Q&A: practice questions with answers

Concept: $\text{Savings}=\text{Income}-\text{Expenditure}$; take income $=100$.

1. Old: income $100$, expenditure $75$, savings $25$.
2. New: income $120$, expenditure $75\times 1.1=82.5$.
3. New savings $=120-82.5=37.5$.
4. Increase $=\frac{37.5-25}{25}\times 100=50\%$.

Trick: Assume income $=100$ in every income–expenditure–savings question.

Answer: (A) 50%

Concept: For equal distances, average speed $=\frac{2xy}{x+y}$.

1. $x=30$, $y=60$ km/h.
2. Average speed $=\frac{2\times 30\times 60}{30+60}=\frac{3600}{90}=40$ km/h.

Trick: Check: total distance $180$ km, time $3+1.5=4.5$ h, $\frac{180}{4.5}=40$.

Answer: (C) 40 km/h

Concept: List the primes between 61 and 100.

1. Primes: $61,67,71,73,79,83,89,97$.
2. Second smallest $=67$, second greatest $=89$.
3. Sum $=67+89=156$.

Yaad rakhein: Primes from 61 to 100 are 8 in number: 61, 67, 71, 73, 79, 83, 89, 97.

Answer: (D) 156

Concept: If $a,b,c,d$ are in proportion, $a\times d=b\times c$.

1. $12\times y=24\times 45$.
2. $y=\frac{1080}{12}=90$.

Trick: $\frac{24}{12}=2$, so $y=2\times 45=90$.

Answer: (D) 90

Concept: Equivalent single discount for $a\%$ and $b\%$ $=a+b-\frac{ab}{100}$.

1. $12+15-\frac{12\times 15}{100}$.
2. $=27-1.8=25.2\%$.

Trick: Price after both $=0.88\times 0.85=0.748$, so discount $=25.2\%$.

Answer: (D) 25.2%

Concept: Test each option: the same operation must link both pairs.

1. Option (B): $15+3.8=18.8$.
2. $21+3.8=24.8$ – same rule.
3. Others fail, e.g. (A): $20\to 18.8$ is $-1.2$ but $21\to 26.8$ is $+5.8$.

Trick: In X–Y options, find the difference for each pair; the option with equal changes wins.

Answer: (B) X = 15, Y = 24.8

Concept: Replace the symbols as given, then apply BODMAS.

1. $16÷96\times 6-4+20$ becomes $16+96÷6\times 4-20$.
2. $96÷6=16$, $16\times 4=64$.
3. $16+64-20=60$.

Trick: Write the decoded expression fully before calculating – most mistakes come from half-converted signs.

Answer: (A) 60

Concept: Check the differences between consecutive terms.

1. Differences: $3,6,9,12$ – multiples of 3.
2. Next difference $=15$.
3. Next term $=47+15=62$.

Trick: Second-level difference is constant ($+3$), so add the next multiple of 3.

Answer: (D) 62

Concept: All face north, so their right is our right. Fix sure positions first.

1. Two people to the right of Q: Q at position 5; P (immediate left) at 4.
2. Two people between Q and B: B at 2.
3. Two between F and P: F at 1 or 7. R–E must sit together; only F at 1 leaves 6–7 free, so R at 6, E at 7.
4. A takes the last seat, position 3.

Trick: Place the person with a fixed count (Q) first, then build around him.

Answer: (C) A

Concept: Decode A = ÷, B = ×, C = +, D = − and solve each option with BODMAS.

1. Option (D): $96-12\times 2+(42÷6)\times 3+20$.
2. $=96-24+7\times 3+20$.
3. $=96-24+21+20=113$.

Trick: Start with the option whose bracket gives a clean value ($42÷6=7$) – fewer steps to test.

Answer: (D) 96 D 12 B 2 C (42 A 6) B 3 C 20

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

1. M at 2; P below M, so P at 1.
2. Three boxes between M and B: B at 6.
3. Only E between B and F: E at 5, F at 4 (above B is impossible – no position 8).
4. A above B: A at 7; L takes 3. Between L (3) and P (1): only M – one box.

Trick: Draw the stack vertically and number it from the bottom – 'second from bottom' becomes position 2.

Answer: (A) One

Concept: Find the gaps between letters using their positions.

1. FHK: $F(6)\to H(8)\to K(11)$, gaps $+2,+3$.
2. UWZ: $21\to 23\to 26$, gaps $+2,+3$; PRU: $16\to 18\to 21$, gaps $+2,+3$.
3. JLP: $10\to 12\to 16$, gaps $+2,+4$ – different.

Trick: Learn EJOTY ($5,10,15,20,25$) to get letter positions quickly.

Answer: (C) JLP

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

1. 'someday in paradise' → yd pl ws.
2. 'in dense forest' → fc ws nm.
3. Common word 'in', common code 'ws'.

Trick: Match common words with common codes – no need to decode the rest.

Answer: (D) ws

Concept: Arrange the letters alphabetically and compare position by position.

1. Original: A R T I C L E.
2. Sorted: A C E I L R T.
3. Same position: A (1st) and I (4th) – 2 letters.

Trick: Write both words one under the other and tick the matching columns.

Answer: (B) 2

Concept: Draw the least-overlap Venn diagram and test each conclusion.

1. All shirts are pants – the shirts circle lies inside pants.
2. I: Some pants are shirts – true (conversion of 'All'). Follows.
3. II: Tie touches pants, not necessarily shirts – does not follow.

Trick: 'All A are B' always gives 'Some B are A'; a 'Some' link through B does not reach A.

Answer: (B) Only conclusion I follows

Concept: An effect must be a direct, logical response to the cause.

1. I: Recording entries/exits and verifying delivery staff directly targets thefts – valid.
2. II: Installing CCTV cameras is a direct anti-theft step – valid.
3. III: Appointing more women constables has no link to bicycle thefts – not valid.

Trick: Ask 'Would this happen because of the cause?' – keep only actions that address that exact problem.

Answer: (B) Both I and II can be the possible effects

Concept: Compare the moves from 1st to 2nd and 2nd to 3rd letter.

1. RYT: $18\to 25\to 20$, i.e. $+7,-5$.
2. JQL: $10\to 17\to 12$, $+7,-5$; FMH: $6\to 13\to 8$, $+7,-5$.
3. MTP: $13\to 20\to 16$, $+7,-4$ – odd one.

Trick: Shortcut: in the group, 3rd letter $=$ 1st letter $+2$ (R→T, J→L, F→H); M→P is $+3$.

Answer: (B) MTP

Concept: Each letter moves back by 9 positions (wrapping from A to Z).

1. $Z(26)\to Q(17)\to H(8)\to Y(25)\to P(16)$.
2. $S(19)\to J(10)\to A(1)\to R(18)\to I(9)$.
3. $N(14)\to E(5)\to V(22)\to M(13)\to D(4)$.
4. Next term: PID.

Trick: Moving back 9 is the same as moving forward 17 – use whichever is easier near A/Z.

Answer: (C) PID

Concept: Test options so that one rule fits both pairs.

1. Option (D): $47\times 2+2=96$.
2. $53\times 2+2=108$ – same rule.
3. Others fail, e.g. (A): $58\times 2-20=96$ but $53\times 2-20=86\ne 112$.

Trick: When the second number is about double, try $\times 2\pm k$ and check the same $k$ on both sides.

Answer: (D) X = 47, Y = 108

Concept: Vowels go one letter back, consonants one letter forward.

1. F→G, R→S, I→H, E→D, N→O, D→E, L→M, Y→Z.
2. New group: G S H D O E M Z.
3. All 8 letters are different – none appears twice.

Trick: Y is treated as a consonant here; check repeats only in the new group.

Answer: (C) 0