Q&A: practice questions with answers

Concept: $\text{SP}=\text{CP}\times \frac{100+\text{Gain}\%}{100}$ and $\text{MRP}=\frac{\text{SP}\times 100}{100-\text{Discount}\%}$.

1. $\text{SP}=210\times \frac{190}{100}=399$.
2. $\text{MRP}=\frac{399\times 100}{95}=420$.

Trick: One line: $\text{MRP}=210\times \frac{190}{95}=210\times 2=420$.

Answer: (C) ₹420

Concept: If B lies on segment AC (between A and C), then $AB+BC=AC$.

1. $(k+3)+2k=5k-5$.
2. $3k+3=5k-5\Rightarrow 2k=8\Rightarrow k=4$.
3. Check: $AB=7,BC=8,AC=15$ ✓.

Yaad rakhein: Betweenness rule: the two parts must add up to the whole.

Answer: (B) 4

Concept: A number is divisible by 11 if (sum of odd-place digits) − (sum of even-place digits) is $0$ or a multiple of 11.

1. For $2y5$: $(2+5)-y=7-y$.
2. $7-y=0\Rightarrow y=7$ (a digit cannot make $7-y=\pm 11$).
3. Check: $275=11\times 25$ ✓.

Trick: For a 3-digit number $abc$, usually middle digit $b=a+c$ (if $a+c<10$).

Answer: (A) 7

Concept: For a cube of side $a$: $V=a^3$ and main (body) diagonal $d=a\sqrt{3}$.

1. $a^3=729\Rightarrow a=9$ cm.
2. $d=9\sqrt{3}$ cm.

Yaad rakhein: Face diagonal $=a\sqrt{2}$, body diagonal $=a\sqrt{3}$.

Answer: (D) $9\sqrt{3}$ cm

Concept: Work done = one-day work × days; the remaining work is finished by B alone.

1. $(A+B)$ one-day work $=\frac{1}{12}+\frac{1}{16}=\frac{7}{48}$.
2. In 3 days: $\frac{21}{48}=\frac{7}{16}$; remaining $=\frac{9}{16}$.
3. B's time $=\frac{9}{16}\times 16=9$ days.

Trick: LCM method: total work $=48$ units, A $=4$, B $=3$ per day; 3 days $=21$ units; left $27÷3=9$.

Answer: (D) 9 days

Concept: Draw the Venn diagram with the least possible overlap and test each conclusion.

1. All hands are legs: Hands circle lies inside Legs.
2. No leg is an eye: Legs and Eyes are separate, so Hands (inside Legs) cannot touch Eyes.
3. II (No hand is an eye) follows. I (All legs are hands) is the converse of a universal – not definite.

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

Answer: (D) Only conclusion II follows

Concept: Trace the path step by step, tracking the facing direction after each turn.

1. A → 6 km North. Left (West) 2 km, left (South) 2 km.
2. Right (West) 3 km, left (South) 2 km, left (East) 5 km to B.
3. Net: West $2+3=5$ and East $5$ cancel; North $6-2-2=2$ km.
4. B is 2 km North of A, so he must drive 2 km South.

Trick: Add North–South and East–West separately; opposite directions cancel.

Answer: (A) 2 km South

Concept: Use Venn diagrams; 'Some' + 'All' gives a definite 'Some' conclusion.

1. Some tablets are laptops – Tablets and Laptops overlap.
2. All laptops are desktops – Laptops lie inside Desktops, so the overlap part is also inside Desktops.
3. Hence some desktops are tablets: I follows. II contradicts I, so it does not follow.

Trick: 'Some A are B' + 'All B are C' ⇒ 'Some A are C' (and 'Some C are A').

Answer: (B) Only conclusion (I) follows

Concept: An effect must follow directly from the cause (truckers' strike over diesel price rise).

1. I: A truck strike stops movement of goods, so supply of fruits and vegetables drops – direct effect.
2. II: Rising demand for diesel vehicles is not caused by a strike against diesel prices.
3. III: Auto fare rise in one city for 48 hours is not linked to the truckers' strike.

Trick: Ask 'Did the strike itself cause this?' – only supply disruption passes.

Answer: (C) Only I can be a possible effect

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

1. RIFE = 3647, FORE = 6438.
2. Common letters R, F, E ↔ common digits 3, 6, 4.
3. Left in RIFE: I = 7; left in FORE: O = 8.

Trick: Strike out the common digits – the odd digit belongs to the odd letter.

Answer: (A) 8

Concept: Check each letter position separately for a fixed jump.

1. 1st letters: J, L, N, P, R (+2).
2. 2nd letters: M, O, Q, S, U (+2).
3. 3rd letters: P, R, T, V, X (+2).

Trick: Every letter moves +2, so just add 2 to each letter of PSV.

Answer: (A) RUX

Concept: Replace letters by signs, then apply BODMAS.

1. $2\times 18-20÷4+15$.
2. $=36-5+15$.
3. $=46$.

Trick: Do $÷$ and $\times$ first, then $+$ and $-$ from left to right.

Answer: (C) 46

Concept: The same rule must link X → 114 and 26 → Y; test the options.

1. Try (C): $38\times 3=114$ ✓ and $26\times 3=78$ ✓.
2. Others fail, e.g. (B) $39\times 3=117\ne 114$; (D) $42\times 3=126$.

Trick: 114 is a multiple of 3 ($114=3\times 38$) – the 'multiply by 3' rule is the first to test.

Answer: (C) X = 38, Y = 78

Concept: Find the differences between consecutive numbers of each set.

1. $(32,78,93)$: $78-32=46$, $93-78=15$.
2. $(29,75,90)$: $46$ and $15$ again.
3. (D) $(38,84,99)$: $84-38=46$, $99-84=15$ ✓.

Trick: Rule: 2nd $=$ 1st $+46$, 3rd $=$ 2nd $+15$ – check the first gap, then the second.

Answer: (D) (38, 84, 99)

Concept: Vowel → next consonant after it; consonant → next vowel after it (vowels A, E, I, O, U).

1. P → U, A → B, I → J, N → O.
2. T → U, E → F, R → U.
3. New group: U B J O U F U – U appears 3 times.

Trick: After P, R and T the next vowel is U for all three.

Answer: (B) U

Concept: Use alphabet positions and compare the gaps in each cluster.

1. JGM: J−3=G, G+6=M. TQW: T−3=Q, Q+6=W. QNT: Q−3=N, N+6=T.
2. NKR: N−3=K, but K+7=R (not +6).
3. So NKR breaks the pattern $-3,+6$.

Trick: Write the gap pair $(-3,+6)$ for each – the one with a different pair is odd.

Answer: (A) NKR

Concept: Find the shift applied to each letter using alphabet positions.

1. XVYU → NLOK: X(24)→N(14), V(22)→L(12), Y(25)→O(15), U(21)→K(11): each −10.
2. USVR → KILH also −10 each.
3. QORN: Q(17)→G(7), O(15)→E(5), R(18)→H(8), N(14)→D(4).

Trick: −10 is the same as +16 on the alphabet wheel; use EJOTY (5, 10, 15, 20, 25) to count fast.

Answer: (C) GEHD

Concept: Look for the pattern even – odd – odd (the middle digit is counted).

1. Scan left to right for an odd digit with an even digit before and an odd digit after.
2. Matches: 8 3 5, 8 7 9, 6 9 3, 4 1 3, 2 7 1.
3. Total $=5$.

Trick: Mark every odd digit first, then keep only those with E before and O after.

Answer: (B) 5

Concept: Fix definite positions first (people facing North: left to right = positions 1 to 7).

1. No one to the right of F ⇒ F = 7. Three between F and E ⇒ E = 3.
2. Two between E and P ⇒ P = 6.
3. R, Q adjacent (Q right of R) with A third left of R ⇒ R = 4, Q = 5, A = 1; B = 2.
4. Order: A B E R Q P F. Between B and P: E, R, Q = 3.

Trick: Start from the extreme person (F at the right end) – everything else hangs on it.

Answer: (C) Three

Concept: Common letters take the common digits; the extra letter takes the extra digit.

1. AMBER = 79612, UMBRA = 12659.
2. Common letters A, M, B, R ↔ common digits 9, 6, 1, 2.
3. AMBER leftover: E = 7; UMBRA leftover: U = 5.

Trick: Cancel matching digits from both codes – U pairs with the unmatched 5.

Answer: (C) 5