Q&A: practice questions with answers

Concept: Overall literacy % is a weighted average of male and female literacy %.

1. Females $=368000-220000=148000$
2. Total literate $=62\%$ of 368000; male literate $=62\%$ of 220000
3. Female literate $=62\%\times (368000-220000)=62\%$ of 148000
4. So female literacy $=62\%$

Trick: If the overall average and one group's value are equal (62%), the other group must also be 62%.

Answer: (D) 62%

Concept: Write the condition as an equation and divide.

1. $\frac{20}{100}A=\frac{4}{5}B$
2. $\frac{A}{5}=\frac{4B}{5}\Rightarrow A=4B$
3. $A:B=4:1$

Trick: $\frac{A}{B}=\frac{4/5}{1/5}=4$.

Answer: (B) 4 : 1

Concept: Curved surface area $=2\pi rh$; volume $=\pi r^{2}h$.

1. $2\times \frac{22}{7}\times 21\times h=5280\Rightarrow 132h=5280\Rightarrow h=40\text{cm}$
2. $V=\frac{22}{7}\times {21}^2\times 40=1386\times 40$
3. $V=55440{\text{cm}}^3$

Trick: $V=\frac{\text{CSA}\times r}{2}=\frac{5280\times 21}{2}=55440$.

Answer: (B) 55,440

Concept: Use ${\sec }^2\theta -1={\tan }^2\theta$ and $\tan \theta =\frac{\sin \theta }{\cos \theta }$.

1. $1-{\sec }^2\theta =-{\tan }^2\theta$
2. $\frac{-{\tan }^2\theta }{{\sin }^2\theta }\times {\cos }^2\theta =-\frac{{\sin }^2\theta }{{\cos }^2\theta }\times \frac{{\cos }^2\theta }{{\sin }^2\theta }$
3. $=-1$

Trick: Put $\theta ={45}^{\circ }$: $\frac{1-2}{1/2}\times \frac{1}{2}=-1$.

Answer: (C) $-1$

Concept: Add the hourly filling rates of all pipes.

1. Rates: $\frac{1}{16}+\frac{1}{28}+\frac{1}{8}$
2. LCM 112: $\frac{7+4+14}{112}=\frac{25}{112}$ tank per hour
3. Time $=\frac{112}{25}=4\frac{12}{25}$ hours

Trick: Take tank $=112$ units: A $=7$, B $=4$, C $=14$ units/h, total 25.

Answer: (A) $4\frac{12}{25}$ hours

Concept: Average of the first $n$ even numbers $=n+1$.

1. Sum of first $n$ even numbers $=n(n+1)$
2. Average $=\frac{n(n+1)}{n}=n+1$
3. For $n=155$: $156$

Yaad rakhein: First $n$ even → $n+1$; first $n$ odd → $n$; first $n$ natural → $\frac{n+1}{2}$.

Answer: (A) 156

Concept: Expand, the $x^2$ terms cancel, leaving a linear equation.

1. $6x^2-12-6x^2-24x+15=14$
2. $-24x+3=14$
3. $-24x=11\Rightarrow x=-\frac{11}{24}$

Trick: Watch the sign: $-3\times (-5)=+15$.

Answer: (D) $-\frac{11}{24}$

Concept: Find one man's and one woman's one-day work.

1. 1 man's 1-day work $=\frac{1}{6\times 9}=\frac{1}{54}$
2. 1 woman's 1-day work $=\frac{1}{6\times 6}=\frac{1}{36}$
3. $2W+3M=\frac{2}{36}+\frac{3}{54}=\frac{1}{18}+\frac{1}{18}=\frac{1}{9}$
4. Days $=9$

Trick: $1M=\frac{2}{3}W$, so $3M=2W$; $2W+2W=4W$ → $\frac{6\times 6}{4}=9$ days.

Answer: (D) 9 days

Concept: Test only odd numbers not ending in 5 for divisibility by primes up to $\sqrt{438}\approx 20.9$.

1. Candidates: 431, 433, 437 (others are even or end in 5)
2. 431 and 433 are not divisible by 2, 3, 5, 7, 11, 13, 17, 19 → prime
3. $437=19\times 23$ → not prime
4. Count $=2$

Trick: Check primes only up to $\sqrt{N}$.

Answer: (B) 2

Concept: Mode is the value that occurs most often.

1. Frequencies: 13 → 3 times, 12 → 2 times
2. All others (10, 11, 15, 19, 20) occur once
3. Mode $=13$

Yaad rakhein: Mode = most frequent; Median = middle value; Mean = sum ÷ count.

Answer: (A) 13

Concept: Second number $=$ first number $÷2$.

1. $108÷2=54$, $78÷2=39$
2. (A) $12÷2=6\ne 24$; (B) $65÷2\ne 13$; (D) $54÷2\ne 18$
3. (C) $96÷2=48$ ✓

Trick: Check the simplest operation (half/double) first.

Answer: (C) 96, 48

Concept: Interchange the signs first, then apply BODMAS.

1. After swapping: $15\times 7-7+48÷2\times 23+4$
2. $=105-7+24\times 23+4$
3. $=105-7+552+4=654$

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

Answer: (D) 654

Concept: Compare positions: 1st $-7$ = 2nd, 2nd $+4$ = 3rd.

1. NGK: $14-7=7$ (G), $7+4=11$ (K) ✓
2. TMQ: $20-7=13$ (M), $13+4=17$ (Q) ✓
3. QJN: $17-7=10$ (J), $10+4=14$ (N) ✓
4. IBE: $9-7=2$ (B), $2+3=5$ (E) ✗

Yaad rakhein: EJOTY: E=5, J=10, O=15, T=20, Y=25.

Answer: (D) IBE

Concept: Some A are B + All B are C ⇒ Some A are C.

1. The guns that are roses lie inside 'bats' as well, so some guns are bats → I follows.
2. Bats may contain things other than roses, so 'All bats are roses' is not certain → II does not follow.

Yaad rakhein: 'All B are C' can never be reversed to 'All C are B'.

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

Concept: Codes of letters are jumbled; match the common letter with the common digit.

1. GIRL → 5317, INKS → 2146
2. Common letter: I
3. Common digit: 1
4. So I = 1

Trick: Common letter ↔ common digit.

Answer: (D) 1

Concept: Rearrange digits in ascending order, then pick positions.

1. 2436857 → 2345678
2. Third from left $=4$
3. Second from right $=7$
4. Sum $=4+7=11$

Trick: n-th from right in a 7-digit number = $(8-n)$-th from left.

Answer: (D) 11

Concept: Each letter position moves $+2$ in every term.

1. 1st letters: G, I, K, M, O
2. 2nd letters: B, D, F, H, J
3. 3rd letters: D, F, H, J, L
4. Next term: OJL

Trick: Read the series column-wise.

Answer: (B) OJL

Concept: Track letter positions: 1234 → 2431 → 4321.

1. MINK → IKNM (letters 2,4,3,1) → KNIM (4,3,2,1 – reverse)
2. PLOT → LTOP → TOLP follows the same
3. CORD → ODRC (2,4,3,1) ✓ → DROC (reverse) ✓
4. Other options break the pattern (e.g. TOES → OTES ✗)

Trick: Third term is just the first word reversed — check that first.

Answer: (D) CORD - ODRC - DROC

Concept: Alternating operations: $\times 3+4$, then $-11$.

1. $18\times 3+4=58$, $58-11=47$
2. $47\times 3+4=145$, $145-11=134$
3. $134\times 3+4=406$

Trick: Large jump then small drop → look for multiply-add and subtract alternately.

Answer: (B) 406

Concept: Look for the pattern Number – Symbol – Number.

1. Series: ? 7 3 ? 2 5 3 ^ # + * @ 2 7 # & 5 2 * # 2
2. '3 ? 2' → symbol between two numbers ✓
3. '7 # &', '2 * #', '* # 2' → fail
4. Only one such symbol

Trick: Scan each symbol and check both neighbours.

Answer: (A) One