Q&A: practice questions with answers

Concept: Write each statement as an equation and eliminate.

1. $2X=6Y-7$ … (i)
2. $P=2X,Q=Y+8,P=Q+50\Rightarrow 2X=Y+58$ … (ii)
3. From (i) and (ii): $6Y-7=Y+58\Rightarrow 5Y=65\Rightarrow Y=13$.
4. Check: $2X=13+58=71=6(13)-7$ ✓

Trick: Both statements give $2X$ – equate them directly.

Answer: (B) 13

Concept: Monthly savings = income − expenses; one month’s savings is used up.

1. Monthly savings $=11000-6000-3000=2000$.
2. Savings are kept for $12-1=11$ months.
3. Yearly savings $=11\times 2000=22000$.

Trick: Just multiply monthly savings by 11 instead of 12.

Answer: (D) ₹22,000

Concept: Take CP = 100; SP = MP × (1 − discount).

1. MP $=165$.
2. SP $=165\times \frac{41}{100}=67.65$.
3. Loss $=100-67.65=32.35$ → $32.35\%$ loss.

Trick: Net effect $=65-59-\frac{65\times 59}{100}=6-38.35=-32.35\%$ (negative = loss).

Answer: (C) $32.35\%$ loss

Concept: Find the value of one ratio unit from the given percentage.

1. $65\%$ of first $=39\Rightarrow$ first $=\frac{39\times 100}{65}=60$.
2. $20$ units $=60\Rightarrow 1$ unit $=3$; second $=42$, third $=18$.
3. Difference $=42-18=24$; $50\%$ of $24=12$.

Trick: Difference $=(14-6)=8$ units $=24$; half $=12$.

Answer: (C) 12

Concept: Same direction → subtract speeds; opposite direction → add speeds; distance = sum of lengths.

1. Relative speed with man $=\frac{250}{50}=5\text{m/s}=18\text{km/h}$ → train speed $=18+7=25\text{km/h}$.
2. Opposite train: relative speed $=25+28=53\text{km/h}=\frac{53\times 5}{18}\text{m/s}$.
3. Time $=\frac{530}{53\times 5/18}=\frac{530\times 18}{265}=36\text{s}$.

Trick: $530$ is $10\times 53$ – so time $=10\times \frac{18}{5}=36$.

Answer: (A) 36

Concept: $\text{Profit}\%=\frac{\text{SP}-\text{CP}}{\text{CP}}\times 100$ (per dozen).

1. CP of 1 dozen = ₹560.
2. SP of 1 dozen $=12\times 49=588$.
3. Profit% $=\frac{28}{560}\times 100=5\%$.

Trick: Number of dozens (83) does not matter – compare one dozen.

Answer: (C) $5\%$

Concept: $\text{Median}=l+\frac{\frac{N}{2}-cf}{f}\times h$.

1. $N=20+19+32+27+12=110$, $\frac{N}{2}=55$.
2. Cumulative frequencies: 20, 39, 71 → median class 250–300 ($l=250,cf=39,f=32,h=50$).
3. Median $=250+\frac{55-39}{32}\times 50=250+25=275$.

Trick: $\frac{16}{32}=\frac{1}{2}$, so median is the midpoint of the class: 275.

Answer: (D) 275

Concept: Expenditure = income − savings; set up the expenditure ratio.

1. Incomes $2x$ and $3x$; expenditures $2x-15000$ and $3x-9000$.
2. $\frac{2x-15000}{3x-9000}=\frac{12}{19}\Rightarrow 38x-285000=36x-108000\Rightarrow x=88500$.
3. Expenditures: $177000-15000=162000$ and $265500-9000=256500$.
4. Total $=162000+256500=418500$.

Trick: Total expenditure = total income − total savings $=5x-24000=442500-24000$.

Answer: (B) ₹4,18,500

Concept: Money left = amount had − amount spent; subtract like terms.

1. $(3x^2+5xy+7y^2)-(2x^2+5xy+4y^2)$
2. $=x^2+0·xy+3y^2=x^2+3y^2$.

Trick: The $xy$ terms cancel; watch that options with outer brackets squared are different expressions.

Answer: (B) ₹$(x^2+3y^2)$

Concept: For $n$ (odd) observations, median $={\left(\frac{n+1}{2}\right)}^{\text{th}}$ value after arranging in order.

1. Ascending: 19, 34, 49, 56, 59, 69, 70, 76, 84, 98, 99.
2. $n=11\Rightarrow \frac{11+1}{2}=6^{\text{th}}$ value $=69$.

Trick: Always sort first – the middle of the unsorted list (99) is a trap.

Answer: (C) 69

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

1. PANT → 6129 and TAPE → 2956.
2. Common letters P, A, T ↔ common digits 6, 2, 9.
3. Left in TAPE: letter E; left in 2956: digit 5. So E = 5.

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

Answer: (D) 5

Concept: When everyone faces the centre, moving to a person’s left means moving clockwise.

1. Fix B; C is 3rd to the left of B.
2. A is 2nd to the left of G, and G is not next to C → only G at the seat just right of B works, giving A at B’s immediate left.
3. D is immediate left of E → E and D take the two seats after C; F sits between A and C.
4. From A going left: F, C, then E → 2 people between.

Trick: Draw the circle first, place the fixed pair (B, C), then try each possible seat for G.

Answer: (B) Two

Concept: Draw the least-overlap Venn diagram and check each conclusion.

1. “All fruits are bananas” → fruit circle lies inside banana circle, so “Some fruits are bananas” is definitely true (I follows).
2. “All green are leaves” → green circle lies inside leaves, so “Some green are leaves” is definitely true (II follows).

Trick: “All A are B” always gives “Some A are B” and “Some B are A”.

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

Concept: Replace each sign with its meaning, then apply BODMAS.

1. $11-91\times 7÷83+27\to 11\times 91÷7+83-27$
2. $91÷7=13$, $11\times 13=143$
3. $143+83-27=199$

Trick: Rewrite the whole expression with the new signs before calculating.

Answer: (D) 199

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

1. M + N → M is sister of N (M female).
2. N − O → N is brother of O.
3. O × P → O is wife of P.
4. P ÷ Q → P is father of Q, so O is mother of Q.
5. M is sister of N, who is brother of O → M is O’s sister = Q’s mother’s sister.

Trick: Mark gender as soon as a relation reveals it (sister, wife → female).

Answer: (A) Mother’s Sister

Concept: Place fixed information first, then the blocks.

1. R = Wednesday. Three people between R and Q → Q = Sunday (going back is impossible).
2. T, S, V are consecutive (T-S-V). Free days: Mon, Tue, Thu, Fri, Sat → only Thu-Fri-Sat fits, so S = Friday.
3. Three between P and S → P = Monday; U = Tuesday.

Trick: A 3-person block needs three consecutive free days – that usually fixes it at once.

Answer: (B) Q

Concept: Identify the highest and lowest numbers, then pick the asked digits.

1. Highest = 862 → third digit = 2.
2. Lowest = 205 → first digit = 2.
3. $2+2=4$

Trick: Compare first digits only to find highest (8) and lowest (2).

Answer: (D) 4

Concept: A letter common to both words is coded by the digit common to both codes.

1. COAT → 2486 and PALE → 5712.
2. The only common letter is A.
3. The only common digit in 2486 and 5712 is 2, so A = 2.

Trick: One common letter ↔ one common digit.

Answer: (C) 2

Concept: Find the gaps between consecutive letters using alphabet positions.

1. MQL: M→Q (+4), Q→L (−5)
2. RVQ: R→V (+4), V→Q (−5)
3. KOJ: K→O (+4), O→J (−5)
4. OSM: O→S (+4), S→M (−6) ✗

Trick: Pattern +4, −5 means the third letter is just one before the first (L before M, Q before R, J before K) – OSM breaks it.

Answer: (D) OSM

Concept: Track net East–West and North–South movement from A.

1. East 12 → left (North) 9 → left (West) 13 → left (South) 12 → left (East) 1.
2. East–West: $12-13+1=0$ → P is directly in line with A.
3. North–South: $9-12=-3$ → P is 3 km south of A.
4. To return, drive 3 km towards the north.

Trick: Add east, subtract west; add north, subtract south.

Answer: (D) 3 km to the north