Q&A: practice questions with answers

Concept: Numerator = sum of reverse alphabet positions (A = 26 … Z = 1); denominator = number of letters.

1. VACCINE: $5+26+24+24+18+13+22=132$; 7 letters → $\frac{132}{7}$
2. MASKS: $14+26+8+16+8=72$; 5 letters → $\frac{72}{5}$
3. SANITIZE: $8+26+13+18+7+18+1+22=113$; 8 letters
4. Code $=\frac{113}{8}$

Trick: Reverse position = $27-$ (forward position).

Answer: (A) $\frac{113}{8}$

Concept: Decode each symbol step by step and build the family tree.

1. M × O: M is the wife of O.
2. O $ N: O is the son of N.
3. N @ Q: N is the brother of Q.
4. Q % R: Q is the father of R; R # S: R is the husband of S.
5. So N is the brother of Q, who is R's father → N is the brother of R's father.

Trick: M is the daughter-in-law of N, not of R — a common trap in option (B).

Answer: (D) N is the brother of R’s father.

Concept: Replace letters with signs and apply BODMAS.

1. $29\times 7-168÷4+71-39+14\times 2$
2. $=203-42+71-39+28$
3. $=161+71-39+28=221$

Trick: Finish all × and ÷ first, then add/subtract left to right.

Answer: (A) $221$

Concept: Letters shift by +3, +2, +1 and the number is cubed.

1. FAN2 → ICO8: F+3 = I, A+2 = C, N+1 = O; $2^3=8$
2. NAP5 → QCQ125: N+3 = Q, A+2 = C, P+1 = Q; $5^3=125$
3. GUN8 → G+3 = J, U+2 = W, N+1 = O; $8^3=512$
4. Answer = JWO512

Trick: Option (D) JVO512 has U+1 — check every letter, not only the number.

Answer: (B) JWO512

Concept: Put each option's signs in place and check which side equals 131.

1. Option (B): $467+231-123-789+345$
2. $=698-123=575$; $575-789=-214$
3. $-214+345=131$ ✓
4. Option (A) gives $467+231-123+789+345=1709$, not 131.

Trick: The last sign before 131 is '='; work only with the left side.

Answer: (B) $+,-,-,+,=$

Concept: Replace letters with signs and apply BODMAS.

1. $124÷4-86÷2+61+17\times 3$
2. $=31-43+61+51$
3. $=100$

Trick: Group positives and negatives: $(31+61+51)-43=143-43$.

Answer: (A) $100$

Concept: Third number = (first)${}^3$ + (second)${}^3$.

1. $(2,3,35)$: $2^3+3^3=8+27=35$
2. $(11,6,1547)$: ${11}^3+6^3=1331+216=1547$
3. (A) $(4,15,3439)$: $4^3+{15}^3=64+3375=3439$ ✓
4. (B) $1000+729=1729$, (C) $343+512=855$, (D) $27+1728=1755$ — no match.

Trick: A large third number from two small numbers suggests squares or cubes.

Answer: (A) $(4,15,3439)$

Concept: Check the opposite-letter pair (sum of positions $=27$) and the +1 link.

1. XCY: X(24) and C(3) are opposites ($24+3=27$); Y = X+1.
2. OLP: O(15), L(12) → $27$; P = O+1. TGU: T(20), G(7) → $27$; U = T+1.
3. BXC: B(2), X(24) → $26$, not opposites (B's opposite is Y).
4. So BXC is odd.

Yaad rakhein: Opposite pairs: A–Z, B–Y, C–X, D–W … (sum $=27$).

Answer: (D) BXC

Concept: Draw Dogs inside Cats and Rats separate from Cats.

1. All dogs are cats → Dogs circle inside Cats.
2. No cat is a rat → Rats circle is outside Cats, hence outside Dogs too.
3. I: Some rats are cats — false (no cat is a rat).
4. II: Some dogs are rats — false (no dog can be a rat).

Trick: All A are B + No B is C ⇒ No A is C.

Answer: (A) Neither conclusion I nor II follows

Concept: Each term is 13 less than the previous one.

1. $159-13=146$
2. $146-13=133$
3. $133-13=120$, $120-13=107$, $107-13=94$, $94-13=81$ ✓

Trick: Check the known consecutive terms ($120\to 107$) to get the common difference first.

Answer: (C) $133$

Concept: Find which classes are inside, overlapping or separate.

1. The Prime Minister and the Finance Minister are both members of the Union Government (Union Council of Ministers).
2. The Prime Minister and the Finance Minister are two different posts — no overlap.
3. So two separate circles inside one big circle.

Trick: Two distinct members of one larger group → two separate circles inside a bigger one.

Answer: (B) Option (B)

Concept: Second term $=\frac{n^2}{3}+n$.

1. $9$: $\frac{81}{3}+9=27+9=36$
2. $18$: $\frac{324}{3}+18=108+18=126$
3. $12$: $\frac{144}{3}+12=48+12=60$

Trick: Same as $n\times (\frac{n}{3}+1)$: $9\times 4$, $18\times 7$, $12\times 5=60$.

Answer: (B) $60$

Concept: When one face is common to all positions, the faces around it in cyclic order give the opposite pairs.

1. '3' is on top in all three figures.
2. Faces around 3 in order: 6 → 2 (fig. 1), 2 → 5 (fig. 2), 5 → 4 (fig. 3).
3. So the ring around 3 is 6, 2, 5, 4; alternate faces are opposite.
4. 6 is opposite 5 (and 2 is opposite 4).

Trick: In a ring of four faces around a common face, the 1st and 3rd are opposite.

Answer: (D) $5$

Concept: Middle number = (first − third)${}^2$.

1. $(19,64,11)$: $(19-11{)}^2=8^2=64$
2. $(27,169,14)$: $(27-14{)}^2={13}^2=169$
3. (D) $(22,121,11)$: $(22-11{)}^2={11}^2=121$ ✓
4. (A) ${11}^2=121\ne 110$, (B) ${12}^2=144$, (C) $9^2=81$ — no match.

Trick: A perfect square in the middle hints at a square of a difference or sum.

Answer: (D) $(22,121,11)$

Concept: Trace the path with coordinates, starting at A $(0,0)$.

1. 6 km North → $(0,6)$; left (West) 3 km → $(-3,6)$.
2. Left (South) 3 km → $(-3,3)$; left (East) 6 km → $(3,3)$.
3. Right (South) 3 km → B $=(3,0)$.
4. B is 3 km East of A, so he must drive 3 km towards West.

Trick: Net North–South: $6-3-3=0$; net East–West: $-3+6=3$ East.

Answer: (B) 3 km towards west

Concept: Alternate addition and subtraction of consecutive squares.

1. $90+{11}^2=90+121=211$
2. $211-{12}^2=211-144=67$
3. $67+{13}^2=67+169=236$
4. $236-{14}^2=236-196=40$

Trick: Big up-down jumps usually mean ± squares or cubes.

Answer: (C) $40$

Concept: Match common words with common codes.

1. 'day of rest' & 'rest after work' share 'rest' → 'per' → rest = per.
2. 'rest after work' & 'all day work' share 'work' → 'fin' → work = fin.
3. In 'rest after work' = 'per fin tds', the remaining code tds = after.

Trick: Eliminate two known codes in a three-word sentence — the third is the answer.

Answer: (C) tds

Concept: Replace symbols, then apply BODMAS.

1. Given: $2÷5+2-5\times 5$
2. After replacing: $2+5-2\times 5÷5$
3. $2\times 5÷5=2$
4. $2+5-2=5$

Trick: Do the multiplication and division part ($2\times 5÷5$) first.

Answer: (A) $5$

Concept: Use the common face and read the faces around it in the same (clockwise) order.

1. Face 1 is the front face in both positions.
2. Around 1 (clockwise): top 5 → right 3 (position 1); top 3 → right 2 (position 2).
3. So the ring around 1 is 5 → 3 → 2 → (the fourth face).
4. In this ring 5 and 2 are alternate faces → opposite.

Trick: In the ring of four faces around a common face, alternate faces are opposite.

Answer: (D) $2$

Concept: Unfold in reverse order; each unfold creates a mirror image across the fold line.

1. Fold 1: top half onto bottom half. Fold 2: right half onto left. The cut is made on the folded bottom-left quarter.
2. Undo fold 2: the bottom-right quarter gets a left-right mirror image of the cut.
3. Undo fold 1: the top half gets an upside-down mirror image of the bottom half.
4. So the bottom row and top row must be vertical mirror images — option (C).

Trick: Across a horizontal fold, shapes flip upside-down; across a vertical fold, they flip left-right.

Answer: (C) Option (C)