Q&A: practice questions with answers

Concept: Compare the candidate with the master address part by part.

1. Enclave, road, city and PIN are the same in all four options – only the flat number differs.
2. MA: 8-2-145/C. (A) 146, (B) 135, (D) 9-2-… – mismatches. (C) matches exactly.

Trick: First find which block differs across options, and compare only that block.

Answer: (C) Flat No. 8-2-145/C, Laxmi Enclave, MG Road, Bhopal - 462011

Concept: Handle the issue calmly and privately, without disturbing the meeting.

1. Talking calmly after the meeting fixes the behaviour and keeps the relationship – (C).
2. (A) creates a public fight, (B) lets it continue, (D) over-reacts to a first incident.

Trick: Choose the option that is calm, private and solves the problem – it beats ignoring, fighting or escalating.

Answer: (C) After the meeting, talk peacefully and present your views.

Concept: Terms increase by a fixed amount.

1. 184 − 144 = 224 − 184 = 264 − 224 = 40.
2. Next = 264 + 40 = 304.

Trick: All terms end in 4 and the step 40 keeps the unit digit 4 – only 304 ends in 4.

Answer: (B) 304

Concept: 'All A are B' + 'X is A' ⇒ 'X is B'.

1. All Elite Club members have a Gold Card; Rahul is a member ⇒ Rahul has a Gold Card.
2. Rich (A) and president (C) are not stated; 'only Rahul' (D) is false – all members have one.

Trick: Reject any conclusion that adds new information or uses 'only'.

Answer: (B) Rahul has a gold card.

Concept: A rule for 'all doctors' applies to every doctor.

1. All doctors are registered; Seema is a doctor ⇒ Seema is registered.
2. Surgeon (A) and government hospital (C) are extra facts; (D) contradicts the statement.

Trick: Draw a circle 'Doctors' inside 'Registered'; Seema sits in Doctors, so she is automatically in Registered.

Answer: (B) Seema is registered with the Medical Council

Concept: Opposite moves of equal length cancel out.

1. 10 m North and 10 m South cancel.
2. Only 5 m East remains ⇒ Ram is East of home.

Trick: Net North–South = 10 − 10 = 0; net East–West = +5 ⇒ pure East.

Answer: (D) East

Concept: Letters move +2 and the number is halved.

1. KL→MN, 480→240 ✔; PQ→RS, 360→180 ✔; AB→CD, 500→250 ✔.
2. WX→YZ fits, but $420÷2=210$, not 215 ⇒ (D) is odd.

Trick: When letters all follow the same shift, check only the numbers – the odd number gives the answer fast.

Answer: (D) WX420 - YZ215

Concept: Letters move +2 and the number increases by 2.

1. NP→PR, 14→16 ✔; RT→TV, 20→22 ✔; HJ→JL, 11→13 ✔.
2. DF→FH fits, but 09 + 2 = 11, not 15 ⇒ (D) is odd.

Trick: Number difference: 2, 2, 2, 6 – the different gap is the odd one.

Answer: (D) DF09 - FH15

Concept: A word can be formed only if all its letters (with counts) exist in the main word.

1. COMMUNICATION has C, O, M, U, N, I, A, T – no S.
2. MUSICIAN needs S ⇒ cannot be formed. ACTION, UNION, COMMON are possible.

Trick: First scan options for a letter absent from the main word – here 'S' instantly kills MUSICIAN.

Answer: (C) MUSICIAN

Concept: Check every letter of each option against the main word.

1. DEMOCRACY letters: D, E, M, O, C, R, A, C, Y.
2. CAMEL needs L, which is missing ⇒ cannot be formed. CORE, MODE, RACE are possible.

Trick: Look for a 'foreign' letter: L is not in DEMOCRACY.

Answer: (D) CAMEL

Concept: $a^2+b^2=(a+b{)}^2-2ab$.

1. $a^2+b^2=131-2\times 8$
2. $=131-16=$ 115

Trick: Whenever $(a+b{)}^2$ and ab are given, just subtract 2ab – no need to find a and b.

Answer: (C) 115

Concept: $\text{Profit ratio}=\text{capital}\times \text{months}$.

1. $A:B=36000\times 12:24000\times (12-x)=2:1$
2. $36\times 12=2\times 24\times (12-x)\Rightarrow 432=48(12-x)$
3. $12-x=9\Rightarrow x=$ 3 months

Trick: Drop the thousands: $36\times 12:24\times t=2:1\Rightarrow t=9$ months of B's money, so B joined after $12-9=3$.

Answer: (B) 3 months

Concept: $\sec ({90}^{\circ }-\theta )=\csc \theta$, and ${\sin }^2\theta =1-{\cos }^2\theta$.

1. ${\cos }^2\theta =\frac{1}{2}\Rightarrow {\sin }^2\theta =1-\frac{1}{2}=\frac{1}{2}$.
2. ${\sec }^2({90}^{\circ }-\theta )={\csc }^2\theta =\frac{1}{{\sin }^2\theta }=2$.
3. Sum = $\frac{1}{2}+2=$ $\frac{5}{2}$.

Trick: ${\cos }^2\theta =\frac{1}{2}$ means $\theta ={45}^{\circ }$: ${\sin }^2{45}^{\circ }=\frac{1}{2}$, ${\csc }^2{45}^{\circ }=2$ ⇒ 2.5 directly.

Answer: (B) $\frac{5}{2}$

Concept: $A=P{(1+\frac{r}{100})}^n$.

1. ${(1+\frac{15}{100})}^2={\left(\frac{23}{20}\right)}^2=\frac{529}{400}$.
2. $P=26450\times \frac{400}{529}=50\times 400=$ ₹20,000 ($26450÷529=50$).

Trick: Check options: $20000\times 1.15=23000$, $\times 1.15=26450$ ✔ – back-calculation in 5 seconds.

Answer: (A) Rs. 20,000

Concept: Exterior angle = sum of the two interior opposite angles.

1. $\angle ACD=\angle BAC+\angle ABC={135}^{\circ }$.
2. $\angle BAC:\angle ABC=4:5\Rightarrow 9\text{ parts}={135}^{\circ }\Rightarrow 1\text{ part}={15}^{\circ }$.
3. $\angle BAC=4\times {15}^{\circ }=$ 60°.

Trick: Ratio 4 : 5 → total 9 parts; $135÷9=15$, answer must be a multiple of 15 – only 60° fits.

Answer: (B) 60°

Concept: Wine left = $x{(1-\frac{y}{x})}^n$, where x = capacity, y = quantity drawn each time, n = number of operations.

1. The operation is done 3 times in all: ${(1-\frac{5}{x})}^3=\frac{27}{64}={\left(\frac{3}{4}\right)}^3$.
2. $1-\frac{5}{x}=\frac{3}{4}\Rightarrow \frac{5}{x}=\frac{1}{4}\Rightarrow x=$ 20 litres.

Trick: Cube root of $\frac{27}{64}=\frac{3}{4}$ ⇒ each draw removes $\frac{1}{4}$ of the cask ⇒ $5\text{L}=\frac{1}{4}$ ⇒ 20 L.

Answer: (D) 20 litres

Concept: $x+\frac{1}{x}=2\Rightarrow x=1$.

1. $\tan \theta +\frac{1}{\tan \theta }=2\Rightarrow \tan \theta =1\Rightarrow \theta ={45}^{\circ }$.
2. $\sin {45}^{\circ }=\cos {45}^{\circ }=\frac{1}{\sqrt{2}}$.
3. ${\sin }^3\theta +{\cos }^3\theta =2\times \frac{1}{2\sqrt{2}}=$ $\frac{1}{\sqrt{2}}$.

Trick: 'Something + its reciprocal = 2' always means that something = 1.

Answer: (B) $\frac{1}{\sqrt{2}}$

Concept: Same direction: first meeting when the faster gains one full round.

1. Relative speed = $45-30=15$ m/s.
2. Time = $4500÷15=$ 300 s.

Trick: Same direction → subtract speeds; opposite direction → add speeds; then divide track length.

Answer: (C) 300 seconds

Concept: $(x+y{)}^2-(x-y{)}^2=4xy$.

1. With $x=\sqrt{7}$, $y=\sqrt{3}$: numerator = $4\times \sqrt{7}\times \sqrt{3}=4\sqrt{21}$.
2. Denominator = $\sqrt{7}\times \sqrt{3}=\sqrt{21}$.
3. Value = $4\sqrt{21}÷\sqrt{21}=$ 4.

Trick: $[(x+y{)}^2-(x-y{)}^2]÷xy$ is always 4 – for any x, y.

Answer: (D) 4

Concept: $\text{Area}=\frac{1}{2}\times (\text{sum of parallel sides})\times \text{height}$.

1. Sum = $9.4+11.8=21.2$ cm; half = 10.6.
2. Area = $10.6\times 8.5=$ 90.1 cm².

Trick: $10.6\times 8.5=10.6\times 8+10.6\times 0.5=84.8+5.3=90.1$.

Answer: (B) $90.1{\mathrm{cm}}^2$