Q&A: practice questions with answers

Concept: Selling price after discount $=\text{MP}\times (100-d)\%$; with no discount, SP = MP.

1. $\text{MP}\times \frac{24}{100}=3330\Rightarrow \text{MP}=\frac{3330\times 100}{24}=13875$
2. With no discount, gain $50\%$: $\text{MP}=1.5\times \text{CP}$
3. $\text{CP}=\frac{13875}{1.5}=9250$

Trick: $\text{CP}=\frac{3330}{0.24\times 1.5}=\frac{3330}{0.36}=9250$.

Answer: (D) $9,250$

Concept: The perpendicular from the centre bisects the chord; use Pythagoras in the half-chord triangle.

1. $OB=6$, $OM=4.5$, $MB=x$.
2. $x^2=6^2-{4.5}^2=36-20.25=15.75=\frac{63}{4}$
3. $x=\frac{\sqrt{63}}{2}=\frac{3\sqrt{7}}{2}$
4. $AB=2x=3\sqrt{7}\text{cm}$

Trick: $AB=2\sqrt{r^2-d^2}=\sqrt{4(36-20.25)}=\sqrt{63}=3\sqrt{7}$.

Answer: (C) $3\sqrt{7}\text{cm}$

Concept: Average of first $n$ natural numbers $=\frac{n+1}{2}$.

1. Sum $=\frac{12\times 13}{2}=78$
2. Average $=\frac{78}{12}=6.5$

Trick: Average of consecutive numbers = (first + last) ÷ 2 $=\frac{1+12}{2}=6.5$.

Answer: (B) $6.5$

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

1. $P=900$, $R=6\%$ per month, $T=12$ months.
2. $\text{SI}=\frac{900\times 6\times 12}{100}=648$

Trick: $6\%$ per month = $72\%$ per year; $72\%$ of 900 $=648$.

Answer: (B) $648$

Concept: $\text{SP}=\text{CP}\times \frac{100\pm \%}{100}$.

1. Loss $30\%$: $\text{CP}\times 0.7=112\Rightarrow \text{CP}=160$
2. Gain $15\%$: $\text{SP}=160\times 1.15=184$

Trick: $\text{New SP}=112\times \frac{115}{70}=16\times \frac{115}{10}=184$.

Answer: (A) $184$

Concept: Time $=\frac{\text{Distance}}{\text{Speed}}$; one-way distance $d$ is covered once downstream and once upstream.

1. $\frac{d}{41}+\frac{d}{20.5}=13$
2. $\frac{d}{41}+\frac{2d}{41}=\frac{3d}{41}=13\Rightarrow d=\frac{533}{3}\text{km}$
3. Total distance $=2d=\frac{1066}{3}\text{km}$

Trick: $\frac{533}{3}$ is only one way — the question asks total distance, so double it.

Answer: (D) $\frac{1066}{3}\text{km}$

Concept: Sum $=$ Average $\times$ Count.

1. Sum $=124\times 8=992$
2. Least number $=\frac{1}{16}\times 992=62$

Trick: $\frac{8\times 124}{16}=\frac{124}{2}=62$ — half the average.

Answer: (C) $62$

Concept: Third proportional of $a$ and $b$: $a:b=b:c\Rightarrow c=\frac{b^2}{a}$.

1. $B=2+4+6=12$
2. $C=\frac{{12}^2}{57}=\frac{144}{57}$
3. $=2.526\dots \approx 2.53$

Trick: $\frac{144}{57}=\frac{48}{19}$; $19\times 2.5=47.5$ so the answer is just above 2.5.

Answer: (A) $2.53$

Concept: Work per day adds up; A's rate = B's rate + C's rate.

1. $A+B=\frac{1}{7}$, $C=\frac{1}{9}$, $A=B+\frac{1}{9}$
2. $2B+\frac{1}{9}=\frac{1}{7}\Rightarrow 2B=\frac{9-7}{63}=\frac{2}{63}$
3. $B=\frac{1}{63}$ → B alone takes 63 days.

Trick: Total work $=63$ units: $A+B=9$, $C=7$, $A=B+7\Rightarrow 2B=2$, $B=1$ unit/day → 63 days.

Answer: (B) $63$

Concept: Check the gaps between consecutive letters using alphabet positions.

1. LTO: $12\to 20\to 15$ → $+8,-5$; NVQ: $14\to 22\to 17$ → $+8,-5$.
2. HPK: $8\to 16\to 11$ → $+8,-5$.
3. PXR: $16\to 24\to 18$ → $+8,-6$ ✗ — the pattern breaks.

Trick: Pehla gap sab me same ($+8$) ho to doosra gap check karo.

Answer: (A) PXR

Concept: Find the relation among the three numbers of the given sets.

1. $(43,48,5)$: $48-43=5$; $(49,70,21)$: $70-49=21$. So third = second − first.
2. (C) $(20,34,14)$: $34-20=14$ ✓.
3. (A) $52-36=16\ne 13$; (B) $52-45=7\ne 4$; (D) $71-48=23\ne 20$.

Trick: Pehle simplest relation (difference) try karo.

Answer: (C) (20, 34, 14)

Concept: Look at the differences between consecutive terms.

1. Differences: $55-49=6$, $8$, $10$, $12$, $14$ — increasing by 2.
2. Next difference $=16$.
3. Missing term $=99+16=115$.

Trick: Differences in AP (+2 each time) → just add the next even number.

Answer: (B) 115

Concept: Place the towns step by step on a grid.

1. Put G at the start; D is north-east of G; C is east of D (so C is north-east side of G, one level above).
2. E is north of C; F is south of E, and G is west of F → F lies on the same horizontal level as G, directly below C.
3. C and F are on the same vertical line, with C above F → C is North of F.

Trick: Start from the town that links the most statements (G) and draw.

Answer: (C) North

Concept: A letter common to two words takes the digit common to their codes.

1. HEIR → {2, 4, 6, 8}; EASY → {1, 3, 2, 7}.
2. Common letter: E; common digit: 2.
3. So E = 2.

Trick: Common letter ↔ common digit.

Answer: (B) 2

Concept: Track the positions 1 2 3 4 of the letters in each step.

1. GEAN → NAGE is $1234\to 4312$; NAGE → GAEN is $1234\to 3241$. Same for MAKE → EKMA → MKAE.
2. FOWL → $4312$ → LWFO ✓; LWFO → $3241$ → FWOL ✓.
3. TURN → $4312$ would be NRTU, BOLD → DLBO, BEAN → NABE but then $3241$ gives BAEN, not EABN.

Trick: Write position numbers under the letters once; then check options fast.

Answer: (C) FOWL - LWFO - FWOL

Concept: Use the definite clues (O, Y, P) and test the cases.

1. O is on floor 2 or 6. If O = 2 then Z = 5, so Y = 3 and P = 2 — clash with O. ✗
2. So O = 6, Z = 3 (two people between). Y odd, not 1 → Y = 5, P = 4.
3. Two between Y and M → M = 2; remaining N = 1.
4. Between N (1) and P (4): floors 2 and 3 → M and Z → two people.

Trick: Start with the person who has the fewest possible floors (O) and branch.

Answer: (B) Two

Concept: Replace letters (A = ÷, B = ×, C = +, D = −) and apply BODMAS.

1. (C) $84÷12-76+36\times 4=7-76+144=75$ ✓.
2. (A) $84\times 12+76-36÷4=1008+76-9=1075$.
3. (B) $84-12÷76\times 36+4$ is not an integer; (D) $84+12-76÷36\times 4$ is not an integer.

Trick: Options giving fractions can be rejected at once (76 is not divisible by 12 or 36).

Answer: (C) 84 A 12 D 76 C 36 B 4

Concept: Interchange the signs as given (+ → −, − → ×, × → ÷, ÷ → +), then apply BODMAS.

1. $15-3÷5+18\times 6$ becomes $15\times 3+5-18÷6$.
2. $=45+5-3$.
3. $=47$.

Trick: Rewrite the whole expression first, then calculate — never mix both steps.

Answer: (D) 47

Concept: Total = rank from top + rank from bottom − 1 (Jon is counted twice).

1. Rank from top $=24$, from bottom $=16$.
2. Total $=24+16-1=39$.

Trick: Always subtract 1 because the person is in both counts.

Answer: (A) 39

Concept: Check the gap inside each cluster and between clusters.

1. PS–NQ: $16\to 19$ ($+3$), $14\to 17$ ($+3$), first letters $-2$.
2. EH–CF and KN–IL: the same pattern ($+3$, $+3$, $-2$).
3. GJ–FK: $7\to 10$ ($+3$) but $6\to 11$ ($+5$) ✗.

Trick: Find one rule from two pairs, then test the rest.

Answer: (D) GJ - FK