Q&A: practice questions with answers

Concept: Apply successive percentage changes as multipliers.

1. After 30% discount: $8000\times 0.70=5600$
2. Add 12% tax: $5600\times 1.12=6272$

Trick: Net factor $0.7\times 1.12=0.784$ → $8000\times 0.784=6272$.

Answer: (D) ₹6,272

Concept: $1-2{\sin }^{2}A=\cos 2A=2{\cos }^{2}A-1$ and $\sqrt{{\csc }^{2}A-1}=\cot A$.

1. $\frac{\sin A(1-2{\sin }^{2}A)}{\cos A(2{\cos }^{2}A-1)}=\frac{\sin A\cos 2A}{\cos A\cos 2A}=\tan A$
2. $\sqrt{{\csc }^{2}A-1}=\cot A$
3. $\tan A+\cot A=\frac{{\sin }^{2}A+{\cos }^{2}A}{\sin A\cos A}=\sec A\csc A$

Trick: Put $A={45}^{\circ }$: first part undefined, so try $A={30}^{\circ }$: $\frac{1}{\sqrt{3}}+\sqrt{3}=\frac{4}{\sqrt{3}}$ = $\sec {30}^{\circ }\csc {30}^{\circ }=\frac{2}{\sqrt{3}}\times 2$ ✓.

Answer: (A) $\sec A\csc A$

Concept: Square: perimeter $=4a$, area $=a^2$.

1. $a=\frac{248}{4}=62$ m
2. Area $={62}^2=3844{\text{m}}^2$

Trick: ${62}^2={60}^2+2\times 60\times 2+2^2=3600+240+4=3844$; a square of a number ending in 2 must end in 4.

Answer: (D) 3844

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

1. $1020:1440:1230=102:144:123$, sum $=369$.
2. Rahul’s share $=1260\times \frac{123}{369}=1260\times \frac{1}{3}=420$

Trick: $1230$ is exactly one-third of the total $3690$ → share $=\frac{1260}{3}$.

Answer: (A) ₹420

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

1. Sum $=40+49+56+73+39=257$
2. Average $=\frac{257}{5}=51.4$ kg

Trick: Deviations from 50: $-10,-1,+6,+23,-11$ → total $+7$ → $50+\frac{7}{5}=51.4$.

Answer: (A) 51.4

Concept: Increasing by 100% means the number becomes double.

1. $x\times \frac{200}{100}=2700$
2. $x=\frac{2700}{2}=1350$

Trick: +100% = ×2, so just halve the result.

Answer: (A) 1350

Concept: If SP of x articles = CP of y articles, then $\text{loss}\%=\frac{x-y}{x}\times 100$ (when $x>y$).

1. SP of 50 = CP of 5; let CP of 1 book = ₹1 → CP of 50 = ₹50, SP of 50 = ₹5.
2. Loss $=50-5=45$ → $\text{loss}\%=\frac{45}{50}\times 100=90\%$

Trick: $\frac{50-5}{50}\times 100=90\%$; SP is smaller than CP, so it is a loss.

Answer: (A) 90% loss

Concept: Eliminate using quick rules, then check the remaining divisor.

1. Ends in 1 → not divisible by 25; odd → not by 28 or 18.
2. $159916901÷19=8416679$ exactly ($19\times 8416679=159916901$).

Trick: Odd number → all even divisors out; 25 needs the last two digits 00, 25, 50 or 75. Only 19 remains.

Answer: (B) 19

Concept: Profit ratio = (capital × time) ratio.

1. $M+N=4896$, $M-N=288$ → M’s share $=2592$, N’s share $=2304$; ratio $=9:8$.
2. Let N’s capital $=x$: $\frac{3(x+70000)}{5x}=\frac{9}{8}$
3. $24x+1680000=45x\Rightarrow x=80000$
4. M’s capital $=80000+70000=150000$

Trick: Check option (A): $3\times 150000:5\times 80000=450000:400000=9:8$ ✓.

Answer: (A) ₹1,50,000

Concept: LCM takes the highest power of each factor appearing in the numbers.

1. Highest power of 3: $3^3$; of 8: $8^3$.
2. Highest power of 14: ${14}^2$; of 19: ${19}^2$.
3. LCM $=3^3\times 8^3\times {14}^2\times {19}^2$ (in primes $2^{11}\times 3^3\times 7^2\times {19}^2$ – the same value).

Trick: LCM = highest powers, HCF = lowest powers – only option D has every highest power.

Answer: (D) $3^3\times 8^3\times {14}^2\times {19}^2$

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

1. QM-RO: Q+1=R, M+2=O. SO-TQ: S+1=T, O+2=Q. WS-XU: W+1=X, S+2=U.
2. UQ-VR: U+1=V but Q+1=R (not +2).

Trick: In the three alike pairs the first letters differ by 4 in cluster 1 and by 3 in cluster 2; in UQ-VR both differ by 4.

Answer: (A) UQ-VR

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

1. I: Marks touch Painting only through possibility – no definite link, so “Some marks are painting” does not follow.
2. II: “Some marks are tattoo” converts to “Some tattoo are mark” – follows.

Yaad rakhein: “Some A are B” always gives “Some B are A”.

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

Concept: Common letters in two words get the common digits.

1. DRUM = 2194, CURD = 4592.
2. Common letters D, R, U ↔ common digits 2, 9, 4.
3. Left: M (DRUM) = 1 and C (CURD) = 5.

Trick: Strike out the shared letters and shared digits – the leftover pair gives the answer.

Answer: (B) 5

Concept: Check the differences between consecutive terms.

1. $316-28=288$, $288-26=262$, $262-24=238$, $238-22=216$
2. Next difference 20: $216-20=196$

Trick: Subtractions decrease by 2 each time: 28, 26, 24, 22, 20.

Answer: (C) 196

Concept: Total $=$ (position from right) $+$ (position from left) $-1$ for the same person.

1. Mukul 5th, Alok 10th from right; Alok is exactly in the middle → Rohan is $10+5=15$th from right.
2. Rohan is 6th from left.
3. Total $=15+6-1=20$

Trick: The gap Mukul→Alok (5 places) repeats Alok→Rohan.

Answer: (A) 20

Concept: Differences form a doubling pattern.

1. Differences: 3, 6, 12, 24 (each ×2).
2. Next difference $=48$ → $52+48=100$

Trick: Each term $=2\times \text{previous}-4$: $2\times 52-4=100$.

Answer: (C) 100

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

1. TALK = 5327, LINE = 6143.
2. Common letter: L. Common digit: 3.
3. So L = 3.

Trick: One common letter ↔ one common digit – no need to decode the rest.

Answer: (D) 3

Concept: Replace the letters by signs, then follow BODMAS.

1. $(63\times 2)-(24\times 3)+(98÷2)-(48÷3)-3$
2. $=126-72+49-16-3$
3. $=84$

Trick: Brackets first: 126, 72, 49, 16 – then add/subtract left to right.

Answer: (B) 84

Concept: Find the position rule from 1st to 2nd cluster and from 1st to 3rd cluster.

1. SAIN → ANIS: letters in order 2, 4, 3, 1 (A N I S). COIN → ONIC: same.
2. 3rd cluster = 1st written in reverse: SAIN → NIAS, COIN → NIOC.
3. MILE → (2,4,3,1) IELM; reverse → ELIM. Matches option C.

Trick: First check the easy rule (3rd = reverse of 1st): only MILE-ELIM and YOUR-RUOY pass; then the middle term decides.

Answer: (C) MILE - IELM - ELIM

Concept: Look for the pattern Number – Symbol – Symbol and count the middle symbols.

1. 1 & & → ✓
2. 2 ^ ^ → ✓
3. 4 & # → ✓
4. 5 ^ 6, 6 ^ 4 → followed by a number ✗; 6 @ → nothing after ✗.

Trick: Scan only the numbers and look at the next two positions – faster than checking every symbol.

Answer: (D) Three