Q&A: practice questions with answers

Concept: Simplify the complex fraction first, then combine.

1. $1+\frac{2}{7}=\frac{9}{7}$, so $\frac{1}{9/7}=\frac{7}{9}$.
2. $\frac{5}{3}-\frac{2}{3}=1$.
3. Value $=1+\frac{7}{9}=\frac{16}{9}$.

Trick: Group like denominators ($\frac{5}{3}-\frac{2}{3}$) before anything else.

Answer: (A) $\frac{16}{9}$

Concept: Divisible by 5 ⇔ last digit 0 or 5; by 3 ⇔ digit sum divisible by 3.

1. Last digit is 5 ⇒ divisible by 5.
2. Digit sum $=4+8+1+3+5+5=26$, not divisible by 3 ⇒ not by 3, 6 or 15.
3. It is odd, so not by 6 either.

Yaad rakhein: 15 needs both 3 and 5; 6 needs both 2 and 3.

Answer: (D) 5

Concept: $\text{SI}=\frac{P\times R\times T}{100}$.

1. $\text{SI}=\frac{400\times 16\times 4.5}{100}=4\times 16\times 4.5$.
2. $=64\times 4.5=288$.

Trick: $P=400$ ⇒ SI $=4\times R\times T$ directly.

Answer: (D) 288

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

1. Sum $=40+49+56+74+38=257$.
2. Average $=\frac{257}{5}=51.4\text{kg}$.

Trick: Deviation from 50: $-10-1+6+24-12=7$; $50+\frac{7}{5}=51.4$.

Answer: (C) 51.4

Concept: Compute each quantity and subtract.

1. $65\%$ of $65=\frac{65\times 65}{100}=42.25$.
2. $\frac{1}{5}$ of $55=11$.
3. Difference $=42.25-11=31.25$.

Trick: ${65}^2=4225$ (numbers ending in 5: $6\times 7=42$, then 25).

Answer: (C) 31.25

Concept: Letters common to both words share the common digits; the leftover letter takes the leftover digit.

1. DRAG → {5, 8, 2, 4}; GRAM → {4, 5, 9, 2}.
2. Common letters R, A, G ↔ common digits 5, 2, 4.
3. Left in GRAM: M ↔ 9 (and D ↔ 8).

Trick: Strike out common letters and common digits — what remains pairs up.

Answer: (B) 9

Concept: The only letter common to both words must take the only digit common to both codes.

1. EARS → {1, 3, 5, 7}; SOUP → {2, 1, 4, 6}.
2. Common letter: S; common digit: 1.
3. So S = 1.

Trick: One common letter ↔ one common digit.

Answer: (C) 1

Concept: Track each letter position separately.

1. 1st letters: T, V, X, Z, B (+2, wrapping Z → B).
2. 2nd letters: A, C, E, G, I (+2).
3. 3rd letters: W, Y, A, C, E (+2).

Trick: All three positions move $+2$; after Z comes A, so $Z+2=B$, $C+2=E$.

Answer: (C) BIE

Concept: Pick the highest and lowest numbers, then the required digits.

1. Highest $=625$ → third digit $=5$.
2. Lowest $=156$ → second digit $=5$.
3. Sum $=5+5=10$.

Trick: Compare first digits only: 6 (625) is largest, 1 (156) smallest.

Answer: (C) 10

Concept: Interchange the signs first, then apply BODMAS.

1. $19+40-8\times 2÷1$ becomes $19\times 40÷8+2-1$.
2. $19\times 40=760$; $760÷8=95$.
3. $95+2-1=96$.

Trick: Rewrite the full expression with new signs before calculating.

Answer: (A) 96

Concept: Number positions 1 (bottom) to 7 (top) and place fixed clues first.

1. No box above G ⇒ G = 7. Three between G and B ⇒ B = 3; D just above B ⇒ D = 4.
2. One between F and D ⇒ F = 2 or 6. Four between F and E: F = 2 needs E = 7 (taken) ⇒ F = 6, E = 1.
3. A above C in slots 5, 2 ⇒ A = 5, C = 2. Top to bottom: G, F, A, D, B, C, E.
4. Boxes above B: G, F, A, D = 4.

Trick: Start from the extreme box (G at top) — it fixes the rest quickly.

Answer: (A) 4

Concept: Compare each letter of the first cluster with the matching letter of the second.

1. UX-ZS: U→Z $+5$, X→S $-5$. OR-TM: $+5$, $-5$. RU-WP: $+5$, $-5$.
2. LO-QI: L→Q $+5$ but O→I $-6$.

Trick: Write positions: L=12, O=15, Q=17, I=9 — the second gap breaks the pattern.

Answer: (C) LO-QI

Concept: Each term decreases by a constant amount.

1. $121-117.9=3.1$, $117.9-114.8=3.1$, … common difference $-3.1$.
2. Next $=108.6-3.1=105.5$.

Trick: Constant difference ⇒ arithmetic progression.

Answer: (A) 105.5

Concept: Track each letter position and the number separately.

1. 1st letters P, R, T, V, X (+2); 2nd K, I, G, E, C (−2); 3rd E, H, K, N, Q (+3).
2. Numbers 17, 10, 1, ?, −23: differences −7, −9, −11, −13 ⇒ $1-11=-10$.
3. Check: $-10-13=-23$ ✓.

Trick: Differences of the numbers themselves form an AP (−7, −9, −11…).

Answer: (B) VEN −10

Concept: Write the digits in ascending order and compare place by place.

1. Original: 4 5 1 2 6 8 9; Ascending: 1 2 4 5 6 8 9.
2. Matching places: 6, 8, 9 (5th, 6th, 7th).
3. So 3 digits keep their position.

Trick: Write both numbers one under the other and tick matching columns.

Answer: (A) Three

Concept: Find every pattern: number – symbol – symbol, and count the middle symbols.

1. 5 * $ → * qualifies (preceded by 5, followed by $).
2. 7 $ * → $ qualifies (preceded by 7, followed by *).
3. 3 & * → & qualifies. Others (e.g. 6 after @, 1 after %) fail.
4. Total = 3.

Trick: Scan only the places where a number is followed by a symbol, then check the next item.

Answer: (C) 3

Concept: Number positions 1 (top) to 7 (bottom).

1. Three above V ⇒ V = 4. One between F and V ⇒ F = 2 or 6.
2. Three between F and U with U above V: F = 2 gives U = 6 (below V ✗) ⇒ F = 6, U = 2; E just below U ⇒ E = 3.
3. W, G, X go to 1, 5, 7. W not next to F ⇒ W = 1; G above X ⇒ G = 5, X = 7.
4. Lowermost box = X.

Trick: Use the "U above V" condition to reject one case immediately.

Answer: (C) X

Concept: "Some A are B" can be converted to "Some B are A"; two "some" statements give no link between the outer terms.

1. II: "Some pants are sweaters" ⇒ "Some sweaters are pants" (conversion) ✓.
2. I: Pants and coats are linked only through some sweaters, which may be different ones ⇒ not definite ✗.

Yaad rakhein: Some + Some ⇒ no conclusion between the end terms.

Answer: (C) Only conclusion (II) follows.

Concept: Compare each letter of the first cluster with the matching letter of the second.

1. LO-HJ: L→H $-4$, O→J $-5$. PS-LN: $-4$, $-5$. IL-EG: $-4$, $-5$.
2. FI-BC: F→B $-4$ but I→C $-6$.

Trick: Positions: I=9, C=3 — a gap of 6, not 5.

Answer: (B) FI-BC

Concept: Compare each letter of the first cluster with the matching letter of the second.

1. TW-VY: $+2$, $+2$. RU-TW: $+2$, $+2$. AD-CF: $+2$, $+2$.
2. EH-GK: E→G $+2$ but H→K $+3$.

Trick: In the three alike pairs, the second cluster is also a "+3" pair like the first (V→Y); G→K is +4.

Answer: (D) EH-GK