Q&A: practice questions with answers

Concept: The largest cube has side = smallest dimension $=6\text{cm}$. Cutting a cube from a corner removes 3 faces but exposes 3 equal new faces.

1. Original TSA $=2(lb+bh+hl)=2(80+48+60)=2\times 188=376$.
2. Removed surface $=3\times 6^2=108$; newly exposed surface $=3\times 6^2=108$.
3. Net change $=0$, so remaining TSA $=376{\text{cm}}^2$.

Trick: A cube cut from a corner never changes the total surface area.

Answer: (B) $376{\text{cm}}^2$

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

1. Times: $\frac{585}{65}=9$, $\frac{368}{92}=4$, $\frac{168}{56}=3$ → total $16$ h.
2. Total distance $=585+368+168=1121$ km.
3. Average $=\frac{1121}{16}=70.0625\approx 70.06\text{km/h}$.

Trick: Never average the speeds; each part divides exactly, so find hours first.

Answer: (D) $70.06$

Concept: Convert averages to totals.

1. $T+S+M=3\times 45=135$.
2. $T+S=2\times 44=88$, $S+M=2\times 47=94$.
3. $S=(T+S)+(S+M)-(T+S+M)=88+94-135=47$.

Trick: Common person = sum of the two pair-totals − total of all three.

Answer: (D) $47$

Concept: Overheads (decoration) are added to cost price. $\text{Loss}\%=\frac{\text{Loss}}{\text{CP}}\times 100$.

1. CP $=255+5=260$.
2. SP $=154$ → loss $=260-154=106$.
3. $\text{Loss}\%=\frac{106}{260}\times 100=\frac{530}{13}\%\approx 40.77\%$.

Trick: SP < CP means loss – this removes both 'profit' options at once.

Answer: (C) $\frac{530}{13}\%$ loss

Concept: Write $\cot$ as $\frac{1}{\tan }$ and simplify.

1. $\tan A-\cot B=\tan A-\frac{1}{\tan B}=\frac{\tan A\tan B-1}{\tan B}$.
2. $\tan B-\cot A=\frac{\tan A\tan B-1}{\tan A}$.
3. Ratio $=\frac{\tan A}{\tan B}=\tan A\cot B$.

Trick: Put $A={60}^{\circ },B={45}^{\circ }$: $\frac{\sqrt{3}-1}{1-\frac{1}{\sqrt{3}}}=\sqrt{3}=\tan {60}^{\circ }\cot {45}^{\circ }$.

Answer: (B) $\tan A\cot B$

Concept: Expand the brackets and combine like terms.

1. $x(4x-4)=4x^2-4x$.
2. $5(x^2-5)=5x^2-25$.
3. Sum $+12$: $9x^2-4x-25+12=9x^2-4x-13$.

Trick: Constant check: $-25+12=-13$ removes two options instantly.

Answer: (C) $9x^2-4x-13$

Concept: Take square roots of perfect squares, including decimals.

1. $\sqrt{196}=14$.
2. $\sqrt{0.0225}=0.15$ (since ${15}^2=225$).
3. $\sqrt{5.76}=2.4$ (since ${24}^2=576$).
4. $14+0.15-2.4=11.75$.

Trick: Decimal places of the root = half the decimal places of the number.

Answer: (C) $11.75$

Concept: Discount% $=\frac{\text{free items}}{\text{total items received}}\times 100$.

1. Customer pays for 6 and gets $6+4=10$ trousers.
2. Free $=4$ out of $10$.
3. Discount $=\frac{4}{10}\times 100=40\%$.

Trick: Buy $x$ get $y$ free → discount $=\frac{y}{x+y}\times 100$.

Answer: (B) $40\%$

Concept: Let the numbers be $n$ and $n+2$ and test squares.

1. $n^2+(n+2{)}^2=164\Rightarrow 2n^2+4n-160=0\Rightarrow n^2+2n-80=0$.
2. $(n+10)(n-8)=0\Rightarrow n=8$.
3. Numbers $8,10$ ($64+100=164$); sum $=18$.

Trick: Half of 164 is 82 – the squares lie around $9^2=81$, so try 8 and 10.

Answer: (D) $18$

Concept: In 'Buy 3 get 1 free', 4 items cost the price of 3; then apply the extra discount.

1. Price of 3 items $=3\times 3000=9000$.
2. 20% discount $=0.2\times 9000=1800$.
3. Amount paid $=9000-1800=7200$.

Trick: Directly: $9000\times 0.8=7200$.

Answer: (A) ₹7,200

Concept: Fix the certain positions first (row of 7, facing north, positions 1–7 from left).

1. Three to the left of V → V at 4.
2. Only A to the right of U → U at 6, A at 7.
3. Three between U and W → W at 2.
4. C < T < B on remaining seats 1, 3, 5 → C1, T3, B5.
5. Between C (1) and B (5): W, T, V = 3 people.

Trick: Count people between = difference of positions − 1 $=5-1-1=3$.

Answer: (D) Three

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

1. Two below B → B at 5. One above D → D at 2.
2. One between D and E → E at 4.
3. F immediately above C → only consecutive free pair is 6–7: F6, C7.
4. G below A → A1, G3.
5. Above B: A, D, G, E = 4 boxes.

Trick: 'Only $n$ below' in a stack of 7 → position $7-n$ from top.

Answer: (B) Four

Concept: A qualifying symbol needs a symbol on both sides, i.e. a run of at least three consecutive symbols.

1. Symbol runs: (#), ($), (* £), (+ Ω), (& %), (@).
2. The longest run has only 2 symbols, so no symbol is both preceded and followed by a symbol.
3. Count $=0$.

Trick: Look only for blocks of 3+ symbols in a row – none exist here.

Answer: (D) 0

Concept: The letter common to both words takes the digit common to both codes.

1. Common letter in FAIR and RENT: R.
2. Common digit in 4627 and 1365: 6.
3. So R = 6.

Trick: Common letter ↔ common digit.

Answer: (D) 6

Concept: Find the shift of each letter position-wise.

1. WFJU → AINX: W+4=A, F+3=I, J+4=N, U+3=X (pattern +4, +3, +4, +3).
2. Check MRZG → QUDJ: M+4, R+3, Z+4 (=D), G+3 ✓.
3. YALP: Y+4=C, A+3=D, L+4=P, P+3=S → CDPS.

Trick: Alternate shifts +4, +3; after Z wrap round to A.

Answer: (B) CDPS

Concept: Compare each letter with its partner.

1. IQNJ → GOLH: each letter −2.
2. FNKG → DLIE: each letter −2 ✓.
3. CKHD −2 each: A, I, F, B → AIFB.

Trick: Uniform shift: just move every letter 2 steps back.

Answer: (C) AIFB

Concept: Replace letters by signs and use BODMAS.

1. Expression: $65+35-35+15÷5\times 24+65÷5\times 8$.
2. $15÷5\times 24=3\times 24=72$; $65÷5\times 8=13\times 8=104$.
3. $65+35-35+72+104=241$.

Trick: $+35-35$ cancels – just add $65+72+104$.

Answer: (C) 241

Concept: Check the differences between consecutive terms.

1. Differences: $21,23,25,27$ (odd numbers increasing by 2).
2. Next difference $=29$.
3. $124+29=153$.

Trick: Terms are ${10}^2-72,{11}^2-72,\dots ,{14}^2-72$; next $={15}^2-72=153$.

Answer: (C) 153

Concept: Build the family tree step by step.

1. S is the daughter of K, and K is the wife of L → S is L's daughter (H and P are L's sons).
2. M is married to S, and N is the son of M → N is S's son.
3. So N is the son of L's daughter.

Trick: Mother's father = नाना; from L's side N is 'daughter's son'.

Answer: (B) Daughter's son

Concept: The series alternates two operations.

1. $800+300=1100$, $1100-250=850$.
2. $850+300=1150$, $1150-250=900$.
3. Next: $900+300=1200$.

Trick: Alternate terms: 800, 850, 900 (+50) and 1100, 1150, 1200 (+50).

Answer: (A) 1200