Q&A: practice questions with answers

Concept: The additional discount is calculated on the price after the first discount.

1. After 40% discount: $1200\times 0.6=$ ₹720.
2. Sold at ₹520, so extra discount $=720-520=$ ₹200.
3. Additional discount% $=\frac{200}{720}\times 100=\frac{250}{9}=27\frac{7}{9}\%$.

Trick: $\frac{200}{720}=\frac{5}{18}$; $\frac{5}{18}\times 100=27.\bar{7}$.

Answer: (B) $27\frac{7}{9}\%$

Concept: Equate total work: (workers $\times$ days) in both cases.

1. $8(15m+19w)=14(9m+4w)$.
2. $120m+152w=126m+56w\Rightarrow 96w=6m$.
3. $m=16w$: one man $=$ 16 women.

Trick: Divide by 2 first: $4(15m+19w)=7(9m+4w)$ keeps numbers small.

Answer: (D) 16

Concept: Form two equations in the larger ($L$) and smaller ($S$) numbers.

1. $L-S=8$ and $2L-5S=13$.
2. Put $L=S+8$: $2S+16-5S=13\Rightarrow 3S=3\Rightarrow S=1$.
3. $L=9$; check $2\times 9-5\times 1=13$.

Trick: Test options: $L=9,S=1$ gives $18-5=13$ – done.

Answer: (D) 9

Concept: Take 1 kg "sold": compare actual cost of goods given with money received.

1. SP of 1 kg $=48\times 1.2\times 0.9=$ ₹51.84.
2. He actually gives 960 g, costing $48\times 0.96=$ ₹46.08.
3. Profit% $=\frac{51.84-46.08}{46.08}\times 100=\frac{5.76}{46.08}\times 100=12.5\%$.

Trick: Multiply factors: $\frac{1.2\times 0.9}{0.96}=\frac{1.08}{0.96}=1.125$ → 12.5% profit.

Answer: (C) 12.5% profit

Concept: If numbers are $19x,7x,13x$ with 19, 7, 13 coprime, HCF $=x$ and LCM $=19\times 7\times 13\times x$.

1. $19\times 7\times 13=1729$.
2. $1729x=8645\Rightarrow x=5$.
3. HCF $=5$.

Trick: $1729$ (the Hardy–Ramanujan number) $\times 5=8645$ – recognise it.

Answer: (B) 5

Concept: Check differences; if they are irregular, check the second differences.

1. Differences: $36-19=17,59-36=23,94-59=35,147-94=53$.
2. Second differences: $6,12,18$ → next $24$.
3. Next difference $=53+24=77$, so $?=147+77=224$.

Trick: When first differences grow unevenly, look for a pattern like $+6,+12,+18$ in the second level.

Answer: (B) 224

Concept: Mark vowels (A, E, I, O, U); every other letter, including Y, is a consonant. Look for the pattern Consonant – Consonant – Vowel.

1. Vowels are at positions 1 (O), 2 (E), 10 (I), 12 (U), 13 (I), 16 (U).
2. Only letters just before a vowel can qualify: F G I → G ✓ (preceded by F); I Y U → Y ✗ (preceded by I); L V U → V ✓ (preceded by L).
3. So the letters are G and V.

Trick: First find every vowel, then check only the two letters before each vowel – fastest way.

Answer: (C) Two

Concept: Place the towns step by step on a grid with X as the origin.

1. Y is north of X; Z is west of X; P is north of Z; Q is east of P (same level as P).
2. Y is north-west of Q → Q lies east of the X–Y line and below Y.
3. So Q is to the north-east of X, i.e. X is to the south-west of Q.

Trick: Find Q's position from X (NE) and reverse it: NE ↔ SW.

Answer: (D) South-west

Concept: Treat the first letter, second letter and number as three separate series.

1. First letter: X → U → R → O (each $-3$).
2. Second letter: K → O → S → W (each $+4$).
3. Number: $253\to 236\to 219\to 202$ (each $-17$).

Trick: Check the number part first: only one option ends in 202.

Answer: (A) OW202

Concept: Find one rule that turns the first number into the second in both given pairs.

1. $91\times 2+2=184$ ✓; $88\times 2+2=178$ ✓ → rule: second $=2\times$ first $+2$.
2. $99\times 2+2=200$ ✓.
3. Others: $104\times 2+2=210\ne 218$, $76\times 2+2=154\ne 152$, $92\times 2+2=186\ne 184$.

Trick: Second number is about double the first → test 'double plus/minus a small number'.

Answer: (A) 99, 200

Concept: Decode each symbol and draw the family tree.

1. S × D: S is the wife of D.
2. D ÷ R: D is the father of R → S is R's mother.
3. R @ Y: R is the mother of Y; Y + H: Y is the brother of H → R is H's mother.
4. S is the mother of H's mother.

Trick: Mother's mother = maternal grandmother (nani).

Answer: (A) Mother's mother

Concept: Decode each symbol and draw the family tree.

1. N @ K: N is the brother of K.
2. K # S: K is the daughter of S; S & R: S is the father of R → N, K and R are siblings.
3. R ! V: R is the wife of V.
4. So N is the brother of V's wife.

Trick: Brother of wife = wife's brother (saala).

Answer: (C) Wife's brother

Concept: Position from left $=$ total $-$ position from right $+1$.

1. Geeta from left $=35-15+1=21$st.
2. Nalini is 14 places to the left of Geeta: $21-14=7$.
3. Nalini is 7th from the left end.

Trick: Left + Right $=$ Total $+1$.

Answer: (B) 7^th

Concept: Find the gaps between consecutive letters using their positions (A = 1 … Z = 26).

1. TWQM: T(20) → W(23) → Q(17) → M(13): $+3,-6,-4$.
2. CFZV: $3\to 6\to 26\to 22$: $+3,-6$ (looping back), $-4$; KNHD: $11\to 14\to 8\to 4$: $+3,-6,-4$.
3. MPIE: $13\to 16\to 9\to 5$: $+3,-7,-4$ ✗.

Trick: Write numbers above letters; the middle gap is usually where the odd one differs.

Answer: (C) MPIE

Concept: Facing the centre: left = clockwise, right = anticlockwise.

1. Fix F. Counting to the right of F, three people sit between F and G → G is 4th to the right of F.
2. Q is immediately right of G; counting left from Q, three sit between Q and M → M is 4th to the left of Q (2nd to the right of F).
3. Remaining seats: H and O together (O immediately right of H), L in the last seat.
4. Counting left (clockwise) from H: M, F, then L → two people.

Trick: In circular puzzles with 7 seats, '3 between' from one side means '2 between' from the other side.

Answer: (A) Two

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

1. All gloves are bandages → Gloves circle inside Bandages.
2. No glove is a sling → Slings is apart from Gloves; it can lie fully outside Bandages too.
3. I (some slings are bandages) is only possible, not certain ✗.
4. II (all bandages are slings) is impossible, since gloves are bandages but not slings ✗.

Trick: A conclusion follows only if it is true in every possible diagram.

Answer: (C) Neither conclusion (I) nor (II) follows

Concept: A word common to two sentences gets the code common to both coded forms.

1. 'car event stop' → mb mj gs; 'stop van lime' → ii mb rb.
2. Common word: stop; common code: mb.
3. So stop = mb.

Trick: Match the common word with the common code – no need to decode other words.

Answer: (B) mb

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

1. DESK → 2794 and KIDS → 6924.
2. Common letters D, S, K ↔ common digits 2, 9, 4.
3. Left-over: E ↔ 7 (in DESK) and I ↔ 6 (in KIDS).

Trick: Cancel common letters and common digits; what remains pairs up.

Answer: (B) 6

Concept: Compare each letter of the first cluster with the matching letter of the second.

1. MJ – IF: $13\to 9$, $10\to 6$: $-4,-4$.
2. RF – NB: $18\to 14$, $6\to 2$: $-4,-4$; UG – QC: $21\to 17$, $7\to 3$: $-4,-4$.
3. RK – OG: $18\to 15$ ($-3$), $11\to 7$ ($-4$) ✗.

Trick: Check the first letters only: R→O ($-3$) breaks the $-4$ pattern at once.

Answer: (A) RK – OG

Concept: Replace letters with signs, then apply BODMAS.

1. Expression: $78÷3+(55÷5)\times 4-16\times 5+65$.
2. $=26+11\times 4-80+65$.
3. $=26+44-80+65=55$.

Trick: Solve the bracket first, then all $÷$ and $\times$, then $+$ and $-$.

Answer: (D) 55