Q&A: practice questions with answers

Concept: Money saved due to the price cut buys the extra quantity at the reduced price.

1. Saving $=6.25\%$ of ₹120 $=\frac{6.25}{100}\times 120=7.5$.
2. This ₹7.5 buys the extra 1 kg.
3. Reduced price $=$ ₹7.5 per kg.

Trick: $\text{Reduced price}=\frac{R\%\times \text{Amount}}{\text{extra quantity}}=\frac{6.25\times 120}{100\times 1}=7.5$.

Answer: (A) ₹7.5

Concept: $\text{Average speed}=\frac{\text{Total distance}}{\text{Total time}}$.

1. Time 1 $=\frac{90}{45}=2$ h; time 2 $=\frac{150}{50}=3$ h.
2. Total distance $=240$ km, total time $=5$ h.
3. Average speed $=\frac{240}{5}=48$ km/h.

Yaad rakhein: Never average the speeds directly ($\frac{45+50}{2}$ is wrong) unless the times are equal.

Answer: (B) 48 km/h

Concept: $\overline{x}=\frac{\sum fx}{\sum f}$.

1. $fx$: $50\times 3=150$, $28\times 4=112$, $85\times 6=510$, $40\times 7=280$.
2. $\sum fx=1052$, $\sum f=3+4+6+7=20$.
3. $\overline{x}=\frac{1052}{20}=52.6$.

Trick: Dividing by 20 = dividing by 2 then by 10: $526÷10=52.6$.

Answer: (C) 52.6

Concept: Curved surface area $=2\pi rh$, so it changes in proportion to $r\times h$.

1. New $r=1.3r$, new $h=0.7h$.
2. New CSA $=2\pi (1.3r)(0.7h)=0.91\times 2\pi rh$.
3. Decrease $=1-0.91=0.09=9\%$.

Trick: Successive change: $+30-30+\frac{30\times (-30)}{100}=-9\%$.

Answer: (D) 9%

Concept: Find the cost price of the mixture from the selling price and profit, then apply alligation.

1. CP of mixture $=\frac{96}{1.2}=$ ₹80 per kg.
2. Alligation: ghee ₹100, oil ₹50, mean ₹80.
3. Ghee : oil $=(80-50):(100-80)=30:20=3:2$.

Trick: Alligation cross-difference: (cheaper − mean) goes with the dearer item, (dearer − mean) with the cheaper.

Answer: (D) 3 : 2

Concept: Convert to kg, then multiply.

1. $1\text{ kg }750\text{ g}=1.75$ kg.
2. $7\times 1.75=12.25$ kg.

Trick: $7\times 1750\text{ g}=12250\text{ g}=12.250$ kg.

Answer: (A) 12.250 kg

Concept: Track each letter position separately using alphabet numbers.

1. 1st letters: G, I, K, M → $+2$ each → O.
2. 2nd letters: J, L, N, P → $+2$ → R.
3. 3rd letters: N, P, R, T → $+2$ → V.
4. Next term: ORV.

Trick: Whole cluster shifts $+2$: just add 2 to every letter of MPT.

Answer: (A) ORV

Concept: Find the shift applied to each letter in the given pairs.

1. EHCF → ILGJ: E→I, H→L, C→G, F→J, each $+4$.
2. HKFI → LOJM: each $+4$ again.
3. MPKN $+4$: M→Q, P→T, K→O, N→R = QTOR.

Trick: Check just the first letter (M $+4$ = Q) and the third (K $+4$ = O) to pick QTOR.

Answer: (A) QTOR

Concept: Facing the centre, 'right' is anticlockwise and 'left' is clockwise. Fix B and place the rest.

1. A is second to the right of B. One person between B and E: E is second to the left of B (right side is A).
2. R immediately right of F: the only free adjacent pair is the 3rd and 4th seats to B's right, so F = 3rd, R = 4th.
3. P is not next to E, so P sits immediately right of B, and Q is immediately left of B.
4. Third to the left of Q: Q → E → R → F.

Trick: Draw the circle once and move only in one direction while counting — most mistakes come from switching direction mid-count.

Answer: (D) F

Concept: Look at the differences between consecutive terms.

1. Differences: $23-18=5$, $33-23=10$, $48-33=15$, $68-48=20$.
2. They increase by 5, so the next difference is 25.
3. $68+25=93$.

Trick: Differences are multiples of 5: $5,10,15,20,25$.

Answer: (B) 93

Concept: Decode each symbol one by one and build the family tree.

1. A + B: A is the brother of B (A is male).
2. B – C: B is the daughter of C; C × D: C is the wife of D, so B and A are children of D.
3. D ÷ E: D is the son of E.
4. A is the son of D, and D is the son of E, so A is E's son's son.

Trick: Mark gender as soon as a relation reveals it — here 'brother' tells you A is male.

Answer: (D) Son's son

Concept: Compare each letter of the first cluster with the corresponding letter of the second.

1. WT-XZ: W→X $+1$, T→Z $+6$.
2. UR-VX: $+1$, $+6$; NK-OQ: $+1$, $+6$.
3. RO-SV: R→S $+1$, but O→V $+7$.
4. RO-SV breaks the pattern.

Trick: Since the first letter always moves $+1$, compare only the second letters' jumps.

Answer: (B) RO-SV

Concept: Facing north, right = east. Place the fixed person first, then the gap clues.

1. No one is right of A: A at seat 7 (right end).
2. Four between D and B: seats 1 and 6. E second to the right of D works only if D = 1, so E = 3, B = 6.
3. C immediately left of F: free adjacent seats 4, 5 → C = 4, F = 5; G = 2.
4. Between G (2) and B (6): E, C, F = three people.

Trick: Persons between seats $p$ and $q$ $=|p-q|-1=6-2-1=3$.

Answer: (D) Three

Concept: Each letter of the cluster moves forward by the same step.

1. 1st: H, J, L, N → $+2$ → P.
2. 2nd: K, M, O, Q → $+2$ → S.
3. 3rd: O, Q, S, U → $+2$ → W.
4. Next: PSW.

Trick: Add 2 to each letter of NQU directly.

Answer: (C) PSW

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

1. All roofs are cats and all cats are grasses: Roofs ⊂ Cats ⊂ Grasses.
2. Some walls are roofs, so those walls are also grasses → some grasses are walls. (I) follows.
3. Grasses may contain items that are not roofs (e.g. cats outside roofs), so 'All grasses are roofs' (II) does not follow.

Trick: 'Some' + 'All' = 'Some' (Some A are B, All B are C ⇒ Some A are C).

Answer: (C) Only conclusion (I) follows.

Concept: Replace letters with signs and solve using BODMAS (÷, ×, then +, −).

1. Option (B): $29+34÷2-4\times 5$.
2. $34÷2=17$, $4\times 5=20$.
3. $29+17-20=26$ ✓.

Trick: Check the option where ÷ splits an even number neatly — whole-number results are usually the intended one.

Answer: (B) 29 C 34 A 2 D 4 B 5

Concept: Number the letters of the first word 1-2-3-4 and track their positions in the other two words.

1. TODE = 1234 → EOTD = 4-2-1-3 → ODTE = 2-3-1-4.
2. FAST: TAFS = 4-2-1-3, ASFT = 2-3-1-4 ✓.
3. BACK: 4-2-1-3 = KABC, 2-3-1-4 = ACBK ✓.

Trick: Test only the second word of each option first; just BACK gives KABC.

Answer: (A) BACK - KABC - ACBK

Concept: Letters common to two words share the digits common to both codes; the leftover letter gets the leftover digit.

1. VOCAL = 46218, OVALS = 68514.
2. Common letters: V, O, A, L ↔ common digits 4, 6, 8, 1.
3. VOCAL leftover: C = 2; OVALS leftover: S = 5.

Trick: Strike out common digits from the second code: 68514 − {6, 8, 1, 4} leaves 5.

Answer: (C) 5

Concept: Check every symbol: the element just before must be even and the one just after must be odd.

1. & (after 7) – before is odd ✗; Ω (after 3) ✗; & (after 5) ✗.
2. @: before 6 (even) but after 8 (even) ✗.
3. $: before 8 (even) but after # (symbol) ✗.
4. #, *, £: preceded by a symbol or odd 1 ✗. Count $=0$.

Trick: First list only symbols preceded by an even number (@, $), then test what follows them.

Answer: (C) None

Concept: The series alternates between two operations.

1. $274\to 252$: $-22$; $252\to 282$: $+30$.
2. $282\to 260$: $-22$; $260\to 290$: $+30$; $290\to 268$: $-22$.
3. Next: $268+30=298$.

Trick: Alternate terms also form simple series: 274, 282, 290, 298 ($+8$).

Answer: (D) 298