Q&A: practice questions with answers

Concept: $\text{SI}=\frac{P\times R\times T}{100}$, with $R$ and $T$ in the same time unit (here months).

1. $P=1200$, $R=3\%$ per month, $T=11$ months.
2. $\text{SI}=\frac{1200\times 3\times 11}{100}=12\times 33=396$.

Yaad rakhein: 3% per month $=36\%$ per year; $1200\times 0.36\times \frac{11}{12}=396$ too.

Answer: (B) ₹396

Concept: Let the consecutive odd numbers be $n$ and $n+2$.

1. $n^2+(n+2{)}^2=394\Rightarrow 2n^2+4n+4=394\Rightarrow n^2+2n-195=0$.
2. $(n+15)(n-13)=0\Rightarrow n=13$.
3. Numbers 13 and 15: $169+225=394$ ✓; sum $=28$.

Trick: $\frac{394}{2}=197\approx {14}^2$, so the numbers sit around 14: 13 and 15.

Answer: (D) 28

Concept: Find each pipe's full-tank time, then add rates (emptying pipe negative).

1. P fills $\frac{5}{7}$ in 30 h → full in $30\times \frac{7}{5}=42$ h; Q fills $\frac{2}{5}$ in 28 h → full in 70 h.
2. In 7 h: $\frac{7}{42}+\frac{7}{70}=\frac{1}{6}+\frac{1}{10}=\frac{4}{15}$ filled.
3. R empties $\frac{4}{15}$ in 8 h → full in $8\times \frac{15}{4}=30$ h.
4. Net rate $=\frac{1}{42}+\frac{1}{70}-\frac{1}{30}=\frac{5+3-7}{210}=\frac{1}{210}$ → 210 h.

Trick: Take capacity $=210$ units (LCM of 42, 70, 30): rates $5+3-7=1$ unit/h.

Answer: (A) 210 hours

Concept: Take total work = LCM of days; one-day work = units per day.

1. Total $=\text{LCM}(10,20)=20$ units; A $=2$, B $=1$ unit/day.
2. Together in 6 days: $6\times 3=18$ units.
3. Left $=20-18=2$ units $=\frac{2}{20}=\frac{1}{10}$.

Yaad rakhein: Work done $=6(\frac{1}{10}+\frac{1}{20})=\frac{9}{10}$; left $=\frac{1}{10}$.

Answer: (C) $\frac{1}{10}$

Concept: Profit is divided in the investment ratio; difference of shares = (difference of ratio terms) × one part.

1. Total ratio $=34+75+6=115$.
2. Q − R $=75-6=69$ parts.
3. Difference $=3600\times \frac{69}{115}=3600\times \frac{3}{5}=2160$.

Trick: $\frac{69}{115}=\frac{3}{5}$ – spot the common factor 23.

Answer: (D) ₹2,160

Concept: Form two equations from the statements and solve.

1. $7P-Q=46$ … (i)
2. After 8 years: $6(Q+8)=6(P+8)-24\Rightarrow Q=P-4$ … (ii)
3. From (i): $7P-P+4=46\Rightarrow P=7$, so $Q=3$.

Yaad rakhein: Check: $7\times 7-3=46$ ✓; after 8 yrs $6\times 11=66$, $6\times 15-24=66$ ✓.

Answer: (D) 3

Concept: $5:12:13$ is a Pythagorean triplet, so the triangle is right-angled; area $=\frac{1}{2}\times \text{base}\times \text{height}$.

1. Sides $5k,12k,13k$; $(5k{)}^2+(12k{)}^2=(13k{)}^2$.
2. Area $=\frac{1}{2}\times 5k\times 12k=30k^2=1080\Rightarrow k^2=36$, $k=6$.
3. Perimeter $=30k=180\text{cm}$.

Yaad rakhein: Triplets 3-4-5, 5-12-13, 8-15-17, 7-24-25 → right triangle, use the two legs.

Answer: (B) 180 cm

Concept: Count days excluding the deposit day (include withdrawal day); 2024 is a leap year (366 days).

1. Days: Feb (23–29) $=7$, March $=31$, April $=23$ → $61$ days.
2. $\text{SI}=\frac{4000\times 6.75\times 61}{100\times 366}=270\times \frac{61}{366}$.
3. $=270\times \frac{1}{6}=45$.

Yaad rakhein: $366=6\times 61$, so 61 days of a leap year $=\frac{1}{6}$ year.

Answer: (D) ₹45

Concept: Expand the brackets and combine like terms.

1. $x(3x-5)=3x^2-5x$; $5(x^2-3)=5x^2-15$.
2. Sum: $3x^2-5x+5x^2-15+16$.
3. $=8x^2-5x+1$.

Yaad rakhein: Put $x=0$: expression $=-15+16=1$ → constant term must be $+1$.

Answer: (B) $8x^2-5x+1$

Concept: Number to add = divisor − remainder.

1. $91673÷88$: $88\times 1041=91608$, remainder $=65$.
2. Add $88-65=23$ → $91696=88\times 1042$.

Yaad rakhein: Least number to subtract = remainder; to add = divisor − remainder.

Answer: (C) 23

Concept: Replace each symbol by its meaning, then apply BODMAS.

1. $12+105\times 3÷14-3$ becomes $12-105÷3+14\times 3$.
2. $=12-35+42$.
3. $=19$.

Yaad rakhein: Swap symbols first on paper, then solve – never solve mentally while swapping.

Answer: (B) 19

Concept: Letters common to both words share the common digits; the leftover letter takes the leftover digit.

1. PEST → 6324, PENS → 8634.
2. Common letters P, E, S ↔ common digits 6, 3, 4.
3. Left: T ↔ 2 and N ↔ 8.

Yaad rakhein: Compare only the non-common letter and digit.

Answer: (B) 8

Concept: Find the shift of each letter position.

1. L→R, G→M, E→K, I→O: each $+6$.
2. J→P, E→K, C→I, G→M: each $+6$ ✓.
3. H+6 = N, C+6 = I, A+6 = G, E+6 = K → NIGK.

Yaad rakhein: Position values: A1, E5, J10, O15, T20, Y25 (EJOTY).

Answer: (D) NIGK

Concept: Check the gaps between consecutive letters.

1. NJL: N−4 = J, J+2 = L.
2. LHJ: −4, +2; QMO: −4, +2.
3. TPS: T−4 = P, but P+3 = S → odd.

Yaad rakhein: Write alphabet positions: T20, P16, S19.

Answer: (C) TPS

Concept: Differences are cubes of natural numbers.

1. $670-1^3=669$, $669-2^3=661$, $661-3^3=634$, $634-4^3=570$.
2. Next: $570-5^3=570-125=445$.

Yaad rakhein: Differences 1, 8, 27, 64 … are $n^3$.

Answer: (B) 445

Concept: Two 'some' statements give no definite relation between the end terms.

1. Some woods are chisels; some chisels are graphs – woods and graphs may not overlap → I does not follow.
2. 'Some chisels are graphs' cannot become 'All graphs are chisels' → II does not follow.

Yaad rakhein: Some + Some = no conclusion.

Answer: (D) Neither conclusion (I) nor (II) follows.

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

1. All fruits are berries; some nuts are berries – those nuts may be berries that are not fruits → I does not follow.
2. 'All fruits are berries' does not mean all berries are fruits → II does not follow.

Yaad rakhein: 'All A are B' never reverses to 'All B are A'.

Answer: (C) Neither conclusion (I) nor (II) follows.

Concept: Track net north–south and east–west displacement.

1. N 16, then right → E 43, right → S 38, right → W 19, right → N 22.
2. North–south: $16-38+22=0$.
3. East–west: $43-19=24$ km east of Y.
4. So Z is 24 km east of Y → drive 24 km towards the west.

Yaad rakhein: Four right turns from north: E, S, W, N.

Answer: (B) 24 km towards the west

Concept: Common letters share common digits; the leftover letter gets the leftover digit.

1. GUNS → 7642, STUN → 2364.
2. Common S, U, N ↔ common digits 2, 6, 4.
3. Left: G ↔ 7 and T ↔ 3.

Yaad rakhein: Strike out common digits; what remains in the second code is T.

Answer: (B) 3

Concept: Find the backward shift of each letter (wrap around after A).

1. DUMB→TMCT: D−10 = T, U−8 = M, M−10 = C, B−8 = T.
2. POYV→FGON: P−10 = F, O−8 = G, Y−10 = O, V−8 = N ✓.
3. LQUX: L−10 = B, Q−8 = I, U−10 = K, X−8 = P → BIKP.

Yaad rakhein: Pattern $-10,-8,-10,-8$; $-10$ is the same as $+16$.

Answer: (D) BIKP