Q&A: practice questions with answers

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

1. $n=10$
2. Average $=\frac{10+1}{2}=5.5$

Trick: For any equally spaced list, average $=\frac{\text{first}+\text{last}}{2}=\frac{1+10}{2}$.

Answer: (C) 5.5

Concept: The difference between two percentages of the same number is itself a percentage of that number.

1. $30\%-20\%=10\%$ of number $=12$
2. Number $=\frac{12\times 100}{10}=120$

Trick: $10\%=12$ $\Rightarrow$ $100\%=120$ – just shift the decimal.

Answer: (B) 120

Concept: Use $(a-b)(a^2+ab+b^2)=a^3-b^3$, $(a+b)(a^2-ab+b^2)=a^3+b^3$ and $(x-y)(x+y)=x^2-y^2$.

1. $(a+b)(a^2-ab+b^2)=a^3+b^3$
2. $(a-b)(a^2+ab+b^2)=a^3-b^3$
3. $(a^3+b^3)(a^3-b^3)=a^6-b^6$

Trick: Check with $a=2,b=1$: $3\times 1\times 3\times 7=63=2^6-1^6$.

Answer: (D) $a^6-b^6$

Concept: For $10$ (even) observations in ascending order, median $=$ average of the $5^{\text{th}}$ and $6^{\text{th}}$ values.

1. $5^{\text{th}}=x$, $6^{\text{th}}=x+2$.
2. ${\displaystyle \frac{x+(x+2)}{2}}=63\Rightarrow 2x+2=126\Rightarrow x=62$.
3. Check: $50<62<64<72$, so the order stays ascending.

Yaad rakhein: Even $n$: median $=\frac{1}{2}[{\left(\frac{n}{2}\right)}^{\text{th}}+{(\frac{n}{2}+1)}^{\text{th}}]$ value.

Answer: (B) 62

Concept: Complementary angles add up to ${90}^{\circ }$.

1. $x+y={90}^{\circ }$, $x-y={18}^{\circ }$
2. Smaller $y=\frac{{90}^{\circ }-{18}^{\circ }}{2}={36}^{\circ }$
3. Larger $={54}^{\circ }$

Trick: Smaller $=\frac{\text{sum}-\text{difference}}{2}$, larger $=\frac{\text{sum}+\text{difference}}{2}$.

Answer: (A) ${36}^{\circ }$

Concept: Three consecutive even numbers can be written $2n(2n+2)(2n+4)=8n(n+1)(n+2)$.

1. $n(n+1)(n+2)$ – three consecutive numbers – is always divisible by $3!=6$
2. So product is divisible by $8\times 6=48$
3. Check: $2\times 4\times 6=48$, so nothing larger always works

Trick: Smallest case $2\times 4\times 6=48$ is itself the answer – the greatest always-divisor can't exceed it.

Answer: (B) 48

Concept: Total digits $=30$. $k^{\text{th}}$ from right $=(30-k+1{)}^{\text{th}}$ from left.

1. $5^{\text{th}}$ from left $=6$
2. ${10}^{\text{th}}$ from right $={21}^{\text{st}}$ from left $=5$
3. Sum $=6+5=11$

Trick: Position from left $=n-k+1$; count in groups of five to avoid slips.

Answer: (D) 11

Concept: Each letter of a term moves $+3$ to give the next term.

1. E→H→K→N→Q
2. G→J→M→P→S
3. K→N→Q→T→W

Trick: Check just the first letters (E, H, K, N → Q) to eliminate options quickly.

Answer: (C) QSW

Concept: In each pair, compare corresponding letters of the two clusters.

1. JN-IM: J $-1$=I, N $-1$=M
2. RV-QU: $-1$, $-1$; PT-OS: $-1$, $-1$
3. MQ-LO: M $-1$=L but Q $-2$=O

Trick: Also, the first cluster has a gap of 4 (J–N) and so must the second; L–O has gap 3.

Answer: (C) MQ-LO

Concept: Find odd digits whose left neighbour is $0,1,4$ or $9$ and right neighbour is even.

1. Odd digits preceded by a perfect square: 7 (after 4, pos. 8), 7 (after 4, pos. 22), 7 (after 9, pos. 24)
2. Their next digits: 9, 9, 7 – all odd
3. No digit satisfies both conditions $\Rightarrow 0$

Trick: Locate the perfect squares (4, 9) first and check only the digit after them.

Answer: (B) 0

Concept: Replace letters by signs, then apply BODMAS.

1. $15÷3+9-2\times 4$
2. $=5+9-8$
3. $=6$

Trick: Write the converted expression fully before solving – most errors come from mis-substitution.

Answer: (A) 6

Concept: Track first and second letters of each pair separately.

1. GL-IF-JM: G $+2$ I $+1$ J; L $-6$ F $+7$ M
2. JO-LI-MP: J $+2$ L $+1$ M; O $-6$ I $+7$ P
3. MR-OL-PS: M $+2$ O $+1$ P; R $-6$ L $+7$ S ✓

Trick: Check the first letters ($+2,+1$) to cut options, then verify the second letters.

Answer: (D) MR-OL-PS

Concept: Fix definite positions first (1 = top, 7 = bottom).

1. Only B above A $\Rightarrow$ B $=1$, A $=2$
2. 4 boxes between A and Z $\Rightarrow$ Z $=7$
3. L, Y two apart in 3–6 $\Rightarrow$ positions 3 and 6; C, X take 4, 5
4. Y not just above C $\Rightarrow$ Y $=6$, L $=3$: B, A, L, C, X, Y, Z

Trick: 'Only one box above' instantly fixes positions 1 and 2.

Answer: (A) C

Concept: A valid reason must directly explain why the company is not profitable.

1. I: Very high operating cost reduces profit – directly explains losses
2. II: The CEO's philanthropy is personal and does not affect company profit

Trick: Ask: 'Does this reason affect the company's income or expenses?' If not, reject it.

Answer: (A) Only I is a possible reason

Concept: Facing the centre, 'left' means clockwise and 'right' means anticlockwise.

1. Fix C; F is 2nd to the left of C
2. Only E between K and F $\Rightarrow$ order C, _, F, E, K (clockwise)
3. B 3rd to left of E; remaining seats for D, L – D not next to B $\Rightarrow$ D next to C
4. Clockwise: C, D, F, E, K, L, B; 4th to right of L $=$ D

Trick: 7 people: 4th to the right $=$ 3rd to the left – count the shorter way to check.

Answer: (A) D

Concept: Count carefully from the given end.

1. ${12}^{\text{th}}$ from left $=6$
2. $2^{\text{nd}}$ from right $=0$
3. Sum $=6+0=6$

Trick: Count left digits in groups of five: (63047)(55683)(66…) – the ${12}^{\text{th}}$ is the second digit of the third group.

Answer: (C) 6

Concept: Decode each symbol step by step and draw the tree.

1. S + T: S is sister of T
2. T − U: T is husband of U (T male)
3. U × V: U is mother of V
4. V − W: V is husband of W $\Rightarrow$ V is male; so V is the son of T

Trick: Gender comes from the later link: '−' (husband) shows V is male.

Answer: (C) Son

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

1. BEAR = 7912, EARN = 1296
2. Common letters E, A, R ↔ common digits 1, 2, 9
3. Left: B ↔ 7 and N ↔ 6

Trick: Strike out common letters and common digits – what remains pairs up directly.

Answer: (B) 6

Concept: Facing north, left and right are the solver's left and right. Number seats 1–7 from left.

1. No one right of Y $\Rightarrow$ Y $=7$; C $=3$; Z $=6$
2. L just right of X and B 3rd left of X: only X $=4$ fits $\Rightarrow$ L $=5$, B $=1$
3. A $=2$: B, A, C, X, L, Z, Y
4. Between A and Z: C, X, L $=3$

Trick: Fix the extreme end person first; 'third to the left' means 2 people in between.

Answer: (B) Three

Concept: Swap the signs first, then solve using BODMAS.

1. After swapping: $12÷12\times 12+12-15$
2. $=1\times 12+12-15$
3. $=12+12-15=9$

Trick: Rewrite the whole expression with new signs before calculating.

Answer: (C) 9