Q&A: practice questions with answers

Concept: Opposite directions: relative speed = sum; distance = sum of lengths.

1. Length $L$ each; speeds $\frac{L}{12}$ and $\frac{L}{16}$.
2. Relative speed $=\frac{L}{12}+\frac{L}{16}=\frac{7L}{48}$
3. Time $=\frac{2L}{7L/48}=\frac{96}{7}=13.71\text{s}$

Trick: Equal lengths: $t=\frac{2t_1{t}_2}{t_1+t_2}=\frac{2\times 12\times 16}{28}$.

Answer: (D) 13.71 seconds

Concept: Speed $=\frac{\text{Distance}}{\text{Time}}$; speeds follow the given ratio.

1. Second train: $\frac{300}{3}=100\text{km/h}$
2. First train $=100\times \frac{5}{8}=62.5\text{km/h}$

Trick: 8 parts = 100 ⇒ 1 part = 12.5 ⇒ 5 parts = 62.5.

Answer: (B) $62.5\text{km/h}$

Concept: Largest equal piece that divides all lengths exactly = HCF.

1. $54=2\times 3^3$, $72=2^3\times 3^2$, $90=2\times 3^2\times 5$
2. HCF $=2\times 3^2=18\text{m}$

Trick: “Maximum equal length / largest size” → HCF; “minimum common” → LCM.

Answer: (B) 18 m

Concept: Apply discounts one after another on the reduced price.

1. After 15%: $2000\times 0.85=1700$
2. Second discount $=1700-1530=170$
3. $\frac{170}{1700}\times 100=10\%$

Trick: $\frac{1530}{1700}=0.9$ ⇒ second discount 10%.

Answer: (D) 10%

Concept: Form two equations and substitute.

1. Let smaller $=s$, larger $=L$: $2s+3L=55$ and $L+5=2s$.
2. Substitute $2s$: $L+5+3L=55\Rightarrow 4L=50$
3. $L=12.5$ (and $s=8.75$)

Trick: Replace “$2s$” directly — no need to find $s$ first.

Answer: (D) 12.5

Concept: Split the series into two alternate series.

1. Odd positions: $4,8,16,32$ – each $\times 2$.
2. Even positions: $4,12,28,?$ – differences $8,16$, so next difference $32$.
3. $?=28+32=60$

Trick: When numbers jump irregularly, check alternate terms first.

Answer: (D) $60$

Concept: Replace letters by signs, then apply BODMAS.

1. A = $÷$, B = $\times$, C = $+$, D = $-$
2. $1-40÷7\times 7+46$
3. $40÷7\times 7=40$ (left to right), so $1-40+46=7$

Trick: $÷7$ and $\times 7$ cancel each other – no fractions needed.

Answer: (D) $7$

Concept: Write the position values of the letters and find the gaps.

1. NRT: $14,18,20$ → $+4,+2$; JNP: $10,14,16$ → $+4,+2$
2. SWY: $19,23,25$ → $+4,+2$
3. QUO: $17,21,15$ → $+4,-6$ ✗

Trick: EJOTY: E5, J10, O15, T20, Y25 – reach any letter quickly.

Answer: (D) QUO

Concept: Check the gap between consecutive letters (wrapping Z → A).

1. MKI: $13,11,9$ → $-2,-2$; QOM: $17,15,13$ → $-2,-2$
2. BZX: B → Z → X is also $-2,-2$ (going back past A)
3. CBY: $3,2,25$ → $-1,-3$ ✗

Trick: In backward series, after A comes Z – B$-2$ = Z.

Answer: (C) CBY

Concept: Treat each letter position and the number separately.

1. 1st letter: O → G → Y → Q → I (each $-8$)
2. 2nd letter: K → C → U → M → E ($-8$); 3rd letter: H → Z → R → J → B ($-8$)
3. Numbers: $41,47,53,59,65$ (each $+6$)

Trick: Moving back 8 = moving forward 18 (since $26-8=18$).

Answer: (C) IEB 65

Concept: Take first differences, then look for a pattern in them.

1. Differences: $9,17,22,30,35$
2. Second differences: $8,5,8,5$ → next is $8$
3. Next difference $=35+8=43$; $?=123+43=166$

Trick: Alternating $+8,+5$ in the differences = two-level series.

Answer: (D) $166$

Concept: Find the shift for each letter of the first pair and verify it on the second pair.

1. FACN → LFIS: F$+6$=L, A$+5$=F, C$+6$=I, N$+5$=S
2. DUAH → JZGM: same $+6,+5,+6,+5$ ✓
3. VJSW: V$+6$=B, J$+5$=O, S$+6$=Y, W$+5$=B → BOYB

Trick: Wrap round: V(22)$+6=28-26=2$ = B.

Answer: (C) BOYB

Concept: Replace letters by signs and use BODMAS.

1. P = $\times$, Q = $÷$, R = $-$, S = $+$
2. $(96÷12)\times 5+(42÷7)\times 8-12\times 5$
3. $=8\times 5+6\times 8-60=40+48-60=28$

Trick: Solve brackets first, then all $\times$, then $+/-$.

Answer: (C) $28$

Concept: Each cluster is of the form X Y X; track letters and numbers separately.

1. Outer letters: R → N → J → F → B (each $-4$)
2. Middle letter: T → P → L → H → D (each $-4$)
3. Numbers: $77,72,67,62,57$ (each $-5$)

Trick: Middle letter is always 2 ahead of the outer letter: B + 2 = D.

Answer: (A) BDB 57

Concept: Total = rank from top + rank from bottom $-1$ (the person is counted twice).

1. Rank from top $=25$, rank from bottom $=67$
2. Total $=25+67-1=91$

Trick: Always subtract 1 – Raman is included in both counts.

Answer: (D) $91$

Concept: Interchange the numbers in each option and test the equation with BODMAS.

1. Interchange 4 and 5: $(21\times 2)÷3+15\times 4-19\times 5+36+7\times 6$
2. $=14+60-95+36+42$
3. $=152-95=57$ ✓

Trick: Original value: $14+75-76+36+42=91$; need 34 less – swapping 4, 5 changes $+75-76$ to $+60-95$ (34 less).

Answer: (D) 4 and 5

Concept: Facing the centre: left = clockwise, right = anticlockwise.

1. E is second to the left of F → one seat lies between F and E.
2. D is immediately right of C and A sits between B and C → D, C, A, B form a block of four consecutive seats.
3. This block cannot fit in the single gap between F and E, so it takes the other four seats; the gap gets G.
4. Order (clockwise): F, G, E, D, C, A, B.

Trick: Place the biggest block first – the leftover seat is the answer.

Answer: (C) G

Concept: Letters common to both words share the common digits.

1. SOAP = 5279, ATOP = 4527
2. Common letters O, A, P ↔ common digits 5, 2, 7
3. Left over: S = 9 and T = 4

Trick: Cancel the common part – the unique letter gets the unique digit.

Answer: (B) $4$

Concept: Look for the pattern Even – Odd – Odd and count the middle digits.

1. … 4 5 3 … ✓
2. … 4 5 1 … ✓
3. … 2 3 5 … ✓
4. … 8 5 7 … ✓ → total 4 such digits

Trick: First mark every even digit, then check only the next two digits.

Answer: (C) More than two

Concept: Look for Vowel – Vowel – Consonant.

1. Vowels in the series: U (1st), E, E, U, A, U (last).
2. Only A has a vowel before it (U) and a consonant after it (Z): U A Z ✓
3. Other vowels are preceded by consonants (N E, P E, R U, R U).

Trick: Find adjacent vowel pairs first – they are rare.

Answer: (D) One