Q&A: practice questions with answers

Concept: Consecutive numbers $n$ and $n+1$ lie close to $\sqrt{\text{product}}$.

1. $\sqrt{870}\approx 29.5$.
2. $29\times 30=870$.
3. Greater number $=30$.

Trick: Product ending in 0 → one number ends in 0 or 5; $29\times 30$ fits.

Answer: (B) 30

Concept: $\text{SI}=\frac{P\times R\times T}{100}$, Amount $=P+\text{SI}$.

1. $9204=\frac{P\times 6.4\times \frac{13}{2}}{100}=0.416P\Rightarrow P=$ ₹22,125.
2. New SI $=\frac{22125\times 7.6\times \frac{20}{3}}{100}=$ ₹11,210.
3. Amount $=22125+11210=$ ₹33,335.

Trick: $R\times T$ first: $6.4\times 6.5=41.6\%$ and $7.6\times \frac{20}{3}=\frac{152}{3}\%$.

Answer: (B) ₹33,335

Concept: Volume of a hollow sphere $=\frac{4}{3}\pi (R^3-r^3)$; mass = volume × density.

1. $R^3-r^3=1331-512=819$.
2. $V=\frac{4}{3}\times \frac{22}{7}\times 819=3432{\text{cm}}^3$.
3. Mass $=3432\times 15=51480\text{g}=51.48\text{kg}$.

Trick: $819=7\times 117$, so $\frac{22}{7}$ cancels neatly.

Answer: (C) 51.48

Concept: Product of two numbers = HCF × LCM.

1. Let HCF $=h$, LCM $=7h$.
2. $7h-h=222\Rightarrow h=37$, LCM $=259$.
3. Product $=37\times 259=9583$.

Trick: Product $=7h^2=7\times {37}^2=7\times 1369=9583$.

Answer: (C) 9583

Concept: Sum of the first $n$ odd natural numbers $=n^2$.

1. Sum $={154}^2$.
2. Average $=\frac{{154}^2}{154}=154$.

Trick: Average of the first $n$ odd numbers is always $n$ itself.

Answer: (B) 154

Concept: Distance $=$ speed × time; for the same distance, speed is inversely proportional to time.

1. Distance $=36\times 5=180\text{km}$.
2. Required speed $=\frac{180}{10}=18\text{km/h}$.

Trick: Time doubles → speed halves: $\frac{36}{2}=18$.

Answer: (B) 18 km/hr

Concept: If $3A=9B=4C=k$, then $A:B:C=\frac{1}{3}:\frac{1}{9}:\frac{1}{4}$.

1. Multiply by LCM 36: $A:B:C=12:4:9$.
2. Total parts $=25$; 1 part $=\frac{44200}{25}=1768$.
3. A $=12\times 1768=$ ₹21,216.

Trick: Take $k=36$ (LCM of 3, 9, 4) to get the ratio directly.

Answer: (B) ₹21,216

Concept: Expand the brackets and combine like terms.

1. $x(3x-6)=3x^2-6x$.
2. $5(x^2-4)=5x^2-20$.
3. Sum $+19$: $8x^2-6x-20+19=8x^2-6x-1$.

Trick: Put $x=1$: $-3+(-15)+19=1$ and $8-6-1=1$ ✓.

Answer: (A) $8x^2-6x-1$

Concept: Use known squares: ${17}^2=289$, ${18}^2=324$, ${27}^2=729$.

1. $\sqrt{289}=17$.
2. $\sqrt{0.0324}=0.18$, $\sqrt{7.29}=2.7$.
3. $17+0.18-2.7=14.48$.

Trick: For decimals, pair digits after the point: $0.0324\to 0.18$ (2 decimal places).

Answer: (A) 14.48

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

1. Times: $\frac{168}{21}=8$ h, $\frac{100}{20}=5$ h, $\frac{371}{53}=7$ h.
2. Total distance $=639\text{km}$, total time $=20$ h.
3. Average $=\frac{639}{20}=31.95\text{km/h}$.

Trick: Never average the speeds directly; the times here come out whole.

Answer: (D) 31.95

Concept: Find the position change of each letter.

1. CSL → FPG: C+3=F, S−3=P, L−5=G.
2. KGX → NDS: K+3=N, G−3=D, X−5=S.
3. DJF: D+3=G, J−3=G, F−5=A → GGA ✓.

Trick: Check only the first letter (+3) to drop options, then verify the rest.

Answer: (B) DJF : GGA

Concept: Each letter moves back by 3.

1. KHIG → HEFD: each −3.
2. DABZ → AXYW: each −3 (A−3=X wraps around).
3. BYZX → B−3=Y, Y−3=V, Z−3=W, X−3=U → YVWU.

Trick: Backward wrap: A−3 = X, B−3 = Y.

Answer: (C) YVWU

Concept: Find the gaps between consecutive letters (positions).

1. ROK: 18, 15, 11 → −3, −4.
2. MJF: 13, 10, 6 → −3, −4.
3. FCY: 6, 3, 25 → −3, −4 (C−4 wraps to Y).
4. LID: 12, 9, 4 → −3, −5 ✗.

Trick: Remember wrap-around: C − 4 = Y.

Answer: (A) LID

Concept: Number positions 1 (bottom) to 7 (top) and fix definite clues first.

1. Two boxes below W → W = 3. One box above Y → Y = 6.
2. One box between Y and U → U = 4.
3. T immediately above X: only free pair is X = 1, T = 2.
4. D below V → D = 5, V = 7. Between V (7) and T (2): Y, D, U, W = 4.

Trick: Fixed-count clues (“only two below”) give exact positions – place them first.

Answer: (C) Four

Concept: Differences are perfect squares.

1. $61-1=60,60-4=56,56-9=47,47-16=31$.
2. Next: $31-25=6$.

Trick: Subtracted terms $1^2,2^2,3^2,4^2,5^2$.

Answer: (A) 6

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

1. ‘your’ is common to ‘keep your goal’ and ‘mind your business’.
2. Common code in ‘yt ru kj’ and ‘kj gb mi’ is ‘kj’.

Trick: Common word ↔ common code.

Answer: (A) kj

Concept: Reverse each number, arrange, then pick the asked digits.

1. Reversed: 8331, 5232, 7263, 3155, 4671.
2. Ascending: 3155 < 4671 < 5232 < 7263 < 8331.
3. Second largest 7263 → second digit 2; smallest 3155 → second digit 1.
4. $2\times 1=2$.

Trick: Order changes after reversal – re-sort before choosing.

Answer: (B) 2

Concept: Draw the minimum possible Venn diagram.

1. All pencils are erasers → Pencils circle lies inside Erasers.
2. Some erasers are crayons: Crayons may touch Erasers away from Pencils → I (Some pencils are crayons) is not certain.
3. Since all pencils are erasers, some erasers are pencils → II follows.

Trick: “All A are B” always gives “Some B are A”.

Answer: (A) Only conclusion (II) follows.

Concept: Find the shift of each letter.

1. ITM → LSO: +3, −1, +2.
2. SSV → VRX: +3, −1, +2.
3. TNN → T+3=W, N−1=M, N+2=P → WMP ✓.

Trick: Check the middle letter (−1) first – it eliminates most options.

Answer: (B) TNN : WMP

Concept: Total = rank from top + rank from bottom − 1.

1. $33+18-1=50$.

Trick: Subtract 1 because the person is counted in both ranks.

Answer: (A) 50