Q&A: practice questions with answers

Concept: Work per day $=\frac{1}{\text{days}}$; subtract the joint work, then divide the rest by the remaining worker's rate.

1. Together in 2 days: $2(\frac{1}{13}+\frac{1}{4})=2\times \frac{17}{52}=\frac{17}{26}$.
2. Remaining work $=1-\frac{17}{26}=\frac{9}{26}$.
3. Naman alone: $\frac{9}{26}\times 13=4.5$ days.

Trick: Total work $=\text{LCM}(13,4)=52$ units; rates 4 and 13; 2 days $=34$ units; left $18$; $\frac{18}{4}=4.5$.

Answer: (A) $4.5$

Concept: $a^m÷a^n=a^{m-n}$ and $a^m\times a^n=a^{m+n}$; work left to right.

1. ${83}^{-6}÷{83}^{16}={83}^{-6-16}={83}^{-22}$.
2. ${83}^{-22}\times {83}^{-8}={83}^{-30}$.

Trick: Just combine the powers: $-6-16+(-8)=-30$.

Answer: (C) ${83}^{-30}$

Concept: Average $=\frac{\text{sum}}{\text{count}}$.

1. Sum $=40+49+56+73+38=256$.
2. Average $=\frac{256}{5}=51.2$ kg.

Trick: Assume 50: deviations $-10,-1,+6,+23,-12$ total $+6$; $50+\frac{6}{5}=51.2$.

Answer: (A) $51.2$

Concept: Exterior + interior angle $={180}^{\circ }$; number of sides $n=\frac{{360}^{\circ }}{\text{exterior angle}}$.

1. Ratio $1:8$ ⇒ exterior $=\frac{{180}^{\circ }}{9}={20}^{\circ }$.
2. $n=\frac{{360}^{\circ }}{{20}^{\circ }}=18$.

Trick: If E : I $=1:k$, then $n=2(k+1)$ ⇒ $2\times 9=18$.

Answer: (C) $18$

Concept: $\text{SI}=\frac{P\times R\times T}{100}$ with rate and time in the same unit.

1. Rate $3\%$ per month, time 12 months ⇒ total rate $=36\%$.
2. $\text{SI}=\frac{1200\times 36}{100}=432$.

Trick: $3\%$ per month $=36\%$ per year – do not take it as $3\%$ per annum (that gives ₹36).

Answer: (C) ₹432

Concept: Check each odd number for divisibility by primes up to $\sqrt{311}\approx 17$.

1. $303=3\times 101$, $305=5\times 61$, $309=3\times 103$ – composite.
2. $307$ and $311$ are not divisible by 2, 3, 5, 7, 11, 13, 17 – prime.
3. Even numbers are composite. Count $=2$.

Trick: Test only up to the square root; 3 divides 303 and 309 (digit sums 6 and 12).

Answer: (B) $2$

Concept: $V=\pi r^{2}h$; with $h=r$, $V=\pi r^3$.

1. $\frac{22}{7}{r}^3=8624$.
2. $r^3=\frac{8624\times 7}{22}=392\times 7=2744$.
3. $r=\sqrt[3]{2744}=14$, so $h=14$ cm.

Trick: $2744={14}^3$ – remember cubes up to 20.

Answer: (C) 14 cm

Concept: Count days excluding the deposit day and including the withdrawal day; 2024 is a leap year (366 days).

1. Feb: $29-7=22$, March: 31, April: 8 ⇒ 61 days.
2. $\text{SI}=4000\times \frac{7.5}{100}\times \frac{61}{366}=300\times \frac{1}{6}=50$.

Trick: $\frac{61}{366}=\frac{1}{6}$ exactly in a leap year – a common exam pairing.

Answer: (B) $50$

Concept: Form two linear equations in mother's age $M$ and daughter's age $D$.

1. $3M=5D+26$ and $M=2D+2$.
2. $3(2D+2)=5D+26$ ⇒ $D=20$.
3. $M=42$; difference $=42-20=22$.

Trick: Check options: $M-D=22$ with $M=2D+2$ gives $D=20$, $M=42$; $3\times 42=126=5\times 20+26$ ✓.

Answer: (D) $22$

Concept: $V=\frac{4}{3}\pi r^3$, with $r=\frac{d}{2}$.

1. $r=11$ cm, $r^3=1331$.
2. $V=\frac{4}{3}\times \frac{22}{7}\times 1331=\frac{117128}{21}$.
3. $V\approx 5577.52{\text{cm}}^3$.

Trick: $\frac{88}{21}\approx 4.1905$; $4.1905\times 1331\approx 5577.5$.

Answer: (D) $5577.52$

Concept: Check every symbol: the element just before it and just after it must both be numbers.

1. Series: 9 6 $ $ 7 © £ $ 1 * 5 4 3 3 $ 6 @ # # # 8 %.
2. 1 * 5 ✓ and 3 $ 6 ✓.
3. Others fail, e.g. 6 $ $, 7 © £, 6 @ #. Count $=2$.

Trick: Scan for the pattern “number – symbol – number” in one pass.

Answer: (C) 2

Concept: Two “some” statements give no definite link between the outer terms.

1. Some penguins are sharks ⇒ conclusion I (No shark is a penguin) directly contradicts it – false.
2. Penguins and dolphins are connected only through “some” sharks – they may not overlap, so II is not certain.

Trick: Some + Some ⇒ no conclusion about the end terms.

Answer: (A) Neither conclusion (I) nor (II) follows.

Concept: Compare positions letter by letter.

1. K→I, G→E, D→B, L→J: each $-2$.
2. N→L, J→H, G→E, O→M: each $-2$.
3. Q→O, M→K, J→H, R→P ⇒ OKHP.

Trick: Same shift on every letter – apply it in order.

Answer: (D) OKHP

Concept: Change each digit as per the rule, then read the required positions.

1. 7364592 → 7→6, 3→2, 6→8, 4→6, 5→4, 9→8, 2→4.
2. New number: 6286484.
3. First from left 6 + first from right 4 $=10$.

Trick: Only the first and last digits are needed: 7→6 and 2→4.

Answer: (C) 10

Concept: Facing the centre: left = clockwise, right = anticlockwise.

1. Fix U. W is 3rd to the right of U (U is 3rd to the left of W).
2. V is 5th to the right of U (four between); I sits between V and W.
3. Remaining 3 seats: only H = 3rd to the right of K fits; J takes the last seat.
4. From J moving right: H, W, then I ⇒ two people.

Trick: Place the fixed-gap pairs first, then the neighbour clue.

Answer: (A) Two

Concept: Track the net north–south and east–west movement.

1. North 34, left (west) 20, left (south) 40, left (east) 20.
2. East–west: $-20+20=0$.
3. North–south: $34-40=-6$ ⇒ Z is 6 km south of Y.
4. So drive 6 km towards north.

Trick: Opposite legs cancel; only $40-34=6$ remains.

Answer: (A) 6 km towards north

Concept: Check the differences.

1. $178-142=36$, $142-117=25$, $117-101=16$, $101-92=9$.
2. Differences are $6^2,5^2,4^2,3^2$; next $2^2=4$.
3. $92-4=88$.

Trick: Falling squares in the differences.

Answer: (D) $88$

Concept: Check the differences.

1. Differences: $+1,+2,+3,+4$.
2. Next $+5$: $509+5=514$.

Trick: Consecutive natural-number additions.

Answer: (C) $514$

Concept: Use “only” clues to fix exact positions (1 = top, 7 = bottom).

1. Only X above W ⇒ X = 1, W = 2.
2. Only U below F ⇒ U = 7, F = 6.
3. Two boxes between W and G ⇒ G = 5.
4. V not immediately above G ⇒ V = 3, E = 4. Between E (4) and U (7): G, F ⇒ two.

Trick: “Only one above/below” fixes the box at position 2 or 6 directly.

Answer: (D) Two

Concept: Find symbols with a number immediately before and after.

1. Series: # 1 * £ 5 6 4 + 7 $ 8 2 @ % & 3 Ω 9.
2. 4 + 7 ✓, 7 $ 8 ✓, 3 Ω 9 ✓.
3. Others fail (1 * £, 2 @ %). Count $=3$.

Trick: Look for “number – symbol – number” in one scan.

Answer: (C) 3