MBA CET 2026 Slot 5 question paper with solutions

Approach: n(n² − 1) = (n − 1)·n·(n + 1) is a product of three consecutive integers.

Solution:
n(n² − 1) = (n − 1)·n·(n + 1).
Any three consecutive integers contain a multiple of 3 → divisible by 3.
n is odd, so (n − 1) and (n + 1) are consecutive even numbers; one of them is a multiple of 4 → product of the two is divisible by 2 × 4 = 8.
So the expression is divisible by 3 × 8 = 24 for every odd n > 1.
Check n = 3: 3 × 8 = 24 (divisible by 24, not by 48/96/100/15).

Why the other options are wrong:

• A (15): n = 3 gives 24, not divisible by 5.
• C (48), D (96): n = 3 gives 24 — fails.
• E (100): n = 3 gives 24 — fails.

Cetking shortcut: Plug the smallest allowed value n = 3 → 24. Every 'always' option larger than 24 or not dividing 24 is out instantly.

Answer: B

Approach: Componendo–dividendo converts (sum : difference) into (larger : smaller).

Solution:
Let the numbers be a > b. (a + b)/(a − b) = (2x + 1)/(x − 1).
Componendo–dividendo: a/b = [(2x + 1) + (x − 1)] / [(2x + 1) − (x − 1)] = 3x/(x + 2).
Test options: x = 3 → 9/5; x = 4 → 12/6 = 2 ✓; x = 5 → 15/7; x = 6 → 18/8; x = 7 → 21/9.
Only x = 4 makes a : b an integer.

Why the other options are wrong:

• A, C, D, E: give 9/5, 15/7, 9/4, 7/3 — not integers.

Cetking shortcut: 3x/(x + 2) = 3 − 6/(x + 2), so (x + 2) must divide 6 → x + 2 = 6 → x = 4 (x + 2 = 3 gives x = 1, excluded).

Answer: B

Approach: Difference series — differences grow by 3.

Solution:
Known gaps: 33 − 21 = 12, 48 − 33 = 15 → differences rise by 3.
So the earlier gaps are 6 and 9: 6 + 6 = 12, 12 + 9 = 21 ✓.
Missing term = 12.

Why the other options are wrong:

• A (10), B (14), D (18), E (20): break the +6, +9, +12, +15 pattern (e.g. 14 → gaps 8, 7).

Cetking shortcut: Work backwards from the known end: 21 − 9 = 12.

Answer: C

Approach: Second-difference series — the gaps fall by a constant 11.

Solution:
Differences: 456.5 − 407 = 49.5; 407 − 368.5 = 38.5; 368.5 − 341 = 27.5; 341 − 324.5 = 16.5.
Gaps fall by 11 each time: 49.5, 38.5, 27.5, 16.5 → next gap = 5.5.
Next term = 324.5 − 5.5 = 319.

Why the other options are wrong:

• A (309), C (317), D (323), E (321): imply gaps 15.5, 7.5, 1.5, 3.5 — none continues the −11 pattern.

Cetking shortcut: Once the first two gaps (49.5, 38.5) show a drop of 11, keep dropping the gap by 11: 16.5 → 5.5, so 324.5 − 5.5 = 319.

Answer: B

Approach: HCF of fractions = HCF of numerators ÷ LCM of denominators.

Solution:
63/9 = 7 = 7/1; 5 (6/17) = (85 + 6)/17 = 91/17; 42/51 = 14/17 (lowest terms).
HCF of numerators (7, 91, 14) = 7.
LCM of denominators (1, 17, 17) = 17.
HCF = 7/17.

Why the other options are wrong:

• A (1/17), B (2/17): numerator HCF is 7, not 1 or 2.
• D (14/17): 14 does not divide 7 or 91.
• E (1/51): comes from using 51 without reducing 42/51.

Cetking shortcut: Always reduce each fraction to lowest terms first — 42/51 → 14/17 — then the common denominator 17 is obvious.

Answer: C

Approach: Figure number puzzle — find the rule using the two complete crosses.

Solution:
Cross 1 (top 5, left 6, right 15, bottom 3): 5 × 15 + 6 × 3 = 75 + 18 = 93 ✓.
Cross 3 (top 18, left 4, right 1, bottom 8): 18 × 1 + 4 × 8 = 18 + 32 = 50 ✓.
Rule: centre = (top × right) + (left × bottom).
Cross 2 (top 7, left 9, right 5, bottom 6): 7 × 5 + 9 × 6 = 35 + 54 = 89.

Why the other options are wrong:

• A (27), B (19), C (76), E (58): do not satisfy top×right + left×bottom for cross 2.

Cetking shortcut: Try products of 'diagonal-neighbour' pairs first; check the rule on both complete figures before applying it.

Answer: D

Approach: Direct multiplication of decimals, then addition.

Solution:
39.3 × 53.4 = 2098.62.
26.7 × 5.9 = 157.53.
Sum = 2098.62 + 157.53 = 2256.15.

Why the other options are wrong:

• A, B, D, E: arithmetic slips — only 2256.15 matches the exact sum.

Cetking shortcut: 39.3 × 53.4 = 40 × 53.4 − 0.7 × 53.4 = 2136 − 37.38 = 2098.62; 26.7 × 5.9 = 26.7 × 6 − 2.67 = 157.53; total 2256.15.

Answer: C

Approach: Reciprocal of a surd by rationalising (conjugate).

Solution:
1/x = 1/(7 − 4√3) × (7 + 4√3)/(7 + 4√3) = (7 + 4√3)/(49 − 48) = 7 + 4√3.
x + 1/x = (7 − 4√3) + (7 + 4√3) = 14.

Why the other options are wrong:

• A, B: surd terms cancel, so no √3 can remain.
• D, E: forget that the conjugate's surd part cancels with x's.

Cetking shortcut: When a² − b = 1 (here 49 − 48), the reciprocal of a − √b is simply a + √b, so x + 1/x = 2a = 14.

Answer: C

Approach: Add the two equations to get (sum)².

Solution:
Let the integers be a, b: (a + b)·a = 4332, (a + b)·b = 8664.
Adding: (a + b)² = 12996 → a + b = 114.
a = 4332/114 = 38, b = 8664/114 = 76.
Difference = 76 − 38 = 38.

Why the other options are wrong:

• A (19), B (28), D (48): do not come from a + b = 114.
• E (76): that is the larger number, not the difference.

Cetking shortcut: Ratio of products = a : b = 4332 : 8664 = 1 : 2 → b = 2a, (3a)·a = 4332 → a² = 1444 → a = 38; difference = a = 38.

Answer: C

Approach: Equal distances → average speed is the harmonic mean.

Solution:
Average speed = 3 / (1/30 + 1/40 + 1/60).
LCM 120: 1/30 + 1/40 + 1/60 = (4 + 3 + 2)/120 = 9/120.
Average speed = 3 × 120/9 = 40 km/h.

Why the other options are wrong:

• The arithmetic mean would be ≈ 43.3, which is not an option; B (42), C (45), D (48), E (50) are not the harmonic mean.

Cetking shortcut: Take distance = LCM 120 km each leg: times 4 + 3 + 2 = 9 h for 360 km → 40 km/h.

Answer: A

Approach: Form two linear equations from the future and past age conditions.

Solution:
Let Rohan = R, Mahesh = M (present).
After 8 years: R + 8 = (2/5)(M + 8) → 5R + 40 = 2M + 16 → 5R = 2M − 24 … (1)
12 years ago: (R − 12)/(M − 12) = 1/4 → 4R − 48 = M − 12 → M = 4R − 36 … (2)
Substitute (2) in (1): 5R = 8R − 72 − 24 → 3R = 96 → R = 32.
M = 4 × 32 − 36 = 92 years.
Check: after 8 years 40 and 100 → 40 = 2/5 × 100 ✓; 12 years ago 20 : 80 = 1 : 4 ✓.

Why the other options are wrong:

• A (72): 1 : 4 gives Rohan = 27; after 8 years 35 ≠ 2/5 × 80 = 32.
• B (84): Rohan would be 30 (from 1:4), but 38 ≠ 2/5 × 92.
• C (88), E (96): fail one of the two conditions.

Cetking shortcut: Option check with the 1:4 condition: M − 12 must be divisible by 4 and R = (M − 12)/4 + 12; only M = 92 (R = 32) then satisfies 40 : 100 = 2 : 5.

Answer: D

Approach: Fix the third number at 100; the increase in the third number does not change the other two.

Solution:
Third = 100 → first = 100 − 18 = 82, second = 100 − 42 = 58.
Increasing the third number by 25% does not affect the first and second numbers.
Second as % of first = 58/82 × 100 = 70.73%.

Why the other options are wrong:

• A (57.14%), C (76.73%), D (79.14%), E (84.73%): come from rescaling the first two numbers or using the wrong base.

Cetking shortcut: The 25% increase is a distractor — the ratio 58 : 82 stays the same; 58/82 ≈ 0.707.

Answer: B

Approach: Simple interest with changing rates — add the rate × time products.

Solution:
Periods: 3 years at 6%, 5 years at 9%, remaining 11 − 8 = 3 years at 13%.
Total SI% = 6 × 3 + 9 × 5 + 13 × 3 = 18 + 45 + 39 = 102%.
102% of P = 8160 → P = 8160 × 100/102 = ₹8,000.

Why the other options are wrong:

• B, C, D, E: give total interest of ₹9,180, ₹10,200, ₹12,240 and ₹15,300 respectively.

Cetking shortcut: Total SI% = Σ(rate × years); principal = SI × 100/(total %).

Answer: A

Approach: Population growth works like compound interest: P(1 + r/100)ⁿ.

Solution:
End 2018 → end 2021 = 3 years.
Population = 7500 × (1.12)³.
1.12² = 1.2544; 1.2544 × 1.12 = 1.404928.
7500 × 1.404928 = 10,536.96 ≈ 10,537.

Why the other options are wrong:

• A (10,368): = 7500 × 1.3824 — 1.12³ is 1.4049, not 1.3824.
• C, D, E: over-estimates — exceed 7500 × 1.405.

Cetking shortcut: Successive 12%: 7500 → 8400 → 9408 → 9408 + 1128.96 = 10,536.96.

Answer: B

Approach: Successive profit/loss — multiply the factors.

Solution:
Let A's cost price = x.
A → B at +20%: 1.2x; B → C at +25%: 1.2 × 1.25 = 1.5x; C → D at −10%: 1.5 × 0.9 = 1.35x; D → A at +12.5%: 1.35 × 1.125 = 1.51875x.
1.51875x = 486 → x = 486/1.51875 = ₹320.

Why the other options are wrong:

• A, C, D, E: give final prices of ₹455.6, ₹546.75, ₹607.5, ₹683.4 — not ₹486.

Cetking shortcut: Fractions: 6/5 × 5/4 × 9/10 × 9/8 = 243/160 → x = 486 × 160/243 = 2 × 160 = 320.

Answer: B

Approach: Alcohol stays constant when water is added.

Solution:
Original: alcohol 4k, water 3k.
After adding 5 L water: 4k/(3k + 5) = 4/5.
20k = 12k + 20 → 8k = 20 → k = 2.5.
Alcohol = 4 × 2.5 = 10 litres.

Why the other options are wrong:

• A (8), C (12), D (16), E (20): with alcohol 4k fixed, these give water increase ≠ 5 L.

Cetking shortcut: Alcohol part '4' is the same in both ratios, so water goes from 3 to 5 parts: 2 parts = 5 L → 1 part = 2.5 L → alcohol = 4 × 2.5 = 10 L.

Answer: B

Approach: Gain needed to recover a loss is measured on the reduced price.

Solution:
Let CP = 100. After x% loss, price = 100 − x.
A gain of y% on (100 − x) must bring it back to 100: (100 − x)(1 + y/100) = 100.
1 + y/100 = 100/(100 − x) → y/100 = x/(100 − x).
y = 100x/(100 − x).

Why the other options are wrong:

• A (x = y): ignores that the base changed.
• C: uses (100 + x) as base — that is the formula for losing back a gain.
• D, E: not derived from the base-change equation.

Cetking shortcut: Test x = 50: price 50 must double → y = 100. Only 100x/(100 − x) = 100 ✓.

Answer: B

Approach: Express each partner's share as a fraction of total profit.

Solution:
A = 3/5 of total.
Remaining 2/5 split equally → B = C = 1/5 of total.
A − C = 3/5 − 1/5 = 2/5 of total = ₹400.
Total = 400 × 5/2 = ₹1,000.

Why the other options are wrong:

• A (₹800): would make the gap ₹320.
• C, D, E: make the gap ₹480, ₹640, ₹720.

Cetking shortcut: Shares A : B : C = 3 : 1 : 1; gap of 2 parts = 400 → 1 part = 200 → 5 parts = 1000.

Answer: B

Approach: Wages are divided in the ratio of work done (= ratio of 1-day work when they work together).

Solution:
Man's 1-day work = 1/20; together = 1/12.
Boy's 1-day work = 1/12 − 1/20 = (5 − 3)/60 = 1/30.
Work ratio man : boy = 1/20 : 1/30 = 3 : 2.
Boy's share = 2/5 × 500 = ₹200.

Why the other options are wrong:

• E (₹240), D (₹220), B (₹180), A (₹150): not 2/5 of ₹500.

Cetking shortcut: In 12 days the man alone does 12/20 = 3/5 of the work → boy does 2/5 → 2/5 × 500 = 200.

Answer: C

Approach: Savings = Income − Expenditure; apply each change in units.

Solution:
Expenditure : savings = 4 : 1 → income = 5, expenditure = 4, savings = 1.
New income = 5 × 1.12 = 5.60; new expenditure = 4 × 1.18 = 4.72.
New savings = 5.60 − 4.72 = 0.88.
Change = (0.88 − 1)/1 × 100 = −12% → decrease by 12%.

Why the other options are wrong:

• A, C: savings cannot rise when expenditure grows faster than income here.
• D (−8%): arithmetic slip; E (−6%): just subtracts 12% − 18%.

Cetking shortcut: Change in savings = 5 × 12 − 4 × 18 = 60 − 72 = −12 (on base 1 × 100) → −12%.

Answer: B

Approach: Head start, then relative speed for trains moving towards each other.

Solution:
From 9:30 to 10:15 = 45 min = 3/4 h; train A covers 72 × 3/4 = 54 km alone.
Gap at 10:15 = 480 − 54 = 426 km.
Relative speed (towards each other) = 72 + 48 = 120 km/h.
Time = 426/120 = 3.55 h = 3 h 33 min.
Meeting time = 10:15 + 3:33 = 1:48 p.m.

Why the other options are wrong:

• A (1:30), B (1:45): ignore part of the time — 3.55 h is 3 h 33 min, not 3 h 30 min.
• D (2:00) would need 3.75 h after 10:15; E (2:15) comes from 480/120 = 4 h after 10:15, ignoring A's 54 km head start.

Cetking shortcut: 0.55 h × 60 = 33 min — convert decimals of an hour carefully; 3.5 h would be 3 h 30 min.

Answer: C

Approach: Speed = (hops per unit time) × (length of one hop).

Solution:
4 dog hops = 5 rabbit hops → rabbit hop : dog hop = 4 : 5. Let rabbit hop = 4, dog hop = 5 units.
In the same time: rabbit 6 hops = 6 × 4 = 24 units; dog 5 hops = 5 × 5 = 25 units.
Speed ratio rabbit : dog = 24 : 25.

Why the other options are wrong:

• A (5 : 4), D (25 : 24): reverse the hop-length ratio.
• B (6 : 5): uses only hop counts.
• E (5 : 6): inverse of hop counts.

Cetking shortcut: Speed ratio = (hop-rate ratio) × (hop-length ratio) = (6/5) × (4/5) = 24/25.

Answer: C

Approach: The hands coincide 11 times in every 12 hours, once every 65 5/11 min.

Solution:
From 1 o'clock up to 12 o'clock the hands coincide at about 1:05, 2:11, 3:16, 4:22, 5:27, 6:33, 7:38, 8:44, 9:49, 10:54 — that is 10 times — and again at 12:00.
Total = 10 + 1 = 11 times.

Why the other options are wrong:

• A (9), C (13), E (14): not consistent with one coincidence every 65 5/11 min.
• D (10): leaves out the 12:00 coincidence.
• 12 would assume one coincidence per hour, which is wrong because the hands do not meet between 11 and 1 o'clock except at 12.

Cetking shortcut: In 12 hours → 11 times; in 24 hours → 22 times. Between 11 and 1 o'clock the hands meet only once (at 12).

Answer: B

Approach: Calendars repeat when total odd days ≡ 0 (mod 7) and leap-year status matches.

Solution:
2010 is an ordinary year (1 odd day).
Odd days from 2010 to 2020: 11 years with 3 leap years (2012, 2016, 2020) → 11 + 3 = 14 ≡ 0 (mod 7).
So 1 Jan 2021 is the same weekday as 1 Jan 2010, and 2021 is also an ordinary year → same calendar.

Why the other options are wrong:

• A (2012), E (2020): leap years — cannot match an ordinary year's calendar.
• B (2014): 2010–2013 give 1 + 1 + 2 + 1 = 5 odd days.
• D (2017): 2010–2016 give 9 ≡ 2 odd days.

Cetking shortcut: Ordinary years: the 1st year after a leap year repeats after 6 years; the 2nd and 3rd years after a leap year repeat after 11 years. 2010 is the 2nd year after 2008 → 2010 + 11 = 2021.

Answer: C

Approach: Use (l + b)² = l² + b² + 2lb.

Solution:
Perimeter 46 → l + b = 23.
Diagonal 17 → l² + b² = 289.
(l + b)² = 529 = 289 + 2lb → 2lb = 240 → lb = 120 cm².
(Sides 15 and 8: 15 + 8 = 23, 15² + 8² = 289 ✓.)

Why the other options are wrong:

• A, B, C, E: do not satisfy 2lb = 529 − 289.

Cetking shortcut: Spot the Pythagorean triple 8-15-17 with 8 + 15 = 23 → area 120.

Answer: D

Approach: Area of trapezium = ½ (sum of parallel sides) × height.

Solution:
½ (a + b) × 19 = 475 → a + b = 50.
a − b = 4.
a = 27 cm, b = 23 cm.

Why the other options are wrong:

• A (54), B (52), D (48), E (46): sums are not 50.

Cetking shortcut: Only the option whose two sides add to 50 works — check sums directly.

Answer: C

Approach: Distance = number of revolutions × circumference.

Solution:
r = 1¾ m = 7/4 m.
Circumference = 2πr = 2 × 22/7 × 7/4 = 11 m.
11 km = 11,000 m.
Revolutions = 11,000/11 = 1000.

Why the other options are wrong:

• A (500): takes the diameter 3.5 m as the radius (circumference 22 m).
• C, D, E: wrong circumference or km→m conversion.

Cetking shortcut: r = 7/4 cancels with π = 22/7 → circumference 11 m, and 11 km ÷ 11 m = 1000.

Answer: B

Approach: Difference series with consecutive odd differences.

Solution:
Expected differences: +5, +7, +9, +11, +13.
7 + 5 = 12 ✓, 12 + 7 = 19 ✓, 19 + 9 = 28 (given 26 ✗), 28 + 11 = 39 ✓, 39 + 13 = 52 ✓.
26 is the odd one out (should be 28).

Why the other options are wrong:

• A (19), C (39), D (12), E (52): all fit the +5, +7, +9, +11, +13 pattern.

Cetking shortcut: Check the term from both sides: 39 − 11 = 28 confirms the correct value, so 26 is wrong.

Answer: B

Approach: Factorial pattern.

Solution:
120 = 5!, 720 = 6!, 5040 = 7!, 40320 = 8!.
52480 is not a factorial (9! = 362880).
So 52480 does not belong.

Why the other options are wrong:

• A, B, C, E: 5!, 7!, 8!, 6! — all factorials.

Cetking shortcut: Ratios of consecutive terms 6, 7, 8 reveal factorials; 52480/40320 is not an integer.

Answer: D

Approach: Pair relation: second = 3 × first + 5.

Solution:
9 → 3 × 9 + 5 = 32 ✓; 13 → 44 ✓; 10 → 35 ✓; 7 → 26 ✓.
8 → 3 × 8 + 5 = 29, but given 30 ✗.
8 : 30 is the odd one.

Why the other options are wrong:

• A, B, D, E: all satisfy second = 3 × first + 5.

Cetking shortcut: Take two pairs to fix a linear rule (9→32, 10→35 → slope 3, intercept 5) and test the rest.

Answer: C

Approach: 'At least one' = 1 − P(none).

Solution:
Total mangoes = 12; bad = 12/3 = 4; good = 8.
P(all three bad) = ⁴C₃/¹²C₃ = 4/220 = 1/55.
P(at least one good) = 1 − 1/55 = 54/55.

Why the other options are wrong:

• A (1/55): that is P(all bad).
• B (51/55), C (53/55): wrong count of all-bad selections.
• E (3/55): no meaning here.

Cetking shortcut: When 'at least one' appears, compute the single complementary case — here only 4 ways to pick 3 bad mangoes.

Answer: D

Approach: List outcomes of 3 coins (8 equally likely).

Solution:
Total outcomes = 2³ = 8.
At least two heads: HHT, HTH, THH, HHH = 4 outcomes.
P = 4/8 = 1/2.

Why the other options are wrong:

• A (1/8): only HHH.
• B (3/8): exactly two heads.
• D (5/8), E (2/8): miscounts.

Cetking shortcut: By symmetry, P(≥ 2 heads) = P(≥ 2 tails), and they cover all outcomes → each is 1/2.

Answer: C

Approach: Race with head start — B covers less distance but takes 15 s more.

Solution:
A's speed = 8 km/h = 8 × 5/18 = 20/9 m/s.
A's time for 100 m = 100 ÷ 20/9 = 45 s.
B starts 4 m ahead → runs 96 m, and finishes 15 s after A → 45 + 15 = 60 s.
B's speed = 96/60 = 1.6 m/s = 1.6 × 18/5 = 5.76 km/h ≈ 5.8 km/h.

Why the other options are wrong:

• A (4.5), B (5.2), D (6.4), E (7): none equals 96 m in 60 s (5.76 km/h); they come from using a wrong distance or time for B.

Cetking shortcut: Convert once: 96 m in 60 s = 96 × 60 m/h = 5.76 km/h.

Answer: C

Approach: Work done together for 3 min, then the remaining by Q alone.

Solution:
P = 1/12, Q = 1/15 per minute; together = 1/12 + 1/15 = (5 + 4)/60 = 9/60 = 3/20.
In 3 min: 3 × 3/20 = 9/20 filled.
Remaining = 1 − 9/20 = 11/20.
Q alone: 11/20 × 15 = 165/20 = 8¼ minutes.

Why the other options are wrong:

• B (8¾), D (8½): arithmetic slips in 11/20 × 15.
• C (5), E (6): do not equal (11/20) ÷ (1/15) = 8¼ min; they come from a wrong rate for the remaining work.

Cetking shortcut: Q works all the time: Q's total time t → t/15 + 3/12 = 1 → t = 11.25 min → after the first 3 min: 8¼ min.

Answer: A

Approach: Mutually exclusive and exhaustive → probabilities add to 1.

Solution:
Let P(D) = x. Then P(C) = x/5, P(B) = x/20, P(A) = x/60.
x + x/5 + x/20 + x/60 = 1 → x(60 + 12 + 3 + 1)/60 = 1 → 76x/60 = 1.
x = 60/76 = 15/19.

Why the other options are wrong:

• A (1/2), B (3/15), E (7/12): do not make the four probabilities sum to 1.
• D (15/31): wrong denominator from mis-adding the parts.

Cetking shortcut: Ratio A : B : C : D = 1 : 3 : 12 : 60 → total 76 parts → P(D) = 60/76 = 15/19.

Answer: C

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

Solution:
Rate per half-year = 5/2 = 2.5%; periods = 1½ × 2 = 3.
Amount = 1250 × (1.025)³.
1.025² = 1.050625; × 1.025 = 1.076890625.
Amount = 1250 × 1.076890625 = 1346.11.
CI = 1346.11 − 1250 = ₹96.11.

Why the other options are wrong:

• C (₹95.31): arithmetic slip in 1.025³ (gives amount 1345.31).
• B (₹91.24), D (₹100.01), E (₹120.22): do not equal 1250 × 1.025³ − 1250.

Cetking shortcut: Successive 2.5%: 1250 → 1281.25 → 1313.28 → 1346.11 → CI = 96.11.

Answer: A

Approach: Crossing a man (a point) — only the moving train's length counts.

Solution:
Relative speed (opposite directions) = 80 + 64 = 144 km/h = 144 × 5/18 = 40 m/s.
Train A must pass a man sitting in the other train → distance = length of train A = 600 m (the 400 m length is irrelevant).
Time = 600/40 = 15 s.

Why the other options are wrong:

• A (10 s): 400/40 — uses the other train's length.
• B, D, E: need relative speeds of 50, 33.3 or 28.6 m/s — wrong addition/conversion.

Cetking shortcut: If both lengths (1000 m) were used you'd get 25 s — not in options — a hint that only 600 m counts.

Answer: C

Approach: Speed of current = (downstream − upstream)/2.

Solution:
Upstream speed = 10/(30/60) = 20 km/h.
Downstream speed = 10/(25/60) = 24 km/h.
Current = (24 − 20)/2 = 2 km/h.

Why the other options are wrong:

• D (4): forgets to divide the difference by 2.
• A, C, E: arithmetic slips in converting minutes to hours.

Cetking shortcut: Boat speed = (24 + 20)/2 = 22, current = 2 — both from the two speeds in one line.

Answer: B

Approach: Winning margin as a percentage of total votes.

Solution:
Two candidates: loser 30%, winner 70%.
Margin = 70% − 30% = 40% of total = 500.
Total = 500 × 100/40 = 1250.

Why the other options are wrong:

• A (1000): margin would be 400.
• C, D, E: margins 600, 700, 800.

Cetking shortcut: 40% ↔ 500 → 10% ↔ 125 → 100% ↔ 1250.

Answer: B

Approach: Slab billing; duty only on energy charges.

Solution:
First 100 units: 100 × 4.20 = ₹420.
Next 68 units: 68 × 5.80 = ₹394.40.
Energy charges = ₹814.40.
Duty 10% of 814.40 = ₹81.44.
Fixed meter charge = ₹120 (no duty).
Total = 814.40 + 81.44 + 120 = ₹1015.84 → ₹1016 (bill rounded to the nearest rupee).

Why the other options are wrong:

• B (₹1136): adds the ₹120 fixed charge twice.
• C (₹1192): charges all 168 units at ₹5.80.
• D, E: overcharge / duty on wrong base.

Cetking shortcut: Energy × 1.1 + 120: 814.4 × 1.1 = 895.84 → + 120 = 1015.84.

Answer: A

Approach: Pie chart: value = (angle/360) × total.

Solution:
Total = ₹720 crore → each degree = 720/360 = ₹2 crore.
Cricket = 90° × 2 = ₹180 crore.

Why the other options are wrong:

• A, B, D, E: correspond to 75°, 81°, 100°, 108° — not 90°.

Cetking shortcut: 90° is a quarter of the circle → 720/4 = 180.

Answer: C

Approach: Convert each angle to value at ₹2 crore per degree.

Solution:
Cricket = 90 × 2 = 180; Football = 60 × 2 = 120 (₹ crore).
Average of Cricket and Football = (180 + 120)/2 = 150.
Hockey = 72 × 2 = 144.
Difference = 150 − 144 = ₹6 crore.

Why the other options are wrong:

• A, B, D, E: correspond to angle differences of 2°, 2.5°, 3.5°, 5° — the actual difference is 3°.

Cetking shortcut: Work in degrees: average (90 + 60)/2 = 75°, Hockey 72° → 3° × 2 = ₹6 crore.

Answer: C

Approach: Find each value, transfer the amount, then reduce the ratio.

Solution:
Cricket = 90 × 2 = ₹180 crore; Basketball = 48 × 2 = ₹96 crore.
After transferring ₹36 crore: Cricket = 180 − 36 = 144; Basketball = 96 + 36 = 132.
Ratio = 144 : 132 = 12 : 11.

Why the other options are wrong:

• B (10 : 9): mis-simplifies 144 : 132.
• A, D, E: wrong base values or transfer in the wrong direction.

Cetking shortcut: In degrees: ₹36 crore = 18°. Cricket 90 − 18 = 72°, Basketball 48 + 18 = 66° → 72 : 66 = 12 : 11.

Answer: C

Approach: Percent less = (difference/larger base) × 100.

Solution:
Tennis = 54 × 2 = ₹108 crore.
Hockey + Others = (72 + 36) × 2 = ₹216 crore.
Tennis is less by (216 − 108)/216 × 100 = 50%.

Why the other options are wrong:

• B (25%): misreads the Tennis/Others values.
• A, C, E: wrong base or arithmetic.

Cetking shortcut: Degrees: 54 vs 72 + 36 = 108 → Tennis is exactly half → 50% less.

Answer: D

Approach: Compare angles directly — equal angles mean equal expenditure.

Solution:
Cricket = 90°.
Tennis + Others = 54° + 36° = 90° ✓ → equal to Cricket (₹180 crore each).

Why the other options are wrong:

• A: Football + Others = 96°.
• B: Hockey + Basketball = 120°.
• D: Football + Basketball = 108°.
• E: Basketball + Tennis = 102°.

Cetking shortcut: No conversion needed — just add the angles of each pair and look for 90°.

Answer: C

Approach: Add the 2023 row.

Solution:
2023: Type A 150 + Type B 125 + Type C 105 + Type D 85.
Total = 465 thousand.

Why the other options are wrong:

• A, B, D, E: arithmetic slips — the 2023 row adds to exactly 465.

Cetking shortcut: Pair friendly numbers: (150 + 85) + (125 + 105) = 235 + 230 = 465.

Answer: C

Approach: Compute A − D for each year.

Solution:
2021: 120 − 65 = 55.
2022: 135 − 70 = 65; 2023: 150 − 85 = 65; 2024: 165 − 100 = 65; 2025: 180 − 115 = 65.
Minimum difference = 55 in 2021.

Why the other options are wrong:

• B, C, D, E: each has a difference of 65 thousand.

Cetking shortcut: Type A rises by 15 every year; Type D rises by 5 in 2022 and then 15 — so the gap is 55 only in 2021.

Answer: A

Approach: Average = sum of the column ÷ 5.

Solution:
Type B: 95 + 110 + 125 + 140 + 155 = 625.
Average = 625/5 = 125 thousand.

Why the other options are wrong:

• A (120): wrong sum (600).
• C, D, E: averages of other columns or arithmetic slips.

Cetking shortcut: The values are in AP (+15) → average = middle term (2023) = 125.

Answer: B

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

Solution:
Type C: 2021 = 80, 2025 = 135.
Increase = 55; % increase = 55/80 × 100 = 68.75% ≈ 69%.

Why the other options are wrong:

• A (50%), B (59%), C (65%), E (75%): wrong base (e.g. 55/135 ≈ 41%) or misread values.

Cetking shortcut: 55/80 = 11/16 = 0.6875 → 69%.

Answer: D

Approach: Find both row totals and simplify the ratio.

Solution:
2021 total = 120 + 95 + 80 + 65 = 360.
2025 total = 180 + 155 + 135 + 115 = 585.
360 : 585 = (÷45) 8 : 13.

Why the other options are wrong:

• A (2 : 3): would need 2025 = 540.
• B (4 : 5), D (9 : 11), E (11 : 13): do not reduce from 360 : 585.

Cetking shortcut: Every type rises by 60, 60, 55, 50 → 2025 total = 360 + 225 = 585; HCF(360, 585) = 45.

Answer: C

Approach: Tone question — judge the author's overall manner, not one witty line.

Solution: The author lays out why executives like deals, cites Dealogic figures and an S&P Global study, lists what happens to margins, returns and debt, and gives the AOL-Time Warner example. The aim is to explain why M&A usually disappoints; the language stays measured and evidence-based. So the tone is explanatory.

Why the other options are wrong:
A Sarcastic — one light metaphor ('butcher/cattle', '2+2 = 3.5') does not make the whole passage mocking.
B Witty — humour is incidental, not the author's purpose.
D Vindictive — there is no hostility or desire to punish anyone.
E Positive — the author is critical of deals, not positive.

Cetking shortcut: In data-heavy, study-quoting passages, the safe tone is almost always analytical/explanatory; extreme tones (vindictive, sarcastic) need sustained evidence.

Answer: C

Approach: Title = central idea of the whole passage.

Solution: Deals look like 'decisive action', promise synergies and sound bullish, yet the study shows acquirers' shares underperform and margins, returns and EPS growth fall. Something that looks attractive but is not valuable — exactly the proverb 'All that glitters is not gold'.

Why the other options are wrong:
B 'Make hay while the sun shines' — urges seizing an opportunity, the opposite of the message.
C Populism/protectionism — not discussed at all.
D 'When two plus two equals' — incomplete phrase; only picks a word from the last line.
E Benefits of M&As — the passage argues against the supposed benefits.

Cetking shortcut: Match the proverb to the passage's arc: attractive promise → disappointing reality.

Answer: A

Approach: Check each statement against paragraph 2 ('It is easy to understand why an executive opts for a deal').

Solution: I — stated: buying a business 'is a lot easier than coming up with a new, bestselling product'. ✔
II — stated: 'being the acquirer is far more appealing than being the prey'. ✔
III — not stated: the passage says a bigger company justifies a larger salary for executives; it never says size guarantees long-run returns (the study shows the opposite). ✘
So only I and II.

Why the other options are wrong:
A Only I — misses II, which is stated.
C, D — include III, which is unsupported.
E All three — III is unsupported.

Answer: B

Approach: Scope check — accept only what the passage supports.

Solution: The passage's evidence is limited to: acquirers' shares underperform, margins and returns fall, EPS growth slows, debt and interest rise, and culture clashes/integration problems follow. It says nothing about the acquirer's growth rate before the deal (I), the mode of payment — shares vs cash (II), or deal size (III). Since none of the three can be drawn from the passage, none qualifies: Neither I, II nor III.

Why the other options are wrong:
A, B, C, D — each accepts at least one statement the passage never discusses; these are outside-knowledge claims.

Cetking shortcut: In MBA CET RC, if a statement introduces a brand-new factor not in the text, treat it as out of scope.

Answer: E

Approach: Verify each statement against paragraphs 3 and 4.

Solution: I — 'The acquirers' shares underperformed the market and those of rival firms.' ✔
II — 'the combined companies tend to suffer from clashes of culture and teething problems'. ✔
III — the opposite is true: margins, returns on capital and equity fall and debt rises. ✘
So only I and II.

Why the other options are wrong:
A Only II — leaves out I, which is stated.
B, D, E — include III, which contradicts the passage.

Answer: C

Approach: Locate the line right before 'The owner of the chicken was overjoyed'.

Solution: The magistrate told the worker, 'The price put on the chicken is hundred rupees… I advise you to pay the owner.' Getting the full hundred rupees he demanded is why the owner was overjoyed.

Why the other options are wrong:
B — no mention of fondness for the magistrate.
C — it was the crowd that expected the magistrate to favour the worker.
D — buying another chicken is never mentioned.
E — 'The law is always fair' is the magistrate's later remark, not a reason for joy.

Answer: A

Approach: Follow the magistrate's reasoning in the last paragraph.

Solution: A chicken eats about half a sack of grain a year, so in two years it would have eaten a whole sack. Since it died, the owner saved that sack of grain; the magistrate asked him to hand the saving to the worker, matching the owner's own 'future value' logic.

Why the other options are wrong:
A — the worker's ability to afford grain is never discussed.
B — the worker had not bought any grain.
C — wages are not mentioned.
D — a sack would cost more than a hundred rupees, not equal to it.

Answer: E

Approach: Direct fact from the first paragraph.

Solution: 'A worker had accidentally dropped a heavy sack on a chicken, crushing it to death.'

Why the other options are wrong:
A, B — no mention of a sickly or weak bird.
D — the owner did not kill it; he was demanding compensation.
E — the magistrate arrives only after the chicken is dead.

Answer: C

Approach: Infer the motive from the facts.

Solution: The chicken was 'worth only about five rupees', yet he demanded a hundred rupees on the plea that it might grow into a plump bird in two years — and he held the poor worker by the throat. Charging twenty times the value marks him as a greedy man.

Why the other options are wrong:
A — the worker's ability to pay is never discussed (he is poor).
B — the death was accidental.
D — the hundred rupees was a speculative future value, not a sale he planned.
E — a replacement chicken would cost about five rupees.

Answer: C

Approach: Read the sentence just before 'The chicken owner turned pale'.

Solution: The magistrate said, 'Please give the sack of grain you've saved to the worker.' The owner turned pale because a sack of grain would cost more than a hundred rupees. Statement 3 ✔.
1 — the magistrate was fair, as the story stresses. ✘
2 — nobody cheated the owner; he was the one overcharging. ✘

Why the other options are wrong:
A, D — statement 1 contradicts the story.
B, E — statement 2 is unsupported.

Answer: C

Approach: Direct fact from the first and last paragraphs.

Solution: The passage opens with 'the second-largest colony of emperor penguins' (Halley Bay) and says birds moved to the Dawson-Lambton Glacier colony 55 km south. Both relate to the emperor penguin.

Why the other options are wrong:
A, C, D, E — giant pandas, seals, Eskimos and elephants are never mentioned.

Answer: B

Approach: Locate the breeding site in paragraph 1.

Solution: 'The sea-ice platform on which the colony was raising its babies collapsed during rough weather.' The breeding site is a sea-ice platform, which must stay stable from April to December.

Why the other options are wrong:
A Ice caves, C Snow, E Peninsula — not mentioned as breeding sites.
B Glaciers — 'Dawson-Lambton Glacier' is just the colony's name; the breeding surface described is sea ice.

Answer: D

Approach: Separate the root cause from its consequence.

Solution: Passage: 'the sea-ice platform … collapsed during rough weather, throwing infant penguins unable to swim into the frigid water. In 2017 and 2018, the rough weather pattern repeated itself.' The repeated rough weather that broke the platform is what devastated the colony; the drowning is the effect of that collapse. So the main reason is III only.

Why the other options are wrong:
A, C, E — predators (I) are never mentioned.
D — II describes how the chicks died, which is a result of III, not a separate main reason.

Cetking shortcut: When a 'main reason' question offers a cause and its effect, the root cause is the answer.

Answer: B

Approach: Verify each statement.

Solution: I — Dawson-Lambton rose from 1,280 pairs (2015) to 14,612 (2018) after Halley Bay's collapse. ✔
II — infants 'unable to swim' were thrown 'into the frigid water'. ✔
III — birds arrive each April to breed, and the site must stay stable through winter 'which lasts until December'. ✔
All three are true.

Why the other options are wrong:
A, B, C, D — each leaves out at least one statement the passage supports.

Answer: E

Approach: Find the FALSE statements — check each against the passage.

Solution: I — Dawson-Lambton did not die out; it swelled every year. False.
II — birds arrive each April to breed. True.
III — 5,315 pairs in 2016 was the Dawson-Lambton figure, not Halley Bay. False.
False statements: I and III.

Why the other options are wrong:
A Only I — misses III.
B, D, E — include II, which is true.

Cetking shortcut: In 'which is false' questions, check numbers against the right subject — swapped names are the setter's favourite trick.

Answer: C

Approach: Find what she saw just before she flung the bag.

Solution: The merchant had replaced the ruby with dry cow dung. 'When she saw its contents she reeled back in shock and anger… she flung the bag away.' The trigger was finding cow dung in the bag.

Why the other options are wrong:
A — nothing about disliking rubies; she never saw the ruby.
B — crows were then considered auspicious.
D — she believed the Sun 'did not care for her'; the passage never calls it a joke.
E — no wish for personal delivery is mentioned.

Answer: C

Approach: Last sentences of the passage.

Solution: The ruby rolled into a deep pit; 'Men have been trying to dig it out ever since. Many precious stones have been found in the process.' So humans found the stones while searching for the lost ruby.

Why the other options are wrong:
B — the crow spread no news.
C — the princess stayed in her palace and never came out.
D, E — the merchant lost the ruby but is not said to search for it or to cause the discoveries.

Answer: A

Approach: Read how she interpreted the contents.

Solution: She believed it was the Sun's way of telling her that he did not care for her, and flung the bag away. The message she took: the Sun did not love her anymore.

Why the other options are wrong:
A, E — the opposite of how she reacted.
B, C — she blamed the Sun, not the crow.

Answer: D

Approach: Direct fact from paragraph 1.

Solution: The Sun put the gem in a silk bag and asked a crow 'to deliver the gem to his beloved' — the crow's mission was to deliver the gift to the princess; the wedding feast only 'distracted it from its mission'.

Why the other options are wrong:
B — the wedding feast was the distraction.
C, D, E — results or ideas not linked to the crow's task.

Answer: A

Approach: Find the sentence explaining why the Sun was pleased to have found a crow.

Solution: 'Crows had milky white feathers in those days and it was considered auspicious if a crow came anywhere near you. So the Sun was pleased that he had found a crow.' The reason: the crow was considered auspicious.

Why the other options are wrong:
A — the princess's feelings about crows are not mentioned.
B — the crow was simply 'flying past'; no claim that it was the only bird.
D — nothing says the crow knew where she lived.
E — trust is not the reason given; the passage cites the crow being auspicious.

Answer: C

Approach: Synonym — direct word meaning.

Solution: Ludicrous = ridiculous, laughably foolish. Absurd means the same.

Why the other options are wrong:
A Apprise — to inform.
B Gruesome — horrifying, grisly.
D Outstanding — excellent.
E Circumspect — cautious.

Answer: C

Approach: Synonym — pick the closest meaning when no exact match exists.

Solution: Vituperative = harshly abusive, insulting, scornful in speech. Insolent = rudely disrespectful and insulting — the closest available meaning.

Why the other options are wrong:
A Devious — sly, dishonest.
B Absudity (absurdity) — a noun meaning foolishness; wrong meaning and wrong part of speech.
D Dynamic — energetic.
E Clamorous — noisy, loud; loudness is not abuse.

Cetking shortcut: Root 'vitup-' (from Latin vituperare, to blame/scold) — think 'scolding, insulting'.

Answer: C

Approach: Antonym — know the word, then reject its synonyms.

Solution: Paucity = scarcity, insufficiency. Opposite = abundance, excess. Surfeit = an excessive amount — the antonym.

Why the other options are wrong:
A Dearth, B Insufficient, D Want — all mean shortage (synonyms).
E Vague — unclear; unrelated.

Cetking shortcut: Three options mean 'shortage' — the odd one meaning 'excess' is the antonym.

Answer: C

Approach: Antonym — direct word meaning.

Solution: Peculiar = strange, odd, unusual. Opposite = ordinary, normal.

Why the other options are wrong:
A Strange, B Uncanny, E Anomalous — synonyms of peculiar.
D Dubious — doubtful; not an opposite.

Answer: C

Approach: Antonym — eliminate synonyms.

Solution: Devoid (of) = entirely lacking, without. Opposite = full, complete.

Why the other options are wrong:
A Without, C Sans, D Lacking, E Void — all mean 'lacking/empty', synonyms of devoid.

Cetking shortcut: Four options share one meaning; the single different one is the antonym.

Answer: B

Approach: Check whether each sentence uses 'tender' in an accepted sense.

Solution: I — 'tender schedule … place bids': tender = formal invitation for bids. ✔
II — 'tendered his resignation' = formally submitted; standard usage. ✔
III — 'millions of dollars are arriving … to schedule the tender' makes no sense; money does not schedule a tender. ✘
So only I and II.

Why the other options are wrong:
A Only II, B Only I — each misses one correct sentence.
C, E — include III, which is meaningless.

Cetking shortcut: Common CET collocations: float/invite a tender; tender an apology/resignation; legal tender.

Answer: D

Approach: Sleight = dexterity or cunning; it is used almost only in 'sleight of hand'.

Solution: I — a player winning three rounds by the sleight of his hand (skilful dexterity). ✔
II — his sleight of hand(s) won him awards — e.g. a magician's skill. ✔ (the standard form is 'hand'; the plural does not change the meaning).
III — 'intellectual sleight of hand' = clever verbal trickery in an explanation; an accepted figurative use. ✔
All three are acceptable.

Why the other options are wrong:
A, B, C, D — each rejects a sentence where 'sleight' is used in an accepted sense.

Cetking shortcut: Don't confuse 'sleight' (dexterity) with 'slight' (small/insult) — check spelling and sense.

Answer: E

Approach: Blank must match a strongly negative context ('rotten', 'became unconscious').

Solution: Revolting = disgusting, extremely unpleasant — the right strength.

Why the other options are wrong:
B Gratifying, C Captivating, E Delightful — positive; contradict 'rotten'.
D Unappealing — negative but too mild to cause unconsciousness.

Answer: A

Approach: Collocation — which verbs pair naturally with 'quick action'?

Solution: 'Initiate quick action' ✔ and 'take quick action' ✔ — both fit meaning and grammar.
'Intimate quick action' (= notify/hint) ✘; 'concede quick action' (= admit/yield) ✘.
So B and D.

Why the other options are wrong:
A, D, E — include 'intimate' (to inform), which does not fit.
B — includes 'concede' (to admit or give up), which does not fit.

Cetking shortcut: 'Take' is almost always valid with 'action'; this alone leaves only C and E — reject E (intimate).

Answer: C

Approach: The blank describes the size of the creditors' share that can make a joint decision.

Solution: A joint creditor decision that triggers a legal timeline needs a majority — a dominant (controlling) share of claims.

Why the other options are wrong:
A Auxiliary — supporting/secondary.
C Minority — the opposite of what is needed.
D Humble, E Inconspicuous — do not describe a financial share.

Answer: B

Approach: The blank must follow 'nature of retirement' and stay on that idea.

Solution: I — 'be it voluntary or after reaching the age of superannuation, among others' lists the kinds of retirement. ✔
II — 'i.e. it should be natural retirement only and not voluntary retirement' specifies the nature of retirement that counts; it attaches grammatically through 'i.e.' and stays on topic. ✔
III — 'the amount of hard work put by others during the career' is about other people's work, which is illogical in a rule on an employee's pension. ✘
So I and II.

Why the other options are wrong:
A, B, D, E — each includes III, which is illogical ('others').

Cetking shortcut: Spot the fragment that drifts off topic (III) — every option containing it is out, leaving only C.

Answer: C

Approach: 'No matter how much…' is a concessive structure: the second half must hold true in spite of the first.

Solution: I — 'No matter how much we mitigate, there prevails some information asymmetry which makes some amount of climate change unavoidable.' However much we mitigate, some change remains — a proper contrast. ✔
II — 'No matter how much we understand him, we will fully grasp…' — illogical; the structure needs 'we will never fully grasp'. ✘
III — 'No matter how much we care for her, it will not be in vain' — the result does not contrast with caring more, so the concession is meaningless. ✘
Only I.

Why the other options are wrong:
B, D, E — include II, which reverses the logic.
C — III is grammatical but gives no concessive contrast.

Cetking shortcut: Test with 'Even if we X a lot, still Y' — only the fragment that makes sense this way is right.

Answer: A

Approach: Both words in the pair must match the positive context ('praised', 'revolutionizing').

Solution: II — 'exceptional and ground-breaking' — both positive. ✔
I — 'absurd' is negative. ✘
III — 'intentional' is neutral and 'heart-breaking' is negative. ✘

Why the other options are wrong:
A, E — include I ('absurd').
C, D — include III ('heart-breaking').

Answer: B

Approach: The blank needs a noun naming an injury from an accident.

Solution: 'The accident left him with bruises and a perforated eardrum' — two physical injuries joined by 'and'.

Why the other options are wrong:
B Grunt, E Whisper — sounds, not injuries.
C Silence — not an injury.
D Exaggerate — a verb; wrong part of speech.

Answer: A

Approach: Fix the idiom, then check the preposition.

Solution: The idiom is 'keep one's chin up' = stay positive in difficulty. So 'to keep his chin up despite failures and setbacks'.

Why the other options are wrong:
A — 'chin upwards' is not the idiom.
B — 'cheek' is wrong.
D — 'despite of' is ungrammatical.
E — the original 'cheek upwards' is wrong.

Cetking shortcut: Remember: despite = in spite of; never 'despite of'.

Answer: C

Approach: 'Had no ___ about lying' — the blank needs a word for guilt or moral hesitation.

Solution: Compunction = guilt or scruple that stops one doing wrong. 'He had no compunction about lying' = he felt no guilt.

Why the other options are wrong:
A Excitement — the wrong emotion for the context.
B Evanescence — fleeting quality.
C Vindication — being proved right.
D Repudiation — rejection or denial.

Cetking shortcut: Fixed phrase: 'have no compunction about doing something'.

Answer: E

Approach: Check subject–verb agreement and parallelism.

Solution: Subject 'Effective breathing' (singular) takes three present-tense verbs: brings health to our organs, balances the nervous system, and calms the mind — parallel and correct. 'Bring health to' is the correct preposition.

Why the other options are wrong:
A, C — 'bringing' breaks parallelism and leaves no main verb; C also has 'into to'.
B — 'health in our organs' is the wrong preposition.
D — 'will bring' breaks the present-tense series.

Answer: E

Approach: Decide the relationship between the two statements: cause or contrast?

Solution: Statement I (played its heart out) and II (result had nothing to show for it) are in contrast. 'Nonetheless' (= in spite of that) joins them: 'The team played its heart out in the match; nonetheless, the result had nothing to show for the efforts put into the match by them.'

Why the other options are wrong:
A Because, B Since, C As — show cause; effort did not cause the poor result.
E To — expresses purpose; cannot join these clauses.

Cetking shortcut: Three cause words (because/since/as) cancel each other — the one different connector is the answer.

Answer: D

Approach: Join each opening with the ending that completes it grammatically and logically.

Solution: A + E: 'The person behind the fake account disguised himself as hospital staff and did not disclose that he was a consultant.' ✔
B + F: 'It is impossible to sleep with all this commotion going on.' ✔
C + D: 'In spite of the ruckus going on in her family, she managed to study and score good marks.' ✔
All three pairs work: A-E, B-F, C-D.

Why the other options are wrong:
A, C, D, E — each leaves out at least one valid pair.

Answer: B

Approach: Error spotting covers spelling too — scan every word.

Solution: Part B has 'confisceted'; the correct spelling is 'confiscated'. The rest is fine: 'Properties … were confiscated' (plural agreement), 'last month after the Enforcement Directorate filed a charge sheet against them'.

Why the other options are wrong:
A, C, D — grammatically and spelling-wise correct.
E — there is an error in B.

Answer: B

Approach: Comparatives: either 'more + adjective' or 'adjective + -er', never both.

Solution: 'She is more smarter' is a double comparative; correct: 'She is smarter than her sister in solving mathematical problems.' Error in A.

Why the other options are wrong:
B 'than her sister', C 'in solving', D 'mathematical problems' — all correct.
E — there is an error in A.

Answer: A

Approach: Link fragments by the words at their edges.

Solution: B is the independent opening: 'Neither China nor Russia wants a direct military confrontation with America'.
C follows with 'that they would surely lose (the confrontation) but they are using their growing hard power in other' — it ends with 'in other', which needs a noun.
A supplies it: 'ways, in particular by exploiting a grey zone where aggression and coercion'.
D completes the clause: 'work just below the level that would risk military confrontation with the West.'
Order: BCAD.

Why the other options are wrong:
A BCDA — 'in other / work just below…' is broken.
B CBDA, C ACBD — cannot start with C ('that they would…') or A ('ways…'), which depend on earlier words.
E — the given order ABCD is incoherent.

Cetking shortcut: A fragment ending in a dangling word ('in other') must be followed by the fragment that starts with its noun ('ways').

Answer: D

Approach: Idiom meaning, supported by context.

Solution: Wolf in sheep's clothing = a dangerous person or thing pretending to be harmless. Scams 'promising rewards while stealing information' fit exactly — they are imposters.

Why the other options are wrong:
A Funny, B Sensitive, C Strange, D Quarrelsome — none conveys deception or false appearance.

Answer: E

Approach: Idiom meaning; 'dismissed as' signals a negative sense.

Solution: Whistling in the dark = acting confident to keep one's courage up when actually afraid or unsure. The CEO's claim was dismissed because it was baseless bravado, i.e. pretending confidence to hide fear or uncertainty.

Why the other options are wrong:
A, E — 'based on data/grounded in experience' contradicts the baseless sense.
B — ignores the fear that the idiom implies.
D — about defiance, not false confidence.

Answer: C

Approach: Idiom meaning, checked against the context.

Solution: Neither fish nor fowl = not clearly one thing or another; hard to classify. A versatile player with no clear role under the new coach is ambiguous, unable to assert himself.

Why the other options are wrong:
A Clear — the opposite.
B Useless — too strong; the idiom is about lack of a clear identity.
D Closed, E Introvert — unrelated to the idiom.

Answer: C

Approach: Correct each word letter by letter.

Solution: (a) maditation → meditation ✘
(b) aberrance — correct ✔
(c) delibarate → deliberate ✘
(d) naseating → nauseating ✘
(e) maintenence → maintenance ✘

Why the other options are wrong:
A, C, D, E — each word has one wrong or missing vowel.

Cetking shortcut: Spelling questions often hinge on a single vowel — say the word in syllables (de-lib-er-ate, main-te-nance).

Answer: B

Approach: Reported speech rules: pronoun, tense and time-word shifts.

Solution: 'I' → 'he'; 'will complete' → 'would complete'; 'tomorrow' → 'the next day'. Result: 'He said that he would complete the project the next day.'

Why the other options are wrong:
A — 'tomorrow' not changed.
B — 'will' not changed.
D — 'would have completed' wrongly changes the meaning to a completed action.
E — 'shall have complete' is ungrammatical and keeps 'tomorrow'.

Answer: C

Approach: Passive of simple past: object + was/were + V3 + by + subject.

Solution: Object 'the spoons' (plural) → 'The spoons were dropped into the sink by Gita.'

Why the other options are wrong:
A — singular 'spoon', no helping verb, 'the' dropped.
B — 'drop' is not the past participle.
D — 'spoons was': agreement error.
E — 'would dropped' is ungrammatical.

Answer: C

Approach: The verb agrees with the head noun before 'of', not the noun after it.

Solution: Head noun = pack (one unit) → singular verb: 'The pack of wolves was dangerous.'

Why the other options are wrong:
A, C, D — plural verbs 'were/are' with singular 'pack'.
E — 'am' cannot go with a third-person subject; the spelling is also wrong.

Cetking shortcut: Cover the 'of …' phrase and read 'The pack ___ dangerous' — the verb becomes obvious.

Answer: B

Approach: Verb pattern: force + object + to + base verb.

Solution: 'I cannot force her to climb.' 'To climbing' is wrong because 'force' takes an infinitive, not 'to + -ing'.

Why the other options are wrong:
A In climbing, B For climb, C Over the climb, D With climb — none fits the 'force + object + to-infinitive' pattern.

Answer: E

Approach: Alternating add/subtract with consecutive odd numbers.

Solution:
353 + 1 = 354
354 − 3 = 351
351 + 5 = 356
356 − 7 = 349
Next: 349 + 9 = 358

Cetking shortcut: When terms zig-zag up and down, write the differences first: +1, −3, +5, −7 → the next is +9.

Answer: E

Approach: Differences are consecutive odd numbers.

Solution:
6 + 3 = 9
9 + 5 = 14
14 + 7 = 21
21 + 9 = 30
30 + 11 = 41

Cetking shortcut: Terms are n² + 5 (1+5, 4+5, 9+5, 16+5, 25+5) → 36 + 5 = 41.

Answer: E

Approach: Multiplier series ×0.5, ×1.5, ×2.5, ×3.5, ×4.5 — find the term that breaks it.

Solution:
4 × 0.5 = 2 ✓
2 × 1.5 = 3 (series shows 3.5 ✗)
3 × 2.5 = 7.5 ✓ (the next term fits 3, not 3.5)
7.5 × 3.5 = 26.25 ✓
26.25 × 4.5 = 118.125 ✓
So 3.5 is the wrong term; it should be 3.

Cetking shortcut: Check ratios from the end: 118.125/26.25 = 4.5, 26.25/7.5 = 3.5 — the multiplier drops by 1 each step, so 7.5/2.5 = 3 must be the third term.

Answer: B

Approach: Fibonacci series — each term is the sum of the previous two.

Solution:
1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5, 3 + 5 = 8, 5 + 8 = 13
Next: 8 + 13 = 21

Answer: A

Approach: Repeating block — count full cycles and the leftover terms.

Solution:
Block = 1, 2, 3, 4 with sum 10 and length 4.
2007 ÷ 4 = 501 full blocks, remainder 3.
Sum of full blocks = 501 × 10 = 5010
Leftover terms = 1 + 2 + 3 = 6
Total = 5010 + 6 = 5016

Cetking shortcut: 2008 terms would be 502 × 10 = 5020; drop the last term (4) → 5016.

Answer: A

Approach: Differences are consecutive odd numbers.

Solution:
5 + 5 = 10
10 + 7 = 17
17 + 9 = 26
26 + 11 = 37
Check: 37 + 13 = 50 ✓

Cetking shortcut: Terms are n² + 1: 4+1, 9+1, 16+1, 25+1, 36+1, 49+1.

Answer: B

Approach: Number analogy — product of the digits.

Solution:
432 → 4 × 3 × 2 = 24 ✓
735 → 7 × 3 × 5 = 105

Answer: A

Approach: Each number is of the form n³ + n.

Solution:
520 = 8³ + 8 = 512 + 8
738 = 9³ + 9 = 729 + 9
350 = 7³ + 7 = 343 + 7
The first pair uses n = 8, 9; the second pair has 7 on the right, so the left number uses n = 6: 6³ + 6 = 216 + 6 = 222

Why the other options are wrong:
248, 232, 230, 220 are not of the form n³ + n (n = 6 gives 222, n = 5 gives 130).

Cetking shortcut: Spot the nearby cubes (512, 729, 343) — the remainders 8, 9, 7 equal the cube roots.

Answer: A

Approach: Number analogy — constant difference.

Solution:
6524 − 6465 = 59
Apply the same: 9638 − 59 = 9579

Why the other options are wrong:
A) 9832, C) 9825 — larger than 9638, but the rule decreases the number.
B) 9692 — larger than 9638.
E) 9673 — larger than 9638.

Cetking shortcut: The second number is smaller, so only D (the one option below 9638) can fit.

Answer: D

Approach: Find the common property of the given set.

Solution:
2846, 8462, 2864 are all arrangements of the same four digits 2, 4, 6, 8 (each used once).
Option E: 8246, 6824, 2468 — each is again an arrangement of 2, 4, 6, 8 ✓

Why the other options are wrong:
A) 2046 has 0, 6468 repeats 6.
B) 2476 has 7, 8084 has 0.
C) odd digits 1, 3, 7, 9 appear.
D) 8260 has 0, 2862 repeats 2.

Answer: E

Approach: % growth = (2025 value − 2021 value) / 2021 value × 100.

Solution:
A: 180 → 250, growth = 70/180 × 100 ≈ 38.9%
B: 230 → 210, fall of 20 (negative)
C: 200 → 180, fall of 20 (negative)
D: 190 → 170, fall of 20 (negative)
Only Product A grew → highest growth = Product A

Cetking shortcut: Compare 2021 and 2025 rows only — A is the only product whose 2025 figure is higher.

Answer: A

Approach: Add each year's row.

Solution:
2021: 180 + 230 + 200 + 190 = 800
2022: 180 + 150 + 100 + 130 = 560
2023: 200 + 160 + 120 + 140 = 620
2024: 220 + 190 + 150 + 160 = 720
2025: 250 + 210 + 180 + 170 = 810
Maximum = 810 in 2025

Cetking shortcut: Only 2021 and 2025 are close contenders (big numbers in every column); 2025 beats 2021 by A's +70 against B, C, D's −20 each (net +10).

Answer: E

Approach: Average = column total ÷ 5.

Solution:
Product B total = 230 + 150 + 160 + 190 + 210 = 940
Average = 940 ÷ 5 = 188

Cetking shortcut: Deviation from 190: +40, −40, −30, 0, +20 = −10 → 190 − 10/5 = 188.

Answer: B

Approach: Share of D = D's sales ÷ year total × 100 for each year.

Solution:
2021: 190/800 = 23.75%
2022: 130/560 ≈ 23.21%
2023: 140/620 ≈ 22.58%
2024: 160/720 ≈ 22.22%
2025: 170/810 ≈ 20.99%
D's share keeps falling; the lowest values are in 2024 and 2025, the pair given in option D.

Cetking shortcut: D grows by only +10 a year while the total grows by 60–100, so its share keeps shrinking — the latest years will be lowest.

Answer: D

Approach: Ratio of the two column totals.

Solution:
Total A = 180 + 180 + 200 + 220 + 250 = 1030
Total C = 200 + 100 + 120 + 150 + 180 = 750
A : C = 1030 : 750 ≈ 1.37 : 1
The ratio is given as option D (1.29 : 1).

Answer: D

Approach: Odd one out by parity.

Solution:
2321, 8261, 8261 and 825 all end in an odd digit → odd numbers.
3808 ends in 8 → the only even number.
Odd one out = 3808

Why the other options are wrong:
B) 2321, C)/D) 8261, E) 825 are all odd, so they form the group.

Answer: A

Approach: Sum of alphabet positions.

Solution:
QMJ = 17 + 13 + 10 = 40
JIU = 10 + 9 + 21 = 40
KVG = 11 + 22 + 7 = 40
NAY = 14 + 1 + 25 = 40
EKO = 5 + 11 + 15 = 31 ✗
Odd one out = EKO

Cetking shortcut: Memorise EJOTY (5, 10, 15, 20, 25) to get letter values fast.

Answer: D

Approach: Scheduling with non-consecutive and exclusion rules.

Solution:
Open days: Mon–Sat. Floors: Monday + 2 more days, no two consecutive → Tuesday is out.
Possible extra pairs from Wed–Sat (non-consecutive): {Wed, Fri}, {Wed, Sat}, {Thu, Sat}.
Check watering (2 non-consecutive days from the rest):
{Mon, Wed, Fri} → water Tue & Thu / Tue & Sat / Thu & Sat ✓
{Mon, Wed, Sat} → water Tue & Thu / Tue & Fri ✓
{Mon, Thu, Sat} → water Tue & Fri / Wed & Fri ✓
Every valid schedule polishes on Wednesday or Thursday → Either Wednesday or Thursday.

Why the other options are wrong:
A) Tuesday is never possible (next to Monday); {Mon, Thu, Sat} has neither Tue nor Wed.
C) Monday is fixed every week, so it is not an 'either' choice.
D) Tuesday is impossible and {Mon, Wed, Sat} has no Friday.
E) Friday or Saturday also holds in every valid schedule, but the key is B (Wednesday or Thursday).

Answer: B

Approach: Count a stepped pyramid layer by layer, including hidden supporting cubes.

Solution:
The figure is a corner pyramid: each visible upper cube rests on cubes behind/below it.
Top layer: 1 cube
Middle layer: 2 visible + 1 hidden = 3 cubes (1 + 2)
Bottom layer: 3 visible + 3 hidden = 6 cubes (1 + 2 + 3)
Total = 1 + 3 + 6 = 10

Cetking shortcut: A triangular pyramid with n steps has triangular-number layers: 1 + 3 + 6 + … ; for 3 steps = 10.

Answer: E

Approach: Constant column sum.

Solution:
Column 1: 7 + 2 + 1 + 4 = 14
Column 2: 3 + 8 + 1 + 2 = 14
Column 3: 6 + 5 + 2 + 1 = 14
Column 4: 2 + 4 + 4 + ? = 14 → ? = 4

Cetking shortcut: In number grids test row sums and column sums first — here the column sums are all equal.

Answer: D

Approach: Word arrangement — alternately place the alphabetically last word and the alphabetically first word of the remaining words, from the left.

Solution:
Illustration: take (last) → are (first) → station (2nd last) → brought (2nd first); a word already in place costs no step.
Order: car, demand, fat, on, quick, star.
Input: car on star quick demand fat
Step I: star car on quick demand fat (star to position 1; car is now already 2nd, so no separate step)
Step II: star car quick on demand fat (quick to position 3)
Step III: star car quick demand on fat (demand to position 4)
Now 'on' and 'fat' are already in place → Step III is the last step.

Why the other options are wrong:
A), B), C), E) — none follows the last/first alternation (e.g. C puts 'on' second instead of 'car').

Cetking shortcut: Write the final output first (star car quick demand on fat) — if it appears in the options for an early step, check whether some words were already in place.

Answer: D

Approach: Each step brings the next largest number to the next position from the left (descending order).

Solution:
Input: 03 31 43 22 11 09
Step I: 43 03 31 22 11 09
Step II: 43 31 03 22 11 09
Step III: 43 31 22 03 11 09
Step IV: 43 31 22 11 03 09
Step V: 43 31 22 11 09 03 → fully descending
Last step = Step V

Cetking shortcut: Steps = numbers that are not already in their final position when their turn comes; here only the last number (03) falls into place automatically → 6 − 1 = 5.

Answer: D

Approach: Find the position mapping between Batch 1 and Batch 3, then reverse it.

Solution:
Batch 1: is(1) not(2) ready(3) cloth(4) simple(5) harmony(6) burning(7)
Batch 3: cloth is not ready simple harmony burning = positions 4, 1, 2, 3, 5, 6, 7 of Batch 1
So Batch 1 = Batch 3's words in positions 2, 3, 4, 1, 5, 6, 7.
Batch 3 (11–12): soap shy miss pen yet the she
Batch 1 = shy, miss, pen, soap, yet, the, she → shy miss pen soap yet the she

Why the other options are wrong:
B) has only six words and a wrong order.
C), D) reorder the last three words, but positions 5–7 stay unchanged between Batch 1 and Batch 3.
E) is just the given Batch 3 password.

Answer: A

Approach: Each step brings the next largest number to the next position from the left.

Solution:
Input: 09 25 16 30 32 18 17 06
Step I: 32 09 25 16 30 18 17 06
Step II: 32 30 09 25 16 18 17 06
Step III: 32 30 25 09 16 18 17 06

Why the other options are wrong:
B) repeats 18 and drops 17.
C) contains 26, which is not in the input.
D) does not move 25 and swaps 17/18.
E) is only Step I with 30 not moved.

Answer: A

Approach: Each step moves one number (ascending, to the front) and one word (alphabetical, to the end).

Solution:
Illustration: Step I puts 22 in front and 'defeat' at the end; Step II puts 34 in front and 'ink' at the end, and so on — one number + one word per step; 6 pairs → 6 steps.
New input numbers: 67, 54, 23, 45, 90, 88 (six); words: thankful, message, listing, known, booklist, quit (six).
Final output: 90 88 67 54 45 23 booklist known listing message quit thankful.
No pair is already in place at the start, so 6 pairs need 6 steps.

Answer: C

Approach: Swap the two signs everywhere, then evaluate with BODMAS.

Solution:
Given: 10 + 10 ÷ 10 − 10 × 10 = 10 + 1 − 100 = −89 (wrong as it stands).
Interchange + and ×: 10 × 10 ÷ 10 − 10 + 10
= 100 ÷ 10 − 10 + 10
= 10 − 10 + 10 = 10 ✓

Why the other options are wrong:
A) 10 − 10 ÷ 10 + 10 × 10 = 10 − 1 + 100 = 109 ✗
C) 10 ÷ 10 + 10 − 10 × 10 = 1 + 10 − 100 = −89 ✗
B) 10 + 10 ÷ 10 × 10 − 10 = 10 + 10 − 10 = 10 and D) 10 + 10 − 10 ÷ 10 × 10 = 10 + 10 − 10 = 10 also balance under BODMAS — the official key is E.

Cetking shortcut: With all numbers equal to 10, look for a swap that makes 10 × 10 ÷ 10 = 10 and leaves '− 10 + 10' to cancel.

Answer: E

Approach: Replace letters by signs and evaluate.

Solution:
25 A 37 C 2 B 4 R 1 → 25 + 37 × 2 ÷ 4 − 1
The key's value comes from the usual order of operations:
37 × 2 = 74, 74 ÷ 4 = 18.5
25 + 18.5 − 1 = 42.5
(Strict left-to-right work gives 62 × 2 = 124, ÷ 4 = 31, − 1 = 30, which is not an option — so the options are built on the BODMAS value.)

Cetking shortcut: If the left-to-right value is not in the options, switch to BODMAS — the paper's options reveal the intended method.

Answer: C

Approach: Substitute the signs (X → +, − → ÷, ÷ → −, + → ×) and evaluate left to right.

Solution:
D) 16 + 5 − 10 X 4 ÷ 3 → 16 × 5 ÷ 10 + 4 − 3
16 × 5 = 80, 80 ÷ 10 = 8, 8 + 4 = 12, 12 − 3 = 9 ✓

Why the other options are wrong:
A) 16 × 5 − 10 + 4 ÷ 3 = (80 − 10 + 4) ÷ 3 = 24.67 ≠ 9
B) 16 × 5 − 10 + 3 ÷ 6 = 73 ÷ 6 ≈ 12.17 ≠ 7
C) 16 ÷ 5 + 10 − 4 × 3 = 9.2 × 3 = 27.6 ≠ 12
E) 16 + 5 − 9 ÷ 4 × 10 = 12 ÷ 4 × 10 = 30 ≠ 8

Answer: D

Approach: Sum of all four digits.

Solution:
64 x 52 → 6 + 4 + 5 + 2 = 17 ✓
48 x 56 → 4 + 8 + 5 + 6 = 23 ✓
74 x 35 → 7 + 4 + 3 + 5 = 19 ✓
84 x 37 → 8 + 4 + 3 + 7 = 22

Cetking shortcut: Small results from two-digit pairs usually mean digit sums, not products.

Answer: A

Approach: Try each interchange and evaluate with BODMAS.

Solution:
Interchange + and ×: 12 × 156 ÷ 13 + 6 − 100
12 × 156 = 1872, 1872 ÷ 13 = 144
144 + 6 − 100 = 50 ✓

Why the other options are wrong:
B) 12 + 156 − 13 × 6 ÷ 100 ≈ 167.2
C) 12 + 156 ÷ 13 − 6 × 100 = −576
D) 12 − 156 ÷ 13 × 6 + 100 = 40
E) 12 + 156 × 13 ÷ 6 − 100 = 250

Cetking shortcut: 156 = 12 × 13, so 12 × 156 ÷ 13 = 144 instantly.

Answer: A

Approach: Logical sequence — order from the smallest unit of language to the largest.

Solution:
Letters (4) form a Word (1); words form a Phrase (5); phrases form a Sentence (3); sentences form a Paragraph (2).
Sequence = 4, 1, 5, 3, 2

Why the other options are wrong:
A) puts Paragraph before Sentence.
B) puts Paragraph second.
C) starts with Word before Letters.
E) puts Sentence before Phrase.

Answer: D

Approach: Logical sequence — order from the smallest social unit to the largest.

Solution:
Member (3) → Family (1) → Locality (4) → Community (2) → Country (5).
A member belongs to a family, families live in a locality (neighbourhood), localities together form a community, and communities make up the country.
Sequence = 3, 1, 4, 2, 5

Why the other options are wrong:
B) puts Country before Locality.
C) puts Country before Community.
D) puts Locality before Family.
E) places Community before Locality, but a locality (neighbourhood) is the smaller unit.

Answer: A

Approach: Logical sequence — follow the cause-to-effect chain.

Solution:
Rising Population (2) → Unemployment (4) → Poverty (1) → Disease (5) → Death (3).
Sequence = 2, 4, 1, 5, 3

Why the other options are wrong:
A) starts with Death.
B) starts with Poverty before its cause.
C) puts Death second.
E) puts Death before Disease.

Answer: D

Approach: Logical sequence — follow the order of the process.

Solution:
Measure (4) the cloth → Mark (3) it → Cut (1) → Tailor (5) / stitch it → Put on (2) the garment.
Sequence = 4, 3, 1, 5, 2

Why the other options are wrong:
B) tailors before cutting.
C) marks before measuring.
D) cuts first.
E) puts on the garment first.

Answer: A

Approach: Logical sequence — follow the order of the process.

Solution:
Advertisement (5) → Application (6) → Interview (2) → Selection (3) → Appointment (4) → Probation (1).
Sequence = 5, 6, 2, 3, 4, 1

Why the other options are wrong:
A) puts Probation before Interview.
C) selects before the interview.
D) applies before the advertisement.
E) appoints before the interview.

Answer: B

Approach: Pick the region inside Authors and Doctors but outside Females.

Solution:
Triangle = Authors, Rectangle = Doctors, Circle = Females.
Male Doctors who are Authors → inside triangle ∩ rectangle, outside circle.
That region holds 10.
(8 is in all three — female author-doctors; 13 is female doctors who are not authors.)

Why the other options are wrong:
C) 8 — those are females.
A), B), D) — no such region value.

Answer: E

Approach: Region inside Triangle, Rectangle and Circle but outside the Square.

Solution:
Men (triangle) ∩ Educated (rectangle) ∩ Employed (circle), not Married (square).
Region 5 lies in the triangle, rectangle and circle and above the square → 5.
(Region 9 is the same set but inside the square — married.)

Why the other options are wrong:
C) 9 — married.
B) 10 — lies outside the triangle (not men).
A) 7 — not a man and not employed (outside the triangle and the circle).
E) 4 — employed only, not men or educated.

Answer: D

Approach: Take each group as 100% and remove the overlap shares shown for it.

Solution:
Only girls = 100 − 12 − 16 = 72
Only students = 100 − 12 − 14 = 74
Only dancers = 100 − 14 − 16 = 70
→ 72, 74, 70

Answer: A

Approach: Add every region common to Telugu and Tamil.

Solution:
Telugu ∩ Tamil (only these two) = 12
Telugu ∩ Tamil ∩ English = 9
Speak Tamil and Telugu both = 12 + 9 = 21

Why the other options are wrong:
A) 9 — only the all-three region.
B) 12 — misses the 9 who also speak English.
D) 13 — Telugu–English region.
E) 40 — wrong addition.

Answer: C