analogy.

Solution:
Opaque (cannot be seen through) ↔ Transparent.
Cryptic (mysterious, hard to understand) ↔ Obvious.

Why the other options are wrong:
B Hidden, C Confusing, D Secret, E Vague – all synonyms of cryptic.

Answer: A

Approach: Classification by category (instrument family).

Solution:
Cello, Violin, Guitar, Harp – all string instruments (sound from vibrating strings).
Flute – a wind instrument (sound from vibrating air column).

Why the other options are wrong:
A–D are all string instruments, so none of them is the odd one.

Answer: E

Approach: Number classification: square of a prime vs square of a composite.

Solution:
121 = 11², 169 = 13², 289 = 17², 361 = 19² → squares of primes.
441 = 21² and 21 = 3 × 7 is composite.

Cetking shortcut: Know squares 11²–25² by heart; check the bases for primality.

Answer: E

Approach: Digit-to-symbol substitution followed by reversal.

Solution:
Number: 9 0 3 6 4 1 2
Code each digit: 9 → ?, 0 → +, 3 → $, 6 → *, 4 → %, 1 → @, 2 → #
Coded string: ? + $ * % @ #
Reverse it: # @ % * $ + ?

Why the other options are wrong:
B – the coded string without reversing.
C – last two symbols swapped (? +).
D – $ and * swapped.
E – + and $ swapped.

Cetking shortcut: Reversing the code = coding the number read backwards: 2146309 → # @ % * $ + ?.

Answer: A

Approach: Number classification: perfect numbers.

Solution:
6 = 1 + 2 + 3; 28 = 1 + 2 + 4 + 7 + 14 → perfect.
496 and 8128 are the next two perfect numbers.
1024 = 2¹⁰; its proper divisors add up to 1023 ≠ 1024 → not perfect.

Cetking shortcut: Even perfect numbers have the form 2^p−1(2^p − 1): 6, 28, 496, 8128 — memorise them.

Answer: E

Approach: Digit pattern within each number.

Solution:
135 → 1, 3, 5 (+2, +2); 357 → 3, 5, 7; 579 → 5, 7, 9.
791 → 7, 9, 1: after 9 the next should be 11, so the pattern breaks.
Second check: digit sums 9, 15, 21 are multiples of 3; 7 + 9 + 1 = 17 is not.

Why the other options are wrong:
A, B, C, D – all follow the +2 digit step and are divisible by 3.

Answer: E

Approach: Letter-shift code: each consonant moves one letter back, each vowel moves one letter forward (as in SUN → RVM).

Solution:
SUN → RVM: S − 1 = R, U + 1 = V, N − 1 = M.
STAR: S − 1 = R, T − 1 = S, A + 1 = B, R − 1 = Q.
Code = R S B Q.

Why the other options are wrong:
B RSUQ – A is shifted to U instead of B.
C RUSB – T becomes U and the letters are out of order.
D RTAQ – T and A are left unchanged.
E RSBP – R becomes P (−2) instead of Q.

Cetking shortcut: First letter must be R and last must be Q; A and B both fit, but the vowel A must go forward to B, so A is the answer.

Answer: A

Approach: Uniform +1 letter shift.

Solution:
PENCIL → QFODJM: every letter +1.
MARKER: M→N, A→B, R→S, K→L, E→F, R→S → NBSLFS.

Why the other options are wrong:
A NBSLSF – E and R codes swapped.
C NBSLTF – R coded as T.
D NBTLSF – R coded as T.
E NBQLSF – R coded as Q.

Answer: B

Approach: Alternating letter shift (+2, −2, +2, …).

Solution:
ENGINE → GLIGPC: E+2=G, N−2=L, G+2=I, I−2=G, N+2=P, E−2=C.
MOTOR: M+2=O, O−2=M, T+2=V, O−2=M, R+2=T → OMVMT.

Why the other options are wrong:
B OVMAT, C OVMVT, D OAVMT – second letter must be O − 2 = M.
E VMAOT – first letter must be M + 2 = O.

Cetking shortcut: Check just the first two letters (O, M): only option A starts OM.

Answer: A

Approach: Numeric code from the sum of letter positions.

Solution:
CHAIR = 3 + 8 + 1 + 9 + 18 = 39 → 39 + 10 = 49 ✓
TABLE = 20 + 1 + 2 + 12 + 5 = 40 → 40 + 10 = 50 ✓
BENCH = 2 + 5 + 14 + 3 + 8 = 32 → 32 + 10 = 42

Cetking shortcut: Both examples are 'sum + 10'; one check is enough to confirm the constant.

Answer: E

Approach: Numeric code from the sum of letter positions.

Solution:
MILK = 13 + 9 + 12 + 11 = 45 → 45 + 2 = 47 ✓
TEA = 20 + 5 + 1 = 26 → 26 + 2 = 28

Answer: C

Approach: Two-generation relation.

Solution:
P is Q's father.
R is P's sister → R is the sister of Q's father.
Father's sister = aunt.

Answer: A

Approach: Pointing-type relation — decode right to left.

Solution:
My father's sister = Aarav's aunt.
Her only son = Aarav's cousin.
Mother of that son = the father's sister herself → aunt.

Why the other options are wrong:
C Cousin – that is the son, not the woman.
A, B, E – no link to sister, mother or niece.

Answer: D

Approach: Pointing-type relation.

Solution:
Rahul is male, so his father's only daughter is Rahul's sister.
The mother of Rahul's sister = Rahul's mother.

Answer: A

Approach: Build a family tree.

Solution:
C is the father of A; A is the brother of B → A and B are siblings.
E is B's daughter; D is E's brother → D is B's son.
A is the brother of D's parent → A is D's uncle (true whether B is father or mother).

Why the other options are wrong:
B Father – D's parent is B, not A.
D Cousin – A is one generation above D.
C, E – no in-law or grandparent link; C is the grandfather.

Answer: A

Approach: Long relation chain — reduce step by step.

Solution:
My mother's husband = Rohan's father.
Father of my father = paternal grandfather.
Only daughter of the grandfather = father's sister (paternal aunt).
Son of the paternal aunt = Rohan's cousin.

Why the other options are wrong:
A Brother – he is not a child of Rohan's parents.
C Uncle – would be grandfather's son.
D Grandfather / E Nephew – wrong generation.

Answer: B

Approach: Block method for a linear arrangement of 7 (positions 1–7, middle = 4).

Solution:
T is at the extreme left → position 1.
Q–P is a 2-book block (P immediately right of Q).
R is immediately next to both S and V, so R is the centre of a 3-book block S–R–V (V on R's right, S on the other side).
Positions 2–7 hold U, the Q–P block and the S–R–V block. Taking U next to T and the Q–P block at the right end gives
T U S R V Q P → position 4 (middle) = R.

Why the other options are wrong:
A P – from T U Q P R V S, which puts S two places away from R, breaking the R–S clue.
B Q, D S, E U – none of these is the centre of a block that touches the middle seat in the intended order.

Answer: C

Approach: Fix definite positions, then place blocks (8 seats, left to right).

Solution:
A is 3rd from left → seat 3.
B is 5th from right → 8 − 5 + 1 = seat 4.
C is immediately right of B → seat 5.
Free seats: 1, 2, 6, 7, 8. D is between F and G → a 3-seat block F–D–G, which only fits in 6–7–8.
H is left of E → H = 1, E = 2.
Seats 6 and 8 are F/G, so 6th from left is F or G; F is not offered → G.

Why the other options are wrong:
A A – seat 3.
B D – seat 7 (centre of the block).
D C – seat 5.
E B – seat 4.

Cetking shortcut: Only a 3-seat gap can hold the F–D–G block; seats 6–8 is the only one.

Answer: C

Approach: Circular arrangement, 6 seats, all facing centre (left = clockwise).

Solution:
Fix B at seat 1; seats numbered 1–6 clockwise.
A is 2nd to the left of B → seat 3.
C is opposite A → seat 6.
D is immediately right of C → seat 5.
F is to the right of A → seat 2.
E takes the last seat → 4.
Opposite of B (seat 1) is seat 4 → E.

Why the other options are wrong:
A A – opposite C.
B B – the person asked about.
C D – opposite F.
E C – opposite A.

Cetking shortcut: Opposite pairs: A–C is given, D and F sit beside them, so the only pair left for B is E.

Answer: D

Approach: Circular arrangement, 8 seats, all facing centre (left = clockwise).

Solution:
Fix Q at seat 1; seats numbered 1–8 clockwise.
P is 2nd to the right of Q → seat 7.
R is opposite Q → seat 5.
V is between P and R → seat 6.
Free seats 2, 3, 4, 8. The only opposite pair among them is 4–8 → W and S.
T is immediately left of U → U = 2, T = 3.
Final (clockwise from Q): Q, U, T, W/S, R, V, P, S/W.
Immediate right of P (seat 7) = seat 6 → V.

Why the other options are wrong:
A Q – 2nd to P's left.
C R – 2nd to P's right.
D S / E T – not adjacent to P on the right.

Answer: B

Approach: Circular arrangement, 8 seats, all facing centre (left = clockwise).

Solution:
Fix Q at seat 1; seats numbered 1–8 clockwise.
P is 2nd to the right of Q → seat 7.
R is opposite Q → seat 5.
V is between P and R → seat 6.
Free seats 2, 3, 4, 8. The only opposite pair among them is 4–8 → W and S.
T is immediately left of U → U = 2, T = 3.
Final (clockwise from Q): Q, U, T, W/S, R, V, P, S/W.
T is at seat 3 → opposite seat 7 → P.

Why the other options are wrong:
A V – seat 6, faces U (seat 2).
B W / D S – they face each other (4–8).
E U – sits next to T.

Answer: C

Approach: Track the facing direction after each turn.

Solution:
Walks South → facing South.
Turns right → facing West.
Turns left → facing South.

Cetking shortcut: One right + one left cancel out, so he faces his original direction, South. Distances are irrelevant.

Answer: B

Approach: Net rotation.

Solution:
+90° (clockwise) − 180° (anticlockwise) + 90° (clockwise) = 0°.
Net rotation 0° → still facing North.

Answer: A

Approach: Resolve each diagonal into components.

Solution:
10 m NE = 10/√2 m North + 10/√2 m East.
10 m SE = 10/√2 m South + 10/√2 m East.
North and South cancel; net = 10√2 m due East.

Answer: A

Approach: Net displacement along each axis.

Solution:
North–South: 5 N − 2 S = 3 km North.
East–West: 3 E − 3 W = 0.
Distance from start = 3 km.

Answer: A

Approach: Opposite directions.

Solution:
South-West was exactly behind her, so she was facing the opposite of South-West.
Opposite of South-West = North-East; she pointed straight ahead, i.e. North-East.

Answer: A

Approach: Compare position difference in the word with position difference in the alphabet.

Solution:
S E P A R A T I O N = positions 1–10; letter values S19 E5 P16 A1 R18 A1 T20 I9 O15 N14.
E(2)–A(6): word gap 4, alphabet gap 5 − 1 = 4 ✓
P(3)–R(5): gap 2, 18 − 16 = 2 ✓
P(3)–T(7): gap 4, 20 − 16 = 4 ✓
R(5)–T(7): gap 2, 20 − 18 = 2 ✓
O(9)–N(10): gap 1, 15 − 14 = 1 ✓
Total = 5 pairs.

Cetking shortcut: For each letter, scan right only as far as the word allows and check both A→Z and Z→A directions.

Answer: E

Approach: Sort and compare position-wise.

Solution:
Original: S A T E L L I T E
Sorted: A E E I L L S T T
Position 5: L = L ✓
Position 6: L = L ✓
Position 8: T = T ✓
All other positions differ → 3 letters unchanged.

Why the other options are wrong:
E 0 – overlooks positions 5, 6 and 8.
A 2 / B 1 / D 4 – miscounts.

Answer: C

Approach: Sort, pick positions, form a word.

Solution:
FUTURISTIC letters sorted: C F I I R S T T U U.
3rd = I, 5th = R, 6th = S, 8th = T.
Meaningful word from I, R, S, T = STIR.
3rd letter of STIR = I.

Answer: A

Approach: Two-rule letter change, then alphabetical sort.

Solution:
E D U C A T I O N
Vowels +1: E→F, U→V, A→B, I→J, O→P
Consonants −1: D→C, C→B, T→S, N→M
New letters: F C V B B S J P M
Sorted: B B C F J M P S V → 4th from left = F.

Answer: E

Approach: Two-rule letter change, then gap counting.

Solution:
C O N G R A T U L A T E
Consonants +2: C→E, N→P, G→I, R→T, T→V, L→N
Vowels → next vowel: O→U, A→E, U→A, E→I
New word: E U P I T E V A N E V I
4th letter = I, 9th letter = N.
Letters between I and N: J, K, L, M → 4.

Cetking shortcut: Only positions 4 (G) and 9 (L) matter: G + 2 = I, L + 2 = N; N − I − 1 = 14 − 9 − 1 = 4.

Answer: D

Approach: Element-by-element scan of the series.

Solution:
Vowels in order: U(5), I(10), O(12), U(14), E(15), A(23), O(27).
Followed by a digit: U 8, I 6, E 1, A 9, O 2.
O(12) → Q and U(14) → E do not count.
Total = 5.

Cetking shortcut: Scan the digits instead: look at the element just before each digit — 5, 8, 6, 1, 4, 9, 2, 7, 3 → vowels before 8, 6, 1, 9, 2.

Answer: E

Approach: Delete, then count.

Solution:
Vowels up to Q: U(5), I(10), O(12) are removed.
New series from left: D 5 P K 8 Z M C 6 Q …
10th from left = Q.

Cetking shortcut: Original position 13 (Q) minus 3 vowels before it = 10.

Answer: D

Approach: Position arithmetic.

Solution:
Positions: 1 D, 2 5, 3 P, 4 K, 5 U, 6 8, 7 Z, 8 M, 9 C, 10 I, 11 6, 12 O, 13 Q, 14 U, 15 E, 16 1, 17 T, 18 N, 19 R, 20 4, 21 G, 22 B, 23 A, 24 9, 25 F, 26 S, 27 O, 28 2, 29 H, 30 J, 31 V, 32 7, 33 Y, 34 X, 35 3 (35 elements).
13th from right = 35 − 13 + 1 = 23rd from left = A.
7th to the right of it = 23 + 7 = 30th from left = J.

Why the other options are wrong:
E 2 – result of starting at G (21st) by miscounting from the right.
B Q, C 6, D E – lie to the left, not the right.

Cetking shortcut: 7th to the right of 13th from right = (13 − 7) = 6th from right = J.

Answer: A

Approach: Scan for the pattern consonant–CONSONANT–vowel.

Solution:
P K U → K ✓
M C I → C ✓
G B A → B ✓
F S O → S ✓
No other consonant is followed by a vowel with a consonant before it (Q in O Q U has a vowel before it).
Total = 4.

Cetking shortcut: Start from each vowel and look at the two elements to its left — both must be consonants: U(5), I(10), A(23), O(27) qualify.

Answer: C

Approach: Filter and add.

Solution:
Digits: 5, 8, 6, 1, 4, 9, 2, 7, 3.
Even digits: 8, 6, 4, 2.
Sum = 8 + 6 + 4 + 2 = 20.

Answer: E

Approach: Rank formula.

Solution:
Total = 8 + 15 − 1 = 22 (Amar is counted twice).

Answer: D