Q&A: practice questions with answers

Concept: Let $x$ = ₹50 notes, $y$ = ₹100 notes.

1. $x+y=33$ and $50x+100y=3200$ → $x+2y=64$
2. Subtract: $y=31$
3. $x=33-31=2$

Trick: If all 33 were ₹100 → ₹3300; extra ₹100 ÷ ₹50 saving per note $=2$ notes of ₹50.

Answer: (C) 2

Concept: Downstream speed $=b+s$, upstream speed $=b-s$.

1. Downstream $=12+10=22$ km/h; upstream $=12-10=2$ km/h
2. Time $=\frac{24.2}{22}+\frac{24.2}{2}=1.1+12.1$
3. Total $=13.2$ hours

Trick: Slow upstream speed dominates the time – answer must exceed 12.1 h.

Answer: (C) 13.2

Concept: Leak rate $=$ pump rate $-$ combined rate.

1. Pump $=\frac{1}{6}$ per hour; with leak $=\frac{1}{22/3}=\frac{3}{22}$ per hour
2. Leak $=\frac{1}{6}-\frac{3}{22}=\frac{11-9}{66}=\frac{1}{33}$
3. Leak empties the tank in 33 hours

Trick: Shortcut: $\frac{a\times b}{b-a}=\frac{6\times \frac{22}{3}}{\frac{22}{3}-6}=\frac{44}{\frac{4}{3}}=33$.

Answer: (D) 33 hours

Concept: ${\tan }^{2}A-{\sin }^{2}A={\sin }^{2}A({\sec }^{2}A-1)={\sin }^{2}A{\tan }^{2}A$.

1. $\sqrt{{\tan }^{2}A-{\sin }^{2}A}=\sin A\tan A$
2. Expression $=\frac{3}{{\sin }^{2}A\sec A}\times 3\sin A\tan A=\frac{9\tan A}{\sin A\sec A}$
3. $\sin A\sec A=\frac{\sin A}{\cos A}=\tan A$ → value $=9$

Trick: Put $A={45}^{\circ }$: $\frac{3}{\frac{1}{2}\sqrt{2}}\times 3\sqrt{1-\frac{1}{2}}=\frac{6}{\sqrt{2}}\times \frac{3}{\sqrt{2}}=9$.

Answer: (D) 9

Concept: Write the percentage as a fraction and cross-multiply.

1. $\frac{66}{100}x=\frac{5}{7}y$
2. $\frac{x}{y}=\frac{5}{7}\times \frac{100}{66}=\frac{500}{462}$
3. $=\frac{250}{231}$

Trick: $\frac{500}{462}$ – halve both: $250:231$.

Answer: (C) 250 : 231

Concept: Place the fixed person first, then the blocks of consecutive days.

1. P = Wednesday; 3 people between P and S ⇒ S = Sunday.
2. Q, T, V must be consecutive (Q–T–V); free days are Mon, Tue, Thu, Fri, Sat ⇒ Q = Thu, T = Fri, V = Sat.
3. 3 between U and T ⇒ U = Monday; R = Tuesday.
4. After Q (Thu): T, V, S = 3 people.

Trick: Fix the "exactly n between" person at the week ends first.

Answer: (A) 3

Concept: Identify the highest and lowest numbers, then pick the required digit.

1. Numbers: 190, 735, 494, 761, 781.
2. Highest = 781 → second digit 8.
3. Lowest = 190 → second digit 9.
4. $9-8=1$.

Trick: Order matters: "A subtracted from B" means $B-A$.

Answer: (D) 1

Concept: Find the positional shift of each letter.

1. Z→T, R→L, V→P, Y→S: each letter moves 6 places back.
2. W→Q, O→I, S→M, V→P: again −6.
3. U→O, M→G, Q→K, T→N ⇒ OGKN.

Trick: Check just the first letter of each option: U−6 = O rules out C and D; M−6 = G and Q−6 = K fixes B.

Answer: (B) OGKN

Concept: Common letters in two words share common digits.

1. LINK = 9236, SINK = 6349.
2. Common letters I, N, K ↔ common digits 9, 3, 6.
3. So L = the leftover digit of LINK = 2, and S = the leftover digit of SINK = 4.

Trick: Remove common digits; the remaining digit belongs to the remaining letter.

Answer: (D) 4

Concept: Apply the rule digit by digit.

1. 5637482: odd digits +1, even digits −2.
2. 5→6, 6→4, 3→4, 7→8, 4→2, 8→6, 2→0 ⇒ 6448260.
3. 6 appears twice, 4 appears twice; 8, 2, 0 once.
4. Digits appearing more than once: 6 and 4 ⇒ 2.

Trick: Write the new number under the old one to avoid slips.

Answer: (C) 2

Concept: Find the rule linking the three numbers of each set.

1. (29, 41, 53): $29+12=41,41+12=53$.
2. (37, 49, 61): $37+12=49,49+12=61$.
3. (53, 65, 77): $53+12=65,65+12=77$ ✓.
4. Others fail: $79+12=91\ne 101$, $48+12=60\ne 50$, $52+12=64\ne 74$.

Trick: Each set is an AP with common difference 12.

Answer: (A) (53, 65, 77)

Concept: Track each part of the cluster separately.

1. First letters: P, O, N, M → next L (−1).
2. Second letters: K, J, I, H → next G (−1).
3. Numbers: 23, 34, 45, 56 → next 67 (+11).
4. Next term = LG67.

Trick: Split the term into letter 1 | letter 2 | number.

Answer: (C) LG67

Concept: Test each possible position of the "4 between" pair.

1. T = Wednesday. 4 between S and R ⇒ pairs (Mon, Sat) or (Tue, Sun); Monday is not allowed ⇒ S, R on Tue and Sun.
2. Case S = Sun: U = Sat, R = Tue; then Q–P–V needs 3 consecutive days among Mon, Thu, Fri – impossible.
3. Case S = Tue: U = Mon, R = Sun; Q = Thu, P = Fri, V = Sat ✓.
4. Sunday ⇒ R.

Trick: Reject a case as soon as a consecutive block cannot fit.

Answer: (C) R

Concept: Find the shift for each letter position.

1. A→D, S→V, X→A, Z→C: each +3 (wrap Z→C).
2. M→P, E→H, J→M, L→O: each +3.
3. V→Y, N→Q, S→V, U→X ⇒ YQVX.

Trick: Only option A keeps the order "+3 on every letter": V+3 = Y, N+3 = Q, S+3 = V, U+3 = X.

Answer: (A) YQVX

Concept: Check every symbol for the pattern: number – symbol – symbol.

1. Series: @ 2 % * 4 2 & £ % 1 £ & 9 7 & 9 7 $ 9 1 $ 2.
2. 2 % * ✓; 2 & £ ✓; 1 £ & ✓.
3. 7 & 9, 7 $ 9 and 1 $ 2 fail (followed by a number).
4. Count = 3.

Trick: Look only at symbols whose left neighbour is a digit, then check the right neighbour.

Answer: (C) 3

Concept: Facing north, left = position 1, right = position 7.

1. No one to the right of E ⇒ E = 7.
2. Two between E and P ⇒ P = 4; C immediately right of P ⇒ C = 5.
3. Three between F and C ⇒ F = 1.
4. D–H adjacent among 2, 3, 6 ⇒ D = 2, H = 3; G = 6.
5. Between G (6) and H (3): P, C ⇒ two.

Trick: Start with the extreme-end clue ("no one to the right").

Answer: (B) Two

Concept: Compare letter positions within and between clusters.

1. SV - PS: S−3 = P, V−3 = S.
2. IL - FI: I−3 = F, L−3 = I.
3. PS - MP: P−3 = M, S−3 = P.
4. MH - KJ: M−2 = K, H+2 = J – a different rule.

Trick: In the three alike pairs the second letter is also +3 from the first (S→V, I→L, P→S); in MH it is −5.

Answer: (A) MH - KJ

Concept: Identify the highest and lowest numbers, then their second digits.

1. Numbers: 497, 581, 452, 460, 775.
2. Highest = 775 → second digit 7.
3. Lowest = 452 → second digit 5.
4. $5-7=-2$.

Trick: "X subtracted from Y" = $Y-X$; a negative result is allowed.

Answer: (D) −2

Concept: Find the rule from the complete pair VFR : % using the options.

1. Try # = KUG: K+10 = U, U+10 = E (wrap), G+10 = Q ⇒ KUG → UEQ ✓.
2. Apply +10 to VFR: V+10 = F, F+10 = P, R+10 = B ⇒ FPB.
3. So # = KUG and % = FPB.

Trick: +10 is the same as −16; wrap after Z (V = 22, $22+10-26=6$ = F).

Answer: (A) # = KUG, % = FPB

Concept: Change each digit by the rule, then add the odd digits of the new number.

1. 248937615: even +1, odd −1.
2. 2→3, 4→5, 8→9, 9→8, 3→2, 7→6, 6→7, 1→0, 5→4 ⇒ 359826704.
3. Odd digits: 3, 5, 9, 7.
4. Sum $=3+5+9+7=24$.

Trick: Even+1 becomes odd and odd−1 becomes even, so the new odd digits come only from old even digits: $(2+4+8+6)+4=24$.

Answer: (D) 24