Q&A: practice questions with answers

Concept: $(a-b)(a+b)=a^2-b^2$

1. $9993=10000-7$, $10007=10000+7$
2. Product $={10000}^2-7^2$
3. $=100000000-49=99999951$

Trick: Numbers equally spaced around a round number: (round number)${}^2$ − (gap)${}^2$.

Answer: (C) 99999951

Concept: Find the value of one ratio part from the given difference.

1. C − D $=9-3=6$ parts $=720$ ⇒ 1 part $=120$
2. C − B $=9-7=2$ parts
3. $=2\times 120=240$

Trick: Difference of shares = difference of ratio terms × value of 1 part.

Answer: (A) ₹240

Concept: Solve the bracket first, then multiplication, then addition/subtraction from left to right.

1. $\frac{2}{3}+\frac{1}{3}=1$
2. $1\times 23=23$
3. $23-13+9=19$

Yaad rakhein: Bracket → Of → Division/Multiplication → Addition/Subtraction.

Answer: (D) 19

Concept: A prime number is a natural number greater than 1 that is divisible only by 1 and itself.

1. So every prime has exactly two factors: 1 and the number.
2. Example: 7 → factors 1, 7; 13 → factors 1, 13.

Yaad rakhein: 1 has only one factor, so it is neither prime nor composite; 2 is the only even prime.

Answer: (B) 2

Concept: Use $1-{\sin }^2\theta ={\cos }^2\theta$ to simplify the denominator.

1. Denominator $=1-{\sin }^2\theta +\cos \theta ={\cos }^2\theta +\cos \theta$
2. $=\cos \theta (\cos \theta +1)$
3. Expression $=\frac{\sin \theta (1+\cos \theta )}{\cos \theta (1+\cos \theta )}=\frac{\sin \theta }{\cos \theta }=\tan \theta$

Trick: Put $\theta ={45}^{\circ }$: $\frac{0.707\times 1.707}{1.707-0.5}\approx 1=\tan {45}^{\circ }$.

Answer: (C) $\tan \theta$

Concept: Take total work as LCM of the days and work in repeating 3-day cycles.

1. Total work = LCM(15, 10, 30) = 30 units; A = 2, B = 3, C = 1 unit/day
2. One 3-day cycle: A alone 2 days + (A+B+C) on 3rd day $=2+2+6=10$ units
3. 30 units need $\frac{30}{10}=3$ cycles $=3\times 3=9$ days

Trick: Cycle questions: work done per cycle → number of full cycles → check if work ends exactly at a cycle end.

Answer: (B) 9 days

Concept: Track how the letters of the first word move in the 2nd and 3rd words.

1. WILD → IWLD: first two letters swapped.
2. WILD → WLDI: 2nd letter (I) shifted to the end.
3. TALK → ATLK → TLKA follows the same rule.
4. VICE → IVCE (swap) → VCEI (I to the end) ✓; BOSE would give BSEO, not OSEB.

Trick: Check both rules on every option; one rule alone may match two options.

Answer: (B) VICE - IVCE - VCEI

Concept: Place B at the centre and fix the other towns one by one on a compass grid.

1. M is west of B; N is east of M — so M, B and N lie on one east–west line.
2. Q is south-east of B and N is north of Q ⇒ N is to the east of B.
3. L (south of B) is south-west of N ✓ — consistent.
4. Hence B is to the West of N.

Trick: If N is east of B, then B is west of N — just reverse the direction.

Answer: (C) West

Concept: Use the “only” clues to fix exact positions from top and bottom.

1. Only A is above E ⇒ A at top, E second.
2. Only F between E and B ⇒ F third, B fourth.
3. Only P below M ⇒ P at bottom, M just above it.
4. L takes the remaining place (5th from top). Between L and P: only M.

Trick: “Only X is above Y” fixes X at top and Y at 2nd immediately.

Answer: (A) One

Concept: Look at consecutive differences/ratios; here two operations alternate.

1. $36\times 2=72$, $72-27=45$
2. $45\times 2=90$, $90-27=63$
3. $63\times 2=126$, $126-27=99$

Trick: When numbers go up and down alternately, test “$\times$ then −” pattern.

Answer: (B) 99

Concept: For each symbol check: left neighbour odd number AND right neighbour a symbol.

1. Symbols followed by a symbol: * (before £) and & (before %).
2. * is preceded by 1 (odd) ✓
3. & is preceded by 5 (odd) ✓
4. Others fail (e.g. @ → followed by 8). Total = 2.

Trick: First find “symbol-symbol” pairs, then check only their left neighbour.

Answer: (B) Two

Concept: Trace the path with right turns: North → East → South → West.

1. A to 10 km North.
2. Right: 3 km East; Right: 6 km South (now 4 km north of A’s level).
3. Right: 3 km West ⇒ back on A’s north line, 4 km north of A (this is B).
4. To return to A: 4 km South.

Trick: East 3 and West 3 cancel; net north $=10-6=4$ km.

Answer: (D) 4 km South

Concept: Find the operation linking 1st → 2nd → 3rd number in both given sets.

1. $3\times 4=12$, $12\times 3=36$
2. $8\times 4=32$, $32\times 3=96$
3. Option: $12\times 4=48$, $48\times 3=144$ ✓

Trick: Third number $=12\times$ first: $12\times 12=144$.

Answer: (D) (12, 48, 144)

Concept: Write letter positions and compare the moves within each pair.

1. LH-KN: L(12)−4=H(8); L−1=K(11); K+3=N(14).
2. NJ-MP and JF-IL follow the same: −4, −1, +3.
3. QM-PR: Q(17)−4=M(13); Q−1=P(16); P+3=S(19), but given R(18) ✗

Trick: Check only one relation (e.g. 2nd letter of first cluster +6 = last letter): H+6=N, J+6=P, F+6=L, M+6=S≠R.

Answer: (D) QM-PR

Concept: Start with the most definite clue (“only P to the right of Q”) and fill the row facing north.

1. Only P is right of Q ⇒ Q at 6th, P at 7th (from left).
2. One person between E and Q ⇒ E at 4th.
3. Two between A and E ⇒ A at 1st.
4. B, R, F in 2nd, 3rd, 5th with B left of R left of F ⇒ A B R E F Q P. 3rd from right = F.

Trick: Facing north: your right = the right end of the row.

Answer: (B) F

Concept: Compare positions: in each triad the first letters go +1, +2 and the second letters go +2, +6.

1. PL-QN-ST: P→Q (+1)→S (+2); L→N (+2)→T (+6).
2. JF-KH-MN: J→K→M; F→H (+2)→N (+6) ✓
3. MI-NK-PQ: M→N→P; I→K (+2)→Q (+6) ✓
4. Other options give +7 in the last step (e.g. O→V).

Trick: Also in each first pair, 2nd letter = 1st letter −4 (P−4=L, M−4=I).

Answer: (A) MI-NK-PQ

Concept: Condition: symbol with an even number just before it AND a symbol just after it.

1. Even numbers in the series: only 8 (in “5 8 $ 7”).
2. The symbol after 8 is $, which is followed by 7 (a number) ✗
3. No other symbol has an even number before it. Count = 0.

Trick: Start from the rarer condition — here even numbers are very few.

Answer: (A) None

Concept: Find odd digits whose both neighbours are also odd (odd–odd–odd triplets).

1. “2 7 5 1 3 4”: 5 (7 before, 1 after) ✓; 1 (5 before, 3 after) ✓
2. “4 1 9 3”: 9 (1 before, 3 after) ✓
3. Other odd runs like “3 7 4” or “9 5 2” break the rule.
4. Count = 3.

Trick: Look for runs of three or more odd digits; each inner digit counts.

Answer: (C) 3

Concept: Find the operation from the complete pair in an option and apply it to both sides.

1. Rule: second number $=\frac{\text{first}}{4}$
2. $76÷4=19$ ✓ and $92÷4=23$ ✓
3. Other options fail, e.g. $98÷4$ is not 19.

Trick: Since $92\to Y$ and $X\to 19$ use the same rule, test $X=4\times 19=76$.

Answer: (C) X = 76, Y = 23

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

1. REVS → 6942; ORES → 6421
2. Common letters R, E, S ↔ common digits 6, 4, 2
3. Left over: V ↔ 9 (and O ↔ 1)

Trick: Remove the common part; the leftover letter takes the leftover digit.

Answer: (B) 9