Q&A: practice questions with answers

Concept: Take the LCM and use ${\sin }^2\theta +{\cos }^2\theta =1$.

1. Sum $=\frac{{\sin }^2\theta +(1-\cos \theta {)}^2}{\sin \theta (1-\cos \theta )}$.
2. Numerator $={\sin }^2\theta +1-2\cos \theta +{\cos }^2\theta =2-2\cos \theta =2(1-\cos \theta )$.
3. Sum $=\frac{2}{\sin \theta }=2cosec\theta$.

Trick: Put $\theta ={90}^{\circ }$: $\frac{1}{1}+\frac{1}{1}=2$, and only $2cosec{90}^{\circ }=2$ among the options.

Answer: (B) $2cosec\theta$

Concept: $\text{SP}=\text{MP}\times \frac{100-\text{Discount}\%}{100}$.

1. $\text{SP}=620\times \frac{85}{100}$.
2. $=527$.

Trick: $10\%$ of 620 $=62$, $5\%=31$; discount $=93$, so $620-93=527$.

Answer: (B) ₹527

Concept: To test a number $n$, check divisibility by primes up to $\sqrt{n}$.

1. 71, 31 and 61 have no prime factor up to their square roots — they are prime.
2. $91=7\times 13$, so 91 is composite.

Yaad rakhein: 91 looks prime but is $7\times 13$; similar traps: $51=3\times 17$, $87=3\times 29$.

Answer: (C) 91

Concept: The difference of ratio parts equals the actual age difference.

1. Ratio $5:8$, difference $=8-5=3$ parts.
2. $3$ parts $=3$ years, so $1$ part $=1$ year.
3. Surya $=8\times 1=8$ years.

Trick: Here 1 part = 1 year, so the ratio terms are the ages themselves (5 and 8).

Answer: (C) 8 years

Concept: Successive increase of $r\%$ for $n$ years: $\text{Final}=P{(1+\frac{r}{100})}^n$.

1. 2019 to 2021 is 2 years.
2. Income $=21000\times {\left(\frac{11}{10}\right)}^2=21000\times 1.21$.
3. $=25410$.

Trick: Two $10\%$ increases $=21\%$: $21000+4410=25410$.

Answer: (C) ₹25,410

Concept: $\text{CP}=\frac{\text{SP}\times 100}{100\pm \text{rate}}$ (+ for profit, − for loss).

1. Shirt: $\text{CP}=\frac{960\times 100}{96}=1000$, loss $=40$.
2. Sweater: $\text{CP}=\frac{840\times 100}{120}=700$, profit $=140$.
3. Net $=140-40=100$ profit.

Trick: Compare totals: CP $=1700$, SP $=1800$, so profit ₹100.

Answer: (D) Profit, ₹100

Concept: Use alphabet positions and find the rule between the pairs.

1. TO-RM-PQ: T(20)→R(18)→P(16) is $-2$ each; O(15)→M(13) is $-2$, M(13)→Q(17) is $+4$.
2. WR-UP-ST: W→U→S is $-2$; R→P is $-2$, P→T is $+4$.
3. UP-SN-QR: U(21)→S(19)→Q(17) is $-2$; P(16)→N(14) is $-2$, N(14)→R(18) is $+4$ ✓.

Trick: First letters fall by 2; second letters go $-2$ then $+4$.

Answer: (C) UP-SN-QR

Concept: Swap the signs first, then solve using BODMAS.

1. Swap × ↔ − and + ↔ ÷: $15-5\times 56÷28+3$.
2. $56÷28=2$, then $5\times 2=10$.
3. $15-10+3=8$.

Trick: Rewrite the whole expression after swapping before calculating anything.

Answer: (B) 8

Concept: Facing the centre, “left” means moving clockwise and “right” means anticlockwise.

1. Fix E; B is third to the left of E.
2. Only E sits between K and F, so K and F are E’s neighbours. F second to the left of C works only when F is to E’s right and K to E’s left.
3. D is not next to B, so D sits between C and F, and G between K and B.
4. Order to the right of G: K, E, then F — two people between G and F.

Trick: Draw the circle and place the fixed person first; test both cases for “only E between K and F”.

Answer: (A) Two

Concept: Check the gaps between alphabet positions (wrap around after Z).

1. YFM: Y(25)→F(6)→M(13) is $+7,+7$ (wrapping after Z).
2. GNU: 7→14→21 is $+7,+7$; KRY: 11→18→25 is $+7,+7$.
3. BGT: 2→7→20 is $+5,+13$ — different.

Trick: Gap of 7 each time: G-N-U, K-R-Y, Y-F-M.

Answer: (C) BGT

Concept: Position from left $=$ total $-$ position from right $+1$.

1. Drisha from left $=19-17+1=3$rd.
2. Vani is 9th from left.
3. People between $=9-3-1=5$.

Trick: Convert both to the same end, then between $=$ difference $-1$.

Answer: (D) 5

Concept: Replace letters with signs, then use BODMAS.

1. A = ×, B = ÷, C = +, D = −.
2. $12-15÷3+6\times 5$.
3. $=12-5+30=37$.

Trick: Do ÷ and × first: $15÷3=5$, $6\times 5=30$.

Answer: (C) 37

Concept: Test each option and find one rule that fits both pairs.

1. Try $X=12$, $Y=81$: $12\times 9=108$ and $9\times 9=81$ ✓.
2. Rule: second number $=$ first $\times 9$.
3. Other options fail, e.g. $9\times 9\ne 126$ and $14\times 9\ne 108$.

Trick: Factor the given number: $108=12\times 9$ hints at “multiply by 9”.

Answer: (C) X = 12, Y = 81

Concept: Track each letter position separately.

1. 1st letters: V, T, R, P, N (each $-2$).
2. 2nd letters: Y, W, U, S, Q (each $-2$).
3. 3rd letters: R, P, N, L, J (each $-2$).

Trick: Every letter moves back by 2, so PSL → NQJ.

Answer: (B) NQJ

Concept: Decode each symbol step by step and draw a family tree.

1. X − Y: X is the son of Y.
2. Y × Z: Y is the husband of Z.
3. Z + A: Z is the mother of A, so A is also a child of Y and Z.
4. A ÷ B: A is the brother of B, so A is male; X and A are both sons of Y and Z.

Trick: Gender comes from “brother”: A is male, so A is X’s brother.

Answer: (C) Brother

Concept: Compare the matching letters of the two clusters in each pair.

1. First letters: V→T, I→G, L→J, R→P (all $-2$).
2. Second letters: Q(17)→X(24), D(4)→K(11), M(13)→T(20) are $+7$.
3. LG-JM: G(7)→M(13) is only $+6$ — odd one.

Trick: Also inside each cluster the gap is 5 (VQ, ID, LG, RM); the break is in the second cluster.

Answer: (C) LG-JM

Concept: Count positions carefully from the required end.

1. From the left: 5, 5, 4, 1, 6, 2, 7, 3, 8, 7, 4, 6 → 12th digit is 6.
2. From the right: 3, 7 → 2nd digit is 7.
3. Sum $=6+7=13$.

Trick: Mark digits in groups of 5 while counting to avoid slips.

Answer: (A) 13

Concept: “All A are B” always gives “Some B are A”; negative statements do not pass through to the bigger set.

1. All belts are watches → some watches are belts, so II follows.
2. No belt is a tie, but watches outside belts may or may not be ties.
3. So “No watch is a tie” is not certain — I does not follow.

Yaad rakhein: Conversion of “All A are B” = “Some B are A” — always true.

Answer: (B) Only conclusion II follows

Concept: Compare sentences with common words to match common codes.

1. “Are” is in sentences 1 and 2; common code Mi → Are = Mi.
2. “Happy” is in sentences 1 and 3; common code Bi → Happy = Bi.
3. In “We Are Happy” = Bi Hi Mi, the remaining word We = Hi.

Trick: Eliminate known codes one by one; the leftover is the answer.

Answer: (D) Hi

Concept: Count from each end as asked and add.

1. From the left: 9, 3, 9 → 3rd digit is 9.
2. From the right: 3, 5, 2 → 3rd digit is 2.
3. Sum $=9+2=11$.

Trick: For counting from the right, read the series backwards from the last digit.

Answer: (C) 11