Q&A: practice questions with answers

Concept: Rule for 7, 11, 13: make groups of three digits from the right and take the alternating sum; if it is divisible by 13, so is the number.

1. The number is odd ⇒ not divisible by 12 or 18.
2. Groups: 788 | 973 | 289 ⇒ $289-973+788=104$
3. $104=13\times 8$ ⇒ divisible by 13 (but $104÷7$ is not exact, so not by 7)

Trick: $7\times 11\times 13=1001$ – the three-digit alternating-sum test works for all three.

Answer: (C) 13

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

1. $SI=\frac{400\times 8\times 4.5}{100}$
2. $=4\times 8\times 4.5=144$

Trick: Yearly interest $=8\%$ of 400 $=32$; $32\times 4.5=144$.

Answer: (C) 144

Concept: Profit = Selling price of the unbroken items − Total cost price.

1. Unbroken tube lights $=56-20=36$
2. SP $=36\times 4.60=165.60$
3. Profit $=165.60-56=109.60$

Trick: Broken items add to cost but earn nothing – always subtract them before computing SP.

Answer: (C) ₹109.60

Concept: Volume of a sphere $=\frac{4}{3}\pi r^3$, radius = half the diameter.

1. $r=\frac{10}{2}=5\text{m}$
2. $V=\frac{4}{3}\times 3.141\times 125$
3. $V=\frac{1570.5}{3}=523.5{\text{m}}^3$

Trick: With $d$ given: $V=\frac{\pi d^3}{6}=\frac{3.141\times 1000}{6}=523.5$.

Answer: (B) 523.5 cubic metre

Concept: One-day work adds up: $\frac{1}{A}+\frac{1}{B}+\frac{1}{C}=\frac{1}{\text{together}}$.

1. $\frac{1}{C}=\frac{1}{3}-\frac{1}{16}-\frac{1}{11}$
2. LCM 528: $\frac{176-33-48}{528}=\frac{95}{528}$
3. C alone $=\frac{528}{95}=5\frac{53}{95}$ days

Trick: C must take more than 3 days but be fastest of the three (A, B are slow), so the answer is just above 5.

Answer: (C) $5\frac{53}{95}$ days

Concept: Expand each bracket and combine like terms.

1. $4(\frac{3}{4}{x}^2-26x+17)=3x^2-104x+68$
2. $-3(x^2+4x-14)=-3x^2-12x+42$
3. Sum: $(3-3)x^2+(-104-12)x+(68+42)=-116x+110$

Trick: The $x^2$ terms cancel; check the constant: $68+42=110$ (positive).

Answer: (A) $-116x+110$

Concept: Write present ages from the past condition, then form the future condition.

1. Let son = $S$, father = $F$ now. $F-7=2(S-7)+13\Rightarrow F=2S+6$
2. After $n$ years: $F+n=2(S+n)$
3. $2S+6+n=2S+2n\Rightarrow n=6$

Trick: Father is "2 × son + 6" now; the extra 6 years is exactly the time needed for "twice".

Answer: (D) 6

Concept: Number to add = divisor − remainder.

1. $57846÷58$: $58\times 997=57826$, remainder $=20$
2. Add $58-20=38$
3. $57846+38=57884=58\times 998$ ✓

Trick: Smallest number to ADD = divisor − remainder; to SUBTRACT = remainder.

Answer: (A) 38

Concept: For a fixed distance, speed is inversely proportional to time.

1. Distance $=95\times 10=950\text{km}$
2. Required speed $=\frac{950}{5}=190\text{km/h}$

Trick: Time halved ⇒ speed doubled: $2\times 95=190$.

Answer: (A) 190 km/hr

Concept: Solve innermost brackets first: ( ) → { } → [ ].

1. $(7-3)=4$, $2\times 4=8$
2. $\{30+8\}=38$
3. $836÷38=22$

Trick: Check: $38\times 22=836$.

Answer: (C) 22

Concept: Look at the differences between consecutive terms.

1. Differences: $21-12=9$, $40-21=19$, $69-40=29$, $108-69=39$
2. Differences increase by 10; next difference $=49$
3. $108+49=157$

Trick: Differences 9, 19, 29, 39, 49 – all end in 9.

Answer: (A) 157

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

1. Three boxes below G ⇒ G at 4.
2. Two boxes between G and F ⇒ F at 1 or 7. Only B is above D ⇒ B = 7, D = 6, so F = 1.
3. C below E below A in the free slots 2, 3, 5 ⇒ C = 2, E = 3, A = 5.
4. Above A: D and B ⇒ two boxes.

Trick: "Only X is above Y" fixes X at the top and Y just below it.

Answer: (B) Two

Concept: Track each letter position separately.

1. 1st letters: U, S, Q, O → each −2 → M
2. 2nd letters: W, U, S, Q → −2 → O
3. 3rd letters: Z, X, V, T → −2 → R

Trick: Every letter moves back by 2, so just subtract 2 from OQT.

Answer: (C) MOR

Concept: A word common to two sentences gets the code common to both.

1. Common word in both sentences: "window".
2. Common code in "mb tb jb" and "lk mb fb": "mb".
3. So window = mb.

Trick: Match common words with common codes.

Answer: (A) mb

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

1. Triangle and Square both lie inside Rectangle, but they need not touch each other ⇒ I does not follow.
2. All squares are rectangles ⇒ some rectangles are squares ⇒ II follows.

Trick: "All A are B" always gives "Some B are A" (conversion).

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

Concept: Decode the expression step by step and build a family tree.

1. E $ F: E is the son of F (E is male).
2. F @ G: F is the wife of G ⇒ E is a son of G too.
3. G ÷ M: G is the father of M; M + N: M is the brother of N ⇒ N is also a child of G.
4. E (male) and N have the same parents ⇒ E is the brother of N.

Trick: The relation asked is of the first person: E’s gender is fixed by "son", so the answer is Brother.

Answer: (D) Brother

Concept: Track each letter position; letters wrap around after A (A − 1 = Z).

1. 1st letters: G, A, U, O → each −6 → I
2. 2nd letters: M, G, A, U → −6 → O
3. 3rd letters: R, L, F, Z → −6 → T

Trick: Moving back 6 from A: A→Z→Y→X→W→V→U.

Answer: (D) IOT

Concept: Check every symbol: the element just before must be odd and the element just after must NOT be even.

1. 3 * 8: after is 8 (even) ✗
2. 9 $ 1: after is 1 (odd) ✓
3. 1 & 5: after is 5 (odd) ✓
4. 5 Ω 6 ✗ (6 even); 7 % 4 ✗ (4 even)

Trick: First list "odd–symbol" spots, then strike out those followed by an even digit.

Answer: (C) Two

Concept: Find the position rearrangement in the given triads and apply it to the options.

1. ROAM (1234) → MORA = 4, 2, 1, 3; MORA → OARM = 2nd, 4th, 3rd, 1st letters.
2. Check CRIB → BRCI (4213) → RICB (2431) ✓
3. FUME → EUFM (4213) → UMFE (2431) ✓

Trick: Write position numbers under the first word and read the new order.

Answer: (B) FUME – EUFM – UMFE

Concept: Use alphabet positions within each cluster and across the pair.

1. KN: +3; GI: +2; K→G −4. SV-OQ and OR-KM follow the same (+3, +2, −4).
2. VY: +3 but RS: R→S is +1 (not +2).
3. So VY-RS is the odd one.

Trick: Second cluster gap (+2) is the quickest check.

Answer: (D) VY-RS