Q&A: practice questions with answers

Concept: Expenditure $=(100-\text{saving}\%)$ of income.

1. Expenditure $=80\%$ of $7915$.
2. $=\frac{4}{5}\times 7915=4\times 1583=6332$.

Trick: $80\%=\frac{4}{5}$: divide by 5, multiply by 4.

Answer: (B) ₹6,332

Concept: Speed in still water $=\frac{\text{downstream}+\text{upstream}}{2}$.

1. Downstream speed $=\frac{91}{13}=7\text{km/h}$.
2. Upstream speed $=\frac{39}{13}=3\text{km/h}$.
3. Still-water speed $=\frac{7+3}{2}=5\text{km/h}$.

Trick: Stream speed $=\frac{7-3}{2}=2$ – useful if asked next.

Answer: (A) 5

Concept: Integer roots need the discriminant $D=b^2-4ac$ to be a perfect square.

1. $D=(a-1{)}^2-4(4a+7)=a^2-18a-27=(a-9{)}^2-108$.
2. Let $D=k^2$: $(a-9-k)(a-9+k)=108$; both factors even → $(2,54)$ or $(6,18)$.
3. $(6,18)$: $a-9=12\Rightarrow a=21$; $(2,54)$: $a=37$. Least odd positive $a=21$.
4. Check: $x^2-20x+91=(x-7)(x-13)$ ✔.

Trick: Option test: put each option in $(a-9{)}^2-108$; only $a=21$ gives $144-108=36$, a perfect square.

Answer: (C) 21

Concept: Rotating a rectangle about its length makes length $=h$ and breadth $=r$; $\frac{V}{CSA}=\frac{\pi r^{2}h}{2\pi rh}=\frac{r}{2}$.

1. $\frac{r}{2}=\frac{4851}{462}=10.5\Rightarrow r=21\text{cm}$.
2. $2\times \frac{22}{7}\times 21\times h=462\Rightarrow 132h=462\Rightarrow h=3.5\text{cm}$.
3. Perimeter $=2(21+3.5)=49\text{cm}$.

Trick: Divide volume by CSA to get $\frac{r}{2}$ at once.

Answer: (B) 49

Concept: The perpendicular from the centre bisects a chord: $r^2=(\text{half chord}{)}^2+(\text{distance}{)}^2$.

1. Let AB be at distance $d$ from O; CD (same side) is at $d+4$.
2. $r^2=7^2+d^2=3^2+(d+4{)}^2\Rightarrow 49=25+8d\Rightarrow d=3$.
3. $r^2=49+9=58\Rightarrow r=\sqrt{58}$; diameter $=2\sqrt{58}$.

Trick: Longer chord is nearer the centre, so on the same side the shorter chord is at $d+4$.

Answer: (B) $2\sqrt{58}$

Concept: Use alphabet positions (A = 1 … Z = 26) and find the change in each letter and in the number.

1. KX 3 → OV −9: $K(11)+4=O(15)$, $X(24)-2=V(22)$, $3-12=-9$.
2. Check IR 11 → MP −1: $I+4=M$, $R-2=P$, $11-12=-1$ ✓.
3. JG −2: $J(10)+4=N(14)$, $G(7)-2=E(5)$, $-2-12=-14$ → NE −14.

Trick: Pattern = (+4, −2, −12). Test it on the second pair before applying.

Answer: (A) NE −14

Concept: Find how the 2nd and 3rd numbers are made from the 1st number.

1. (36, 27, 41): $36-9=27$ and $36+5=41$.
2. (45, 36, 50): $45-9=36$ and $45+5=50$ ✓.
3. Check (53, 44, 58): $53-9=44$, $53+5=58$ ✓. Others fail, e.g. $74+5=79\ne 89$.

Trick: Rule: (x, x − 9, x + 5). Equivalently 3rd − 2nd = 14 in every set.

Answer: (D) (53, 44, 58)

Concept: Facing the centre: left = clockwise, right = anticlockwise. 7 seats in all.

1. Fix S. Two people between S and T from the left of S → T is 3rd to the left of S; Y is 4th to the left of S.
2. R is 4th to the right of T → R is the immediate right of S.
3. The empty seats are on the left of S (1st, 2nd) and right of Y. V cannot sit next to R or T → V is 1st left of S; U cannot be next to V → U is between Y and R; Q is between V and T.
4. From Q, count three to the right: V, S, R.

Trick: In a 7-seat circle, "4th to the right" = "3rd to the left" — use whichever is shorter.

Answer: (D) R

Concept: When codes are jumbled, match common letters with common digits.

1. LOST → 6832 and SALT → 2136.
2. Common letters: L, S, T; common digits: 6, 3, 2.
3. The only letter left in SALT is A, and the only digit left in 2136 is 1 → A = 1.

Trick: Remove common letters and common digits — the leftovers match each other.

Answer: (C) 1

Concept: Look at the differences between consecutive terms.

1. Differences: $-1,+4,-9,+16,+25?$ → they are squares with alternating signs: $-1^2,+2^2,-3^2,+4^2$.
2. Next difference $=-5^2=-25$.
3. $1524-25=1499$.

Trick: Alternating up–down series → check $\pm n^2$ differences.

Answer: (B) 1499

Concept: Draw the minimum possible Venn diagram: "All A are B" puts circle A fully inside circle B.

1. Pulse ⊂ Rice ⊂ Wheat ⊂ Corn (nested circles).
2. (I) Pulse lies inside Corn → "All pulse are corn" follows.
3. (II) Rice lies inside Corn → some corn are surely rice → follows.

Trick: Chain of "All" statements: All first are last; and "Some last are any middle" is always true.

Answer: (B) Both conclusions (I) and (II) follow

Concept: Change each digit according to whether it is even or odd, then read the new number.

1. 413257: 4 (even) → $4+3=7$; 1 → 3; 3 → 5; 2 → 5; 5 → 7; 7 (odd) → $7+2=9$.
2. New number: 735579.
3. First + last $=7+9=16$.

Trick: Only first and last digits matter: $4+3=7$ and $7+2=9$ — skip the middle.

Answer: (D) 16

Concept: Track the position on a coordinate grid (East = +x, North = +y); a right turn from East faces South.

1. A = (0, 0). 9 km East → (9, 0).
2. Right → South 16 km → (9, −16). Right → West 28 km → (−19, −16).
3. Right → North 21 km → (−19, 5). Right → East 19 km → P = (0, 5).
4. P is 5 km directly North of A → he must drive 5 km South.

Trick: Net E–W: $9-28+19=0$; net N–S: $-16+21=+5$ (North) → go back 5 km South.

Answer: (A) 5 km to the South

Concept: Check each letter position and the number separately.

1. 1st letters: H, I, J, K → L (+1).
2. 2nd letters: K, L, M, N → O; 3rd letters: P, Q, R, S → T.
3. Numbers: 22, 31, 40, 49 (+9) → 58.

Trick: All three letters move +1, number moves +9 → LOT58.

Answer: (B) LOT58

Concept: Place the fixed person first, then use the sum and "immediately below" conditions.

1. C is on floor 6.
2. B is on an odd floor except 3 → 1 or 5. If B = 1, D = 6 (taken by C) ✗. So B = 5, D = 2.
3. Free floors: 1, 3, 4. E immediately below F → E = 3, F = 4; A = 1.
4. Above E (floor 3): F, B, C = 3 people.

Trick: Use "sum = 7" pairs (1+6, 2+5, 3+4) to fix positions quickly.

Answer: (C) 3

Concept: Each letter position and the number follow their own step.

1. 1st letters: S, T, U, V → W (+1).
2. 2nd: P, Q, R, S → T; 3rd: M, N, O, P → Q.
3. Numbers: 8, 14, 20, 26 (+6) → 32.

Trick: Every letter +1, number +6 → WTQ 32.

Answer: (C) WTQ 32

Concept: Try each option by swapping the two numbers and applying BODMAS.

1. Swap 3 and 8: $24\times 8+(32÷4)-10\times 3+26$.
2. $=192+8-30+26$
3. $=196$ ✓ (LHS = RHS).

Trick: RHS 196 is large → the big product $24\times 8=192$ is a good first guess.

Answer: (C) 3 and 8

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

1. "1 8 €": 8 is preceded by 1 and followed by € ✓.
2. "9 3 £": 3 is preceded by 9 and followed by £ ✓.
3. Other numbers before a symbol (3 £, 9 @, 9 #) are preceded by symbols ✗. Count = 2.

Trick: Scan only numbers that stand just before a symbol, then check their left neighbour.

Answer: (C) 2

Concept: Find the shift from the given pair and check it on each option.

1. Option D: # = RVU → OSR: $R-3=O$, $V-3=S$, $U-3=R$.
2. Same rule: JNM → $J-3=G$, $N-3=K$, $M-3=J$ → GKJ ✓.
3. Other options do not give one consistent shift on both sides.

Trick: Here each letter moves back 3 — test options rather than guessing # first.

Answer: (D) # = RVU, % = GKJ

Concept: Identify the highest and lowest numbers, then their second digits.

1. Highest = 875 → second digit 7.
2. Lowest = 167 → second digit 6.
3. Second digit of lowest − second digit of highest $=6-7=-1$.

Trick: "A subtracted from B" means B − A — read the order carefully.

Answer: (C) −1