Q&A: practice questions with answers

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

1. Rate $4\%$ per month, time $7$ months
2. $\text{SI}=\frac{1200\times 4\times 7}{100}=336$
3. (If the rate were $4\%$ per annum, $\text{SI}=1200\times \frac{4}{100}\times \frac{7}{12}=28$.)

Trick: Always check whether the rate is per month or per annum before plugging in.

Answer: (A) ₹336

Concept: $\text{Side}=\frac{\text{Perimeter}}{4}$, $\text{Area}={\text{side}}^2$.

1. $\text{Side}=\frac{52}{4}=13\text{m}$
2. $\text{Area}={13}^2=169{\text{m}}^2$

Trick: Area $=\frac{{\text{Perimeter}}^2}{16}=\frac{2704}{16}=169$.

Answer: (C) $169$

Concept: Total work in man-days equals total work in woman-days; compare to find relative efficiency.

1. $4\times 18=72$ man-days $=9\times 8=72$ woman-days
2. So 1 man $=$ 1 woman
3. 3 women + 3 men $=6$ persons
4. $\text{Days}=\frac{72}{6}=12$

Trick: $M_1{D}_1=M_2{D}_2$ – equal products mean equal efficiency.

Answer: (C) 12 days

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

1. ${66}^{-5}÷{66}^{11}={66}^{-5-11}={66}^{-16}$
2. ${66}^{-16}\times {66}^{-12}={66}^{-16-12}={66}^{-28}$

Trick: Exponent $=-5-11+(-12)=-28$.

Answer: (C) ${66}^{-28}$

Concept: Expand each bracket and combine like terms.

1. $3(\frac{7}{3}{x}^2-28x+14)=7x^2-84x+42$
2. $-7(x^2+4x-14)=-7x^2-28x+98$
3. Sum: $(7x^2-7x^2)+(-84x-28x)+(42+98)=-112x+140$

Trick: The $x^2$ terms cancel; the $x$-coefficient is negative and the constant positive – only one option fits.

Answer: (D) $-112x+140$

Concept: Multiply numerator and denominator by $(1+\cos A)$ and use $1-{\cos }^{2}A={\sin }^{2}A$.

1. $\sqrt{\frac{(1+\cos A{)}^2}{1-{\cos }^{2}A}}=\sqrt{\frac{(1+\cos A{)}^2}{{\sin }^{2}A}}$
2. $=\frac{1+\cos A}{\sin A}$
3. $=\frac{1}{\sin A}+\frac{\cos A}{\sin A}=cosecA+\cot A$

Trick: Put $A={90}^{\circ }$: expression $=1$; $cosec{90}^{\circ }+\cot {90}^{\circ }=1+0=1$ ✓

Answer: (D) $cosecA+\cot A$

Concept: Mean proportional of $a$ and $b$ is $\sqrt{ab}$.

1. $\sqrt{25\times 36}=\sqrt{900}$
2. $=30$ (or $5\times 6=30$)

Trick: $\sqrt{ab}=\sqrt{a}\times \sqrt{b}=5\times 6$.

Answer: (B) $30$

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

1. Feb: $29-10=19$, March: $31$, April: $11$ → $61$ days
2. $\text{SI}=\frac{4000\times 7.5\times 61}{100\times 366}$
3. $=\frac{300\times 61}{366}=\frac{300}{6}=50$

Trick: $366=6\times 61$ – the 61 cancels neatly, confirming the day count.

Answer: (D) $50$

Concept: After a $7\%$ decrease, $93\%$ of the number remains.

1. $93\%\text{ of }x=2790$
2. $x=\frac{2790\times 100}{93}=30\times 100=3000$

Trick: $2790÷93=30$, so the number is $3000$.

Answer: (A) $3000$

Concept: Test odd numbers in the range for divisibility by primes up to $\sqrt{486}\approx 22$.

1. Odd numbers: $473=11\times 43$, $475=5\times 95$, $477=9\times 53$
2. $481=13\times 37$, $483=3\times 161$, $485=5\times 97$
3. $479$ is not divisible by $2,3,5,7,11,13,17,19$ → prime

Trick: Remember tricky composites like $481=13\times 37$ and $473=11\times 43$.

Answer: (A) $1$

Concept: Draw the least-overlap Venn diagram; a conclusion follows only if it is true in every possible diagram.

1. All horses lie inside cats; lions are outside horses.
2. Lions may lie completely outside cats, so 'Some lions are cats' is not certain – I does not follow.
3. Nothing forces cats to be inside lions – II does not follow.

Trick: 'No A is B' tells nothing about B and the bigger set containing A.

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

Concept: Place persons by position from the left; total = position from left + position from right − 1.

1. Pranali 21st, Anuj 23rd from left – gap of 2.
2. Anuj is exactly midway, so Harish is 2 places beyond Anuj: 25th from left.
3. Harish is 8th from right: total = 25 + 8 − 1 = 32.

Trick: Same person counted from both ends: L + R − 1.

Answer: (B) 32

Concept: Find the alphabetical gaps between consecutive letters of each cluster.

1. OVP: O +7 → V, V −6 → P
2. LSM: L +7 → S, S −6 → M; IPJ: I +7 → P, P −6 → J
3. RYT: R +7 → Y, but Y −5 → T (not −6)

Trick: Pattern +7, −6 means the third letter is just next to the first (O–P, L–M, I–J); R–T breaks it.

Answer: (D) RYT

Concept: Track each letter position and the number separately.

1. 1st letters: C, Z, W, T, Q → each −3 → N
2. 2nd letters: K, H, E, B, Y → −3 → V; 3rd letters: S, P, M, J, G → −3 → D
3. Numbers: 11, 23, 47, 95, 191 → ×2 + 1 → 383

Trick: Every letter moves back by 3 (wrapping A → X); numbers follow ×2 + 1.

Answer: (A) NVD 383

Concept: Look at the differences between consecutive terms.

1. Differences: $6,9,12,15$ (increasing by 3)
2. Next difference $=18$
3. $100+18=118$

Trick: Differences in an AP of +3.

Answer: (B) 118

Concept: Write the digits in descending order and compare position by position.

1. Original: 3 1 2 4 6 9 7 8
2. Descending: 9 8 7 6 4 3 2 1
3. Compare each place: 3–9, 1–8, 2–7, 4–6, 6–4, 9–3, 7–2, 8–1 – no match

Trick: Line the two numbers one under the other and scan column-wise.

Answer: (B) None

Concept: Decode each symbol step by step and build a family tree.

1. E + F: E is the brother of F (E is male).
2. F $ G: F is the son of G; G @ M: G is the wife of M.
3. M ÷ N: M is the father of N, so N is a child of G and M – a sibling of F and E.
4. Hence E is the brother of N.

Trick: Children of the same couple are siblings; a male sibling = brother.

Answer: (D) Brother

Concept: Track each letter position and the number separately.

1. 1st letters: I, G, E, C → −2 → A
2. 2nd letters: Q, M, I, E → −4 → A; 3rd letters: A, B, C, D → +1 → E
3. Numbers: $15,8,-1,-12$ – differences $-7,-9,-11$ → next $-13$: $-12-13=-25$

Trick: Differences of the numbers decrease by 2 each time.

Answer: (C) AAE −25

Concept: Facing the centre, a person's right is anticlockwise and left is clockwise. Fix U first.

1. Place U; J sits immediately to the right of U.
2. L is second to the right of U, and V is second to the right of L.
3. The two empty seats go to K and T; T is second to the left of K only when T sits opposite U.
4. Going left from T: L, J, then U → two persons between.

Trick: Six seats: 'second to the right of second to the right' means the person is opposite-adjacent – sketch first.

Answer: (A) Two

Concept: Compare each letter of the word with the matching letter of its code.

1. MERIT → RJWNY: M+5=R, E+5=J, R+5=W, I+5=N, T+5=Y
2. Check DRAWN → IWFBS: every letter +5 ✓
3. SHAPE +5: S→X, H→M, A→F, P→U, E→J → XMFUJ

Trick: A uniform shift: verify with just the first letter (S+5 = X) to pick the option.

Answer: (B) XMFUJ