Q&A: practice questions with answers

Concept: Mode is the value that occurs most often.

1. Frequencies: 19 → 3 times, 11 → 2 times, others once.
2. Highest frequency is for 19.

Trick: Just count repeats – no calculation needed.

Answer: (A) 19

Concept: Take CP $=x$; apply the markup and the discount one after the other.

1. $\text{LP}=1.5x$
2. $\text{SP}=1.5x\times 0.7=1.05x$, so profit $=0.05x$
3. $0.05x=91\Rightarrow x=1820$
4. $\text{LP}=1.5\times 1820=2730$

Trick: Net effect of +50% and −30%: $50-30-\frac{50\times 30}{100}=5\%$ profit.

Answer: (C) 2,730

Concept: Check each divisor with its divisibility rule.

1. Last digit is 5 (odd) → not divisible by 2; divisible by 5 ✔
2. Digit sum $=2+4+5+0+1+5=17$ → not divisible by 3, hence not by 15
3. For 11: $(5+0+4)-(1+5+2)=1$ → not divisible by 11

Yaad rakhein: A number ending in 0 or 5 is always divisible by 5.

Answer: (D) 5

Concept: Third proportional of $a$ and $b$ is $x$ where $a:b=b:x$, i.e. $x=\frac{b^2}{a}$.

1. $x=\frac{{51}^2}{9}$
2. $=\frac{2601}{9}=289$

Trick: $\frac{51}{9}=\frac{17}{3}$, so $x=51\times \frac{17}{3}=17\times 17=289$.

Answer: (D) 289

Concept: Successive discounts multiply: $\text{SP}=\text{MP}\times \frac{100-d_1}{100}\times \frac{100-d_2}{100}$.

1. $4500\times 0.75=3375$
2. $3375\times 0.8=2700$

Trick: 25% and 20% together $=25+20-\frac{25\times 20}{100}=40\%$ off: $0.6\times 4500=2700$.

Answer: (A) 2,700

Concept: Compare cost and selling price of one pen: $\text{Profit}\%=\frac{\text{SP}-\text{CP}}{\text{CP}}\times 100$.

1. CP of one pen $=\frac{150}{12}=12.5$
2. SP $=44$, profit $=31.5$
3. $\text{Profit}\%=\frac{31.5}{12.5}\times 100=252\%$

Trick: Compare per dozen: SP $=44\times 12=528$ vs CP 150 → profit 378, $\frac{378}{150}\times 100=252$.

Answer: (D) 252

Concept: Surface area of a sphere $=4\pi r^2$.

1. $4\times 3.14\times 6^2$
2. $=12.56\times 36=452.16{\text{cm}}^2$

Trick: $4\pi r^2=4\times 113.04$: area of one great circle ($\pi r^2=113.04$) taken four times.

Answer: (C) 452.16 ${\text{cm}}^2$

Concept: Literate females = total literates − literate males.

1. Total literates $=0.78\times 374000=291720$
2. Literate males $=0.72\times 170000=122400$
3. Females $=204000$; literate females $=169320$
4. $\frac{169320}{204000}\times 100=83\%$

Trick: Alligation: males 170 and females 204 (ratio 5 : 6) mix to 78%; $\frac{78-72}{f-78}=\frac{6}{5}\Rightarrow f=83$.

Answer: (B) 83%

Concept: Same distance, so $\text{Distance}=\text{Speed}\times \text{Time}$ is common to both.

1. Distance $=140\times 13=1820\text{km}$
2. Malaika's time $=\frac{1820}{65}=28$ hours

Trick: For equal distance, time ∝ $\frac{1}{\text{speed}}$: $13\times \frac{140}{65}=13\times \frac{28}{13}=28$.

Answer: (D) 28 hours

Concept: For equal time, profit is shared in the ratio of investments.

1. Ratio $=1310:1350:1140=131:135:114$, total $=380$
2. Dev's share $=\frac{114}{380}\times 1630$
3. $=0.3\times 1630=489$

Trick: $\frac{114}{380}=\frac{3}{10}$ exactly – Dev gets 30% of the profit.

Answer: (C) ₹489

Concept: Look at the differences between consecutive terms.

1. Differences: 4, 9, 16, 25 = $2^2,3^2,4^2,5^2$
2. Next difference $=6^2=36$
3. $81+36=117$

Trick: Slowly growing gaps that are perfect squares → add the next square.

Answer: (D) 117

Concept: Decode each symbol and draw the family tree.

1. E @ F: E is the wife of F
2. F $ G: F is the son of G (F is male)
3. G ÷ M: G is the father of M; M + N: M is the brother of N
4. So F and N are both children of G – F is N's brother; E is F's wife

Trick: Wife of a sibling's brother = brother's wife (bhabhi).

Answer: (B) Brother's wife

Concept: Compare letters at the same position in successive clusters.

1. W→B, B→G, G→L: +5 each time
2. V→A→F→K: +5; H→M→R→W: +5
3. Next: L+5=Q, K+5=P, W+5=B → QPB

Trick: First two letters are always consecutive in reverse (WV, BA, GF, LK → QP).

Answer: (A) QPB

Concept: Compare the first letter of each cluster with the first letter of the pair, and second with second.

1. PT-KQ: P−5=K, T−3=Q
2. JN-EK: J−5=E, N−3=K; MQ-HN: M−5=H, Q−3=N
3. SW-NU: S−5=N but W−2=U ✘

Trick: Write positions (P16, T20, K11, Q17) – the pattern $-5,-3$ shows up quickly.

Answer: (D) SW-NU

Concept: Two 'All' statements with a common predicate give no definite link between the subjects.

1. Letters and Schedules are both inside Mails but need not overlap → (I) does not follow.
2. All schedules are mails, so some mails are schedules → (II) follows.

Yaad rakhein: 'All A are B' always implies 'Some B are A'.

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

Concept: Find the rule linking the middle number to the outer numbers: here middle $=3\times \text{first}+\text{third}-1$.

1. (16, 63, 16): $3\times 16+16-1=63$ ✔; (36, 111, 4): $108+4-1=111$ ✔
2. (47, 144, 4): $141+4-1=144$ ✔
3. Others: $144+15-1=158\ne 162$, $132+20-1=151\ne 155$, $3+6-1=8\ne 12$

Trick: Test the rule on both given sets before checking options.

Answer: (A) (47, 144, 4)

Concept: Replace letters by signs, then use BODMAS.

1. $48-14\times 3+27÷3$
2. $=48-42+9$
3. $=15$

Trick: Do × and ÷ first: 42 and 9; then $48-42+9$.

Answer: (C) 15

Concept: Check the gaps between consecutive letters (wrap Z→A).

1. RXCJ: R+6=X, X+5=C, C+7=J
2. OUZG: +6, +5, +7; KQVC: +6, +5, +7
3. NTYE: N+6=T, T+5=Y, Y+6=E ✘ (should be F)

Trick: Use positions R18, X24, C3(=29), J10(=36) to see the gaps.

Answer: (D) NTYE

Concept: Find the shift for each position from the given pair.

1. BGLY→DJNB: +2, +3, +2, +3
2. Check JSTK→LVVN: +2, +3, +2, +3 ✔
3. PBZT: P+2=R, B+3=E, Z+2=B, T+3=W → REBW

Trick: Alternate +2, +3 pattern; remember Z+2 wraps to B.

Answer: (C) REBW

Concept: Facing north, left = west end. Fix the certain positions first.

1. Only J is left of O → J at 1, O at 2
2. Four people between J and I → I at 6
3. M-K-N block in 3–5; M not next to I → M 3, K 4, N 5
4. L takes the last seat 7

Trick: 'Only X sits to the left of Y' instantly fixes X at the extreme left and Y second.

Answer: (B) L