Q&A: practice questions with answers

Concept: Savings = salary − expenditure; write both savings in terms of the old salary $S$.

1. Old savings $=35\%$ of $S=0.35S$.
2. New salary $=1.1S$, savings $=40\%$ of $1.1S=0.44S$.
3. $0.44S-0.35S=0.09S=3150\Rightarrow S=35000$.
4. Present salary $=1.1\times 35000=$ ₹38,500.

Trick: The question asks the present salary – not the old ₹35,000 (option D is the trap).

Answer: (C) 38,500

Concept: Divisible by 45 ⇔ divisible by both 5 (last digit 0 or 5) and 9 (digit sum multiple of 9).

1. $b$ is a positive integer ⇒ $b=5$ (not 0).
2. Digit sum $=7+a+3+5+5=20+a$ ⇒ $a=7$ (sum 27).
3. $a+b=7+5=12$.

Trick: "Positive" rules out $b=0$; then only one $a$ in 0–9 makes the sum a multiple of 9.

Answer: (C) 12

Concept: Assume CP = 100; loss% is always on the (new) cost price.

1. CP $=100$, SP $=125$.
2. New CP $=120$, new SP $=125\times 0.9=112.5$.
3. Loss $=7.5$; loss% $=\frac{7.5}{120}\times 100=6.25\%$.

Trick: New SP/CP $=\frac{1.25\times 0.9}{1.2}=0.9375$ ⇒ $6.25\%$ loss.

Answer: (A) 6.25%

Concept: For an odd count of consecutive integers the average is the middle term.

1. Middle (3rd) integer $=10$ ⇒ numbers are $8,9,10,11,12$.
2. Smallest $=8$.

Trick: Smallest $=\text{average}-\frac{n-1}{2}=10-2=8$.

Answer: (C) 8

Concept: Mean proportional between $p$ and $q$ is $\sqrt{pq}$.

1. $x=\sqrt{(a+b)(a-b)}$.
2. $(a+b)(a-b)=a^2-b^2\Rightarrow x=\sqrt{a^2-b^2}$.

Yaad rakhein: $(a+b)(a-b)=a^2-b^2$ – never $a^2+b^2$ (option B is the trap).

Answer: (D) $\sqrt{a^2-b^2}$

Concept: Check each position of the letter cluster and the number separately.

1. 1st letters H(8), L(12), P(16), T(20): $+4$ → X(24).
2. 2nd letters D(4), I(9), N(14), S(19): $+5$ → $19+5=24$ = X.
3. 3rd letters K(11), O(15), S(19), W(23): $+4$ → $23+4=27\to 1$ = A (wrap after Z).
4. Numbers 10, 15, 20, 25: $+5$ → 30. Term = XXA 30.

Trick: Write positions A=1…Z=26 and count beyond 26 cyclically ($27\to 1$).

Answer: (D) XXA 30

Concept: Fix the definite positions first (D and V), then place the rest using the remaining clues.

1. Four people right of D → D is 3rd from left; V is 4th.
2. F is 3rd to the left of T: T cannot be at 4, 6 or 7 (F would land on V/D), so T = 5, F = 2.
3. E is neighbour of both H and T → E = 6, H = 7; L takes seat 1.
4. Row: L F D V T E H. Between L(1) and H(7) there are 5 people.

Trick: 'Only n people to the right' pins a seat exactly: position $=7-n$ from the left.

Answer: (A) Five

Concept: Compare words letter by letter; a shorter word comes before its extension (Mist before Mistake).

1. All start with 'Mi'; 3rd letters: g (Migrate), l (Mild, Milk), s (Mist, Mistake) → g < l < s.
2. Mild vs Milk: 4th letter d < k → Mild, Milk.
3. Mist vs Mistake: Mist is a prefix → Mist first.
4. Order: Migrate(4), Mild(2), Milk(5), Mist(3), Mistake(1).

Trick: Prefix rule: the shorter word always comes first (Mist → Mistake).

Answer: (A) 4, 2, 5, 3, 1

Concept: Decode each symbol from left to right and build the family tree.

1. B = C → B is brother of C; C ? O → C is daughter of O; so O is father of B and C.
2. O % P → O is father of P; hence B, C, P are siblings.
3. P € X → P is wife of X.
4. B is the brother of X's wife → wife's brother (brother-in-law).

Trick: Trace generation first (O on top, B/C/P below), then attach spouses with a dashed line.

Answer: (C) Wife's brother

Concept: Letters common to both words get the common digits; the leftover letter gets the leftover digit.

1. PINS → 3 2 4 7; HIPS → 4 6 2 7.
2. Common letters I, P, S ↔ common digits 2, 4, 7.
3. Leftover: N ↔ 3 (in PINS) and H ↔ 6 (in HIPS).

Trick: Code questions with two words: 'uncommon letter = uncommon digit'.

Answer: (A) 6

Concept: Find one operation on the whole first number that gives the second in both given pairs.

1. $54\times 2+2=110$ ✓ and $56\times 2+2=114$ ✓ → rule: $2n+2$.
2. Option A: $62\times 2+2=126$ ✓.
3. B: $2(58)+2=118\ne 120$; C: $2(45)+2=92\ne 90$; D: $2(48)+2=98\ne 96$.

Trick: When the second number is a little more than double, test $2n+k$ first.

Answer: (A) 62, 126

Concept: We need a triple 'perfect square – even digit – even digit' (squares: 1, 4, 9).

1. Mark every even digit whose left neighbour is 1, 4 or 9: … 4 6 7 … (6 after 4), … 9 8 7 … (8 after 9).
2. In both cases the right neighbour is 7 (odd), so the condition fails.
3. No other even digit follows a 1, 4 or 9 → count = 0.

Trick: First scan only for the squares (1, 4, 9) – then check their right neighbours; it is much faster than checking every digit.

Answer: (D) None

Concept: Write the alphabetical positions and look at the gaps between consecutive letters.

1. UQV: 21, 17, 22 → $-4,+5$; RNS: 18, 14, 19 → $-4,+5$; LHM: 12, 8, 13 → $-4,+5$.
2. OKM: 15, 11, 13 → $-4,+2$ – the second gap breaks the pattern.
3. So OKM is the odd one.

Trick: In three of four clusters the 3rd letter is just one step after the 1st (U→V, R→S, L→M); O→M is not.

Answer: (A) OKM

Concept: Find how the letters move in each step of the given triads.

1. TREK → RTEK: first two letters swap. RTEK → KRTE: last letter moves to the front.
2. MAPS → AMPS (swap) → SAMP (last to front) ✓ same logic.
3. WISE → IWSE (swap) → EIWS (E moved to front) ✓.
4. A: YAMN expected (given YANM); B: POEN expected; C: EISD expected – all wrong.

Trick: Check the 2nd step with the last letter only: it must jump to position 1 with the rest unchanged.

Answer: (D) WISE - IWSE - EIWS

Concept: Arrange the letters alphabetically, locate the required two letters, then count the letters between them in the alphabet.

1. LANGUID → A, D, G, I, L, N, U.
2. 3rd from left = G (7); 3rd from right = L (12).
3. Letters between G and L: H, I, J, K → $12-7-1=4$.

Trick: Letters strictly between positions $a$ and $b$ = $b-a-1$.

Answer: (D) 4

Concept: Convert to positions and compare the gaps.

1. EGF: 5, 7, 6 → $+2,-1$; BDC: 2, 4, 3 → $+2,-1$; HJI: 8, 10, 9 → $+2,-1$.
2. VYW: 22, 25, 23 → $+3,-2$ – different.
3. So VYW is the odd one.

Trick: Pattern 'x, x+2, x+1' = three consecutive letters with the last two swapped (E F G → E G F); V W X would give VXW, not VYW.

Answer: (C) VYW

Concept: Apply the rule digit by digit: odd digit $+1$, even digit $-1$.

1. 4 7 3 2 1 5 6 8 → 3 8 4 1 2 6 5 7.
2. New number = 38412657; its first digit from the left is 3.
3. (Only the first digit was really needed: 4 is even → $4-1=3$.)

Trick: Read the question before working: when only the first digit is asked, transform just that digit.

Answer: (C) 3

Concept: Treat the two letters and the number as three independent series.

1. 1st letters O(15) → M(13) → K(11) → ? : $-2$ → I(9).
2. 2nd letters N(14) → P(16) → R(18) → ? : $+2$ → T(20).
3. Numbers 35 → 44 → 53 → ? : $+9$ → 62. Answer IT62.

Trick: Opposite-moving letter pairs (one $-2$, other $+2$) are a common NTPC pattern.

Answer: (D) IT62

Concept: The word common to both sentences has the code common to both.

1. 'unit flash zebra' → mi de cz; 'zebra dance king' → de uv id.
2. Only 'zebra' appears in both sentences; only 'de' appears in both codes.
3. So zebra = de.

Trick: Common word ↔ common code; eliminate codes that appear once.

Answer: (D) de

Concept: Take successive differences; here the differences grow by an alternating amount.

1. Differences: $3,9,19,25,35$.
2. Second differences: $+6,+10,+6,+10$ → next $+6$ → difference $=35+6=41$.
3. Missing term $=101+41=142$.

Trick: If first differences look random, take the second differences – an alternating $6,10,6,10$ shows up.

Answer: (C) 142