Q&A: practice questions with answers

Concept: Equivalent discount of $a\%$ and $b\%$ $=a+b-\frac{ab}{100}$.

1. $40+20-\frac{40\times 20}{100}$
2. $=60-8=52\%$

Trick: On ₹100: $100\to 60\to 48$, so total discount $=52\%$.

Answer: (C) 52%

Concept: Rise in level $=\frac{\text{Volume displaced}}{\text{Base area of tank}}$.

1. Volume displaced $=50\times 4=200$ m${}^3$.
2. Base area $=40\times 20=800$ m${}^2$.
3. Rise $=\frac{200}{800}=0.25$ m $=25$ cm.

Trick: Always convert the final metres to cm: $\times 100$.

Answer: (D) 25 cm

Concept: If $\frac{A}{2}=\frac{B}{3}$, then $A:B=2:3$.

1. Total parts $=2+3=5$.
2. B's part $=\frac{3}{5}\times 2000=1200$.

Trick: Check: A $=800$, $\frac{800}{2}=400=\frac{1200}{3}$ ✓.

Answer: (A) 1,200

Concept: HCF = product of common prime factors with the lowest powers.

1. $240=2^4\times 3\times 5$, $360=2^3\times 3^2\times 5$, $480=2^5\times 3\times 5$.
2. HCF $=2^3\times 3\times 5=120$.

Trick: $240=2\times 120$, $360=3\times 120$, $480=4\times 120$, and 2, 3, 4 have HCF 1.

Answer: (D) 120

Concept: $a^m÷a^n=a^{m-n}$.

1. ${10}^{150}÷{10}^{146}={10}^{150-146}$
2. $={10}^4=10000$

Yaad rakhein: Same base in division ⇒ subtract the powers.

Answer: (A) 10000

Concept: Vowels move one step forward (+1), consonants one step back (−1).

1. A→B, R→Q, T→S, I→J, C→B, U→V, L→K, A→B, T→S, E→F.
2. New group: B Q S J B V K B S F.
3. B appears 3 times (from A, C, A); S only twice; J and K once.

Trick: Both A (vowel, +1) and C (consonant, −1) turn into B — look for such collisions.

Answer: (D) B

Concept: For people facing the centre, left = clockwise and right = anticlockwise. Fix R and place others.

1. Three people between R and E from R's left: E is 4th to the left of R.
2. Two between E and Q: Q is immediately to the left of R.
3. B is 3rd to the right of Q, i.e. 2nd to the right of R.
4. F immediately left of P fills the next two seats (P, F); A takes the last seat, between B and R.

Trick: Clockwise order: R, Q, P, F, E, B, A — B sits to the immediate right of A.

Answer: (C) B

Concept: Decode each symbol one pair at a time and build the family tree.

1. A + B: A is the father of B.
2. B − C: B is the wife of C (so B is female).
3. C + D: C is the father of D; D × E: D is the brother of E, so E is also C's and B's child.
4. B is E's mother and A is B's father.

Trick: Go from E upward: E → mother (B) → her father (A).

Answer: (B) Mother’s father

Concept: Letters common to both words take the digits common to both codes.

1. WHELP = 24681, HELPS = 12674.
2. Common letters H, E, L, P ↔ common digits 1, 2, 4, 6.
3. Left in WHELP: letter W and digit 8 ⇒ W = 8 (and S = 7).

Trick: Remove the shared letters and shared digits; what remains pairs up.

Answer: (D) 8

Concept: Find the rule: (first × 3) = second, (second × 4) = third.

1. $4\times 3=12$, $12\times 4=48$; $7\times 3=21$, $21\times 4=84$.
2. (15, 45, 180): $15\times 3=45$, $45\times 4=180$ ✓.
3. (5, 45, 180): $5\times 3=15\ne 45$; (15, 45, 170): $45\times 4\ne 170$; (15, 25, 180): $15\times 3\ne 25$.

Trick: Equivalently third $=12\times$ first: $15\times 12=180$.

Answer: (B) (15, 45, 180)

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

1. All villas are buildings: Villas circle lies inside Buildings.
2. Some buildings are apartments: Apartments overlaps Buildings.
3. I: “All buildings are villas” — Buildings can be bigger than Villas, so not certain.
4. II: “Some villas are not apartments” — Apartments may contain all villas; not certain.

Trick: There is no direct link between villas and apartments, so nothing definite can be said about them.

Answer: (B) Neither conclusion I nor II follows

Concept: Split the series into two alternate series.

1. Odd positions: 194, 199, 204 (each $+5$).
2. Even positions: 249, 244, ? (each $-5$).
3. ? $=244-5=239$.

Trick: When terms jump up and down, check alternate terms.

Answer: (A) 239

Concept: A valid reason must directly explain the event in the statement (same place, same time).

1. Statement: trains on the Arakkonam–Chennai route are late today.
2. I: holiday specials between Kolkata and Patna — different route, unrelated. Not a reason.
3. II: derailment at Arakkonam Junction last night blocking the tracks — directly delays trains on this route. Valid.

Trick: Match the location and timing of the reason with the statement.

Answer: (B) Only II is a possible reason

Concept: Find the operation linking the pair: first number $÷9$ = second number.

1. $153÷9=17$, $216÷9=24$.
2. $243÷9=27$ ✓.
3. Others: $225÷9=25\ne 35$, $189÷9=21\ne 31$, $171÷9=19\ne 18$.

Trick: Divide first by second in the given pairs: $\frac{153}{17}=\frac{216}{24}=9$.

Answer: (C) 243, 27

Concept: $\text{Total}=\text{Rank from top}+\text{Rank from bottom}-1$.

1. Total $=8+17-1$
2. $=24$

Yaad rakhein: Subtract 1 because the person is counted in both ranks.

Answer: (B) 24

Concept: Use alphabet positions and check the gaps between letters.

1. IPL: I(9) → P(16) $+7$, P → L(12) $-4$.
2. ELH: E(5) → L(12) $+7$, L → H(8) $-4$.
3. CJF: C(3) → J(10) $+7$, J → F(6) $-4$.
4. LSP: L(12) → S(19) $+7$, but S → P(16) is $-3$ — odd one.

Trick: Pattern $+7,-4$ in three clusters; LSP breaks the second gap.

Answer: (C) LSP

Concept: Track each letter position separately; each moves $+12$ (wrapping after Z).

1. 1st letters: A → M → Y → K → W ($+12$ each).
2. 2nd letters: C → O → A → M → Y ($+12$ each).
3. 3rd letters: Y → K → W → I → U ($+12$ each).
4. Next cluster: WYU.

Trick: $+12$ is the same as $-14$; after Z continue from A (e.g. Y(25) $+12=37-26=11$ = K).

Answer: (B) WYU

Concept: Each letter position moves back by 5 (wrapping before A to Z).

1. 1st letters: D → Y → T → O → J ($-5$ each).
2. 2nd letters: J → E → Z → U → P ($-5$ each).
3. 3rd letters: C → X → S → N → I ($-5$ each).
4. Next cluster: JPI.

Trick: In each cluster the third letter is just before the first (D-C, Y-X, T-S, O-N), so the answer must be J _ I.

Answer: (D) JPI

Concept: Letters common to both words share the digits common to both codes.

1. FIRE = 3718, FARE = 1438.
2. Common letters F, R, E ↔ common digits 1, 3, 8.
3. FIRE leaves I = 7; FARE leaves A = 4.

Trick: Only one letter differs (I vs A), and only one digit differs (7 vs 4).

Answer: (A) 4

Concept: Swap the signs first, then solve by BODMAS.

1. Swap $+\leftrightarrow ÷$ and $\times \leftrightarrow -$: $27+14-21÷3\times 4$.
2. $21÷3=7$, $7\times 4=28$.
3. $27+14-28=13$.

Trick: Rewrite the whole expression before calculating — don't swap in your head.

Answer: (C) 13