Q&A: practice questions with answers

Concept: The greatest number leaving the same remainder when dividing several numbers = HCF of their differences.

1. Differences: $2368-1278=1090$, $4318-2368=1950$.
2. $\text{HCF}(1090,1950)=10$ (also divides $4318-1278=3040$), so $x=10$.
3. $1278÷10$ leaves remainder $y=8$.
4. $3x-14y=30-112=-82$.

Trick: Same remainder ⇒ take HCF of differences, then any one number mod x gives y.

Answer: (A) −82

Concept: Area of rectangle $=l\times b$.

1. $l=b+27$, so $b(b+27)=2268$.
2. $b^2+27b-2268=0\Rightarrow (b+63)(b-36)=0$.
3. $b=36$ m (and $l=63$ m; check $36\times 63=2268$).

Trick: Test options: $36\times 63=2268$ ✓ — fastest.

Answer: (D) 36

Concept: Combine the whole numbers first, then add the fraction over a common denominator.

1. $71+30-31=70$.
2. $70+\frac{62}{7}=\frac{490}{7}+\frac{62}{7}=\frac{552}{7}$.

Trick: Options differ only in the numerator: $70\times 7+62=552$.

Answer: (C) $\frac{552}{7}$

Concept: Net rate = filling rate − emptying rate.

1. Net rate $=\frac{1}{7}-\frac{1}{56}=\frac{8-1}{56}=\frac{1}{8}$ tank per minute.
2. Full tank takes 8 minutes.
3. $\frac{3}{4}$ tank takes $\frac{3}{4}\times 8=6$ minutes.

Trick: LCM method: tank $=56$ units; rates $+8$ and $-1$ → net $7$ units/min; $\frac{3}{4}\times 56=42$ units → $6$ min.

Answer: (C) 6

Concept: $x^2+y^2=(x+y{)}^2-2xy$ and $x^4+y^4=(x^2+y^2{)}^2-2x^2{y}^2$.

1. $x^2+y^2={14}^2-2\times 45=196-90=106$.
2. $x^4+y^4={106}^2-2\times {45}^2=11236-4050=7186$.

Trick: Here $x=9$, $y=5$: $9^4+5^4=6561+625=7186$ ✓.

Answer: (D) 7186

Concept: Total cost includes extra expenses; successive discounts multiply.

1. Total CP $=4400+3600=8000$.
2. MP $=8000\times \frac{125}{100}=10000$.
3. SP $=10000\times \frac{81}{100}\times \frac{81}{100}=6561$.

Trick: $0.81\times 0.81=0.6561$, so SP $=0.6561\times 10000$.

Answer: (C) 6,561

Concept: Translate the first sentence into an equation — it directly gives the difference.

1. $F+S=2S+19\Rightarrow F-S=19$.
2. Check with the second condition: $12(F+15)=13(S+15)-17\Rightarrow 12F-13S=-2$.
3. With $F=S+19$: $12S+228-13S=-2\Rightarrow S=230$, $F=249$; difference $=19$.

Trick: Subtract 2S from both sides of the first condition — the second condition is not needed.

Answer: (C) 19

Concept: SP $=$ CP $\times (1+\text{markup})\times (1-\text{discount})$.

1. SP $=$ CP $\times \frac{160}{100}\times \frac{15}{100}=0.24$CP.
2. $0.24\text{CP}=18510$
3. CP $=\frac{18510}{0.24}=77125$.

Trick: $1.6\times 0.15=0.24$; divide 18510 by 24 and multiply by 100.

Answer: (D) 77,125

Concept: Find the position change from word 1 → 2 and 2 → 3.

1. BEAN → EBAN: swap the 1st and 2nd letters. EBAN → BANE: move the 1st letter to the end.
2. Check MAKE → AMKE → MKEA: same rule.
3. MACK → AMCK (swap) → MCKA (A moved to end) ✓. Others fail, e.g. RACE → RCAE is not a swap of the first two letters.

Trick: Write positions as 1234 → 2134 → 1342 and test each option.

Answer: (A) MACK - AMCK - MCKA

Concept: Use alphabet positions of the first letters of each pair.

1. QR – WX: $Q(17)\to W(23)$, gap $+6$; both pairs are consecutive letters.
2. LM – RS: $12\to 18$, $+6$. ST – YZ: $19\to 25$, $+6$.
3. GH – OM: $7\to 15$, $+8$, and OM is not consecutive – odd one.

Trick: Each pair: consecutive letters, second pair 6 steps ahead.

Answer: (D) GH - OM

Concept: Each letter position moves by a fixed step (counting cyclically after Z).

1. 1st letters: D, H, L, P, T (each $+4$).
2. 2nd letters: K, O, S, W, A ($+4$, W → A).
3. 3rd letters: R, V, Z, D, H ($+4$).

Trick: All three positions jump $+4$ – just add 4 to PWD.

Answer: (C) TAH

Concept: Find the change in each letter and in the number.

1. GN 14 → ER 1: $G-2=E$, $N+4=R$, $14-13=1$.
2. HP 18 → FT 5: $H-2=F$, $P+4=T$, $18-13=5$.
3. TK 4 → $T-2=R$, $K+4=O$, $4-13=-9$ → RO −9.

Trick: Rule: first $-2$, second $+4$, number $-13$.

Answer: (C) RO −9

Concept: Look for the pattern number – symbol – symbol and count the middle symbol.

1. 1 * £ → * qualifies.
2. 2 & % → & qualifies.
3. Others fail: # is followed by 1, the later & by 3, Ω by 4, @ by 8; £, % and $ are preceded by symbols.

Trick: Scan only symbols that come right after a digit, then check the next element.

Answer: (C) Two

Concept: Find the operation between consecutive numbers.

1. $10\to 20\to 40\to 80$: each $\times 2$.
2. $3\to 6\to 12\to 24$: each $\times 2$.
3. $6\to 12\to 24\to 48$: each $\times 2$ ✓.

Trick: Option A ends $20\to 30$, C has $8\to 12$ – they break the doubling.

Answer: (D) 6 - 12 - 24 - 48

Concept: Replace letters by operators and apply BODMAS.

1. Option C: $96÷12-45+3\times 14$.
2. $=8-45+42$.
3. $=5$ ✓.

Trick: Try the option with ÷ on 96 and 12 first – it gives a small number like 8.

Answer: (C) 96 A 12 D 45 C 3 B 14

Concept: Check the differences between consecutive terms.

1. $501-1=500$, $500-3=497$, $497-5=492$, $492-7=485$.
2. Subtracted numbers are consecutive odd numbers.
3. Next: $485-9=476$.

Trick: Also $501-n^2$: $501-0,501-1,501-4,\dots ,501-25=476$.

Answer: (D) 476

Concept: People between = Total − (position from left + position from right), when they do not overlap.

1. Manju has 15 people on her left; Nisha has 8 on her right.
2. $16+9=25<92$, so they do not overlap.
3. Between $=92-16-9=67$.

Trick: No overlap → Total − sum of positions.

Answer: (D) 67

Concept: Find the change in each letter and in the number.

1. IV 17 → FR 6: $I-3=F$, $V-4=R$, $17-11=6$.
2. KJ 12 → HF 1: $K-3=H$, $J-4=F$, $12-11=1$.
3. OE −6 → $O-3=L$, $E-4=A$, $-6-11=-17$ → LA −17.

Trick: Rule: $-3$, $-4$, number $-11$.

Answer: (B) LA −17

Concept: A letter common to two words gets the digit common to both codes (order may be jumbled).

1. PAID = 3517, ARCS = 2458.
2. Common letter: A.
3. Common digit: 5 → A = 5.

Trick: Match common letters with common digits.

Answer: (D) 5

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

1. $28+13-1=40$.
2. 27 students above Hitesh, 12 below, plus Hitesh himself.

Trick: Subtract 1 because the person is counted twice.

Answer: (B) 40