Q&A: practice questions with answers

Concept: Percentage $=\frac{\text{class frequency}}{\text{total}}\times 100$.

1. Total $=50+70+85+90+60+45=400$.
2. 90 and above (90–100) $=45$.
3. $\frac{45}{400}\times 100=11.25\%$.

Trick: Total 400 ⇒ divide count by 4 to get %.

Answer: (B) $11.25\%$

Concept: For equal time, profit is shared in the ratio of investments.

1. $92500:112500=37:45$.
2. A’s profit $=9000\times \frac{37}{45}=7400$.

Trick: B’s 45 parts $=9000$ ⇒ 1 part $=200$ ⇒ A $=37\times 200$.

Answer: (C) ₹7,400

Concept: Find B’s full time, then A’s rate $=\frac{1}{25}-\frac{1}{B}$.

1. $66\frac{2}{3}\%=\frac{2}{3}$ in 30 days ⇒ B alone $=45$ days.
2. A’s rate $=\frac{1}{25}-\frac{1}{45}=\frac{9-5}{225}=\frac{4}{225}$.
3. Time for $\frac{4}{15}$ work $=\frac{4}{15}÷\frac{4}{225}=15$ days.

Trick: $66\frac{2}{3}\%=\frac{2}{3}$.

Answer: (B) 15 days

Concept: Employees in a department $=\%\times$ total; females $=100\%-75\%=25\%$ of them.

1. D $=8\%$ of 450 $=36$.
2. Females $=25\%$ of 36 $=9$.

Trick: 36 is the whole department, not the females.

Answer: (A) 9

Concept: Replace each factor by its remainder and multiply step by step.

1. Remainders by 35: $72\to 2$, $73\to 3$, $78\to 8$, $76\to 6$.
2. $2\times 3=6$; $6\times 8=48\to 13$.
3. $13\times 6=78\to 8$.

Trick: Reduce after every multiplication to keep numbers small.

Answer: (D) 8

Concept: Employees $=\frac{\%}{100}\times$ total.

1. F $=22\%$.
2. $\frac{22}{100}\times 450=99$.

Trick: $1\%$ of 450 $=4.5$ ⇒ $22\times 4.5=99$.

Answer: (C) 99

Concept: Least number divisible by all = LCM.

1. $4=2^2$, $5$, $8=2^3$, $10=2\times 5$, $12=2^2\times 3$.
2. LCM $=2^3\times 3\times 5=120$.

Trick: Take the highest power of each prime. 240 is divisible too, but not least.

Answer: (B) 120

Concept: Savings = Income − Expenditure; take income 100.

1. Before: income 100, expenditure 75, savings 25.
2. After: income 128, expenditure 90, savings 38.
3. Change $=\frac{38-25}{25}\times 100=52\%$ increase.

Trick: Income 100 makes every figure a direct percentage.

Answer: (B) 52% increase

Concept: Convert each average into a total.

1. $A+B+C=210$; $A+B+C+D=240\Rightarrow D=30$, so $E=35$.
2. $B+C+D+E=236\Rightarrow B+C=236-65=171$.
3. $A=210-171=39$.
4. Average of A, D, E $=\frac{39+30+35}{3}=\frac{104}{3}\approx 34.67\approx 35$.

Trick: Replacing A by E dropped the total by $240-236=4$ ⇒ $A=E+4=39$.

Answer: (B) 35 kg

Concept: $x^3+y^3+z^3-3xyz=(x+y+z)[(x+y+z{)}^2-3(xy+yz+zx)]$.

1. $x^3+y^3+z^3-3xyz=17\times (289-333)=17\times (-44)=-748$.
2. $x^3+y^3+z^3=-748+513=-235$.
3. $x^3+y^3+z^3+xyz=-235+171=-64$.
4. $\sqrt[3]{-64}=-4$.

Trick: Cube root of a negative number is negative; −64 is the value under the root, not the answer.

Answer: (D) −4

Concept: The correct spelling is vengeance (revenge for an injury or wrong).

1. It begins with v, not ‘w’ – so ‘wengeance’ and ‘wengence’ are wrong.
2. After ‘veng’ comes -eance (the ‘e’ keeps the ‘g’ soft): veng-e-ance.
3. ‘vengance’ drops this ‘e’, so it is wrong.

Yaad rakhein: veng + e + ance – same soft-g ‘e’ as in ‘pigeon’, ‘surgeon’.

Answer: (D) vengeance

Concept: With a perfect continuous tense, a point of time takes ‘since’, a period of time takes ‘for’.

1. ‘hours’ is a period (duration), not a starting point.
2. So ‘since hours’ must be for hours: “She has been working tirelessly for hours.”
3. ‘She has been working’ (present perfect continuous) and ‘tirelessly’ are correct.

Yaad rakhein: since + point (since Monday, since 2010); for + period (for hours, for two years).

Answer: (A) since hours

Concept: Verbs of perception such as hear, see, smell are stative verbs and are normally not used in the continuous (-ing) form.

1. ‘to be hearing’ uses ‘hear’ in a continuous form – incorrect.
2. Correct: “I was sorry to hear of his misfortune.”
3. ‘be sorry to hear of’ is the standard expression of sympathy; the other parts are fine.

Yaad rakhein: Stative verbs (hear, see, know, love, believe) – avoid ‘-ing’: ‘sorry to hear’, not ‘sorry to be hearing’.

Answer: (C) be hearing

Concept: Pocket an insult = to accept an insult silently without protesting or reacting.

1. To ‘pocket’ something figuratively means to put up with it and keep it to oneself.
2. So the meaning is bear an insult quietly.
3. ‘resent an affront’ and ‘plan a revenge’ are the opposite reaction; ‘express true feelings’ is unrelated.

Yaad rakhein: Pocket an insult = insult ko chupchaap ‘jeb mein rakh lena’, i.e. swallow it.

Answer: (B) bear an insult quietly

Concept: The correct spelling is momentary (lasting for a very short time).

1. It comes from moment (single ‘m’ in the middle) + -ary.
2. ‘mommentary’ doubles the ‘m’; ‘momentery’ and ‘momentory’ use the wrong suffix vowel.
3. So mo-ment-ary is right.

Yaad rakhein: moment + ary = momentary (like ‘document → documentary’).

Answer: (B) momentary

Concept: Rain is an uncountable noun, so it takes ‘little’ (not ‘few’/‘many’); a future prediction uses ‘will’.

1. ‘The forecast predicts that there will be little rain’ – ‘will’ suits a prediction and ‘little rain’ means hardly any rain.
2. ‘many rain’ and ‘few rain’ use countable quantifiers with an uncountable noun – wrong.
3. ‘must be a little rain’ wrongly expresses compulsion/certainty, not a forecast.

Yaad rakhein: little/much + uncountable (rain, water); few/many + countable (drops, days).

Answer: (B) No substitution required

Concept: Muster = to gather or assemble (troops, people, courage).

1. Its opposite is to scatter or send apart – disperse.
2. ‘mobilize’, ‘convene’ and ‘assemble’ all mean bringing together – they are synonyms, not antonyms.

Yaad rakhein: Muster (ikattha karna) ↔ Disperse (bikherna).

Answer: (B) disperse

Concept: Sumptuous = splendid, lavish and expensive-looking (e.g. a sumptuous feast).

1. Opulent = rich, luxurious, lavish – same meaning.
2. ‘stingy’ (miserly), ‘meager’ (scanty) and ‘bereft’ (deprived) are all opposite in sense.

Yaad rakhein: Sumptuous = Opulent = Lavish = Luxurious.

Answer: (B) opulent

Concept: ‘Success’ here is uncountable and the verb ‘depends’ is singular, so we need a quantifier for uncountable nouns.

1. Much of our success depends on our own efforts – ‘much of’ + uncountable + singular verb.
2. ‘Few’ and ‘Many’ are used with plural countable nouns and take plural verbs.
3. ‘Less’ is not used as a pronoun subject with ‘of our…’ in this sense.

Yaad rakhein: Much of + uncountable (much of the work, much of our success).

Answer: (C) Much

Concept: The fixed expression is go on a pilgrimage; ‘pilgrim’ is the person, ‘pilgrimage’ is the journey.

1. ‘goes for a pilgrim’ wrongly uses the person-noun ‘pilgrim’.
2. Correct: “Every year the family goes on a pilgrimage to the temple at Tirupathi.”
3. ‘from the pilgrimage’ and ‘at the pilgrim’ have wrong prepositions/nouns.

Yaad rakhein: Pilgrim = yatri; Pilgrimage = tirth-yatra. Go on a pilgrimage / journey / tour.

Answer: (C) on a pilgrimage