Q&A: practice questions with answers

Concept: Express both candidates' votes as % of total voters; the gap equals the winning margin.

1. Let total voters $=V$. Votes cast $=95\%$ of $V$.
2. A gets $75\%$ of $V$, so B gets $95\%-75\%=20\%$ of $V$.
3. Margin $=55\%$ of $V=5500\Rightarrow V=10,000$.

Trick: Margin % = A% − B% = $75-20=55$; then $5500÷0.55$.

Answer: (D) $10,000$

Concept: Here the speed asked is the cycling speed, i.e. distance ÷ actual moving time (stoppage time excluded).

1. Total time $=60$ min; stoppages $=2\times 5=10$ min.
2. Moving time $=50$ min $=\frac{5}{6}$ h.
3. Speed $=5÷\frac{5}{6}=6\text{km/h}$.

Trick: Moving speed $=\frac{\text{distance}}{\text{total time}-\text{stoppage time}}$.

Answer: (B) $6$

Concept: Substitute $c=-2(a+b)$ from the given condition.

1. Numerator $=4a^2+4b^2+16(a+b{)}^2=20a^2+20b^2+32ab$.
2. Denominator $=20(a+b{)}^2-8ab=20a^2+20b^2+32ab$.
3. Ratio $=1$.

Trick: Put $a=b=1$: $c=-4$; $\frac{4+4+64}{80-8}=\frac{72}{72}=1$.

Answer: (B) $1$

Concept: $\text{SI}=\frac{P\times R\times T}{100}$; add the two interests.

1. $\frac{29000\times 3\times R}{100}+\frac{45000\times 5\times R}{100}=62400$.
2. $(87000+225000)\frac{R}{100}=62400\Rightarrow 3120R=62400$.
3. $R=20\%$.

Trick: Sum of P×T: $312000$; 1% of it is 3120, and $62400÷3120=20$.

Answer: (B) $20\%$

Concept: $V\propto r^3$, so new volume factor $=(1.2{)}^3$.

1. $(1.2{)}^3=1.728$.
2. Increase $=72.8\%$.

Trick: Successive 20% three times: $20\to 44\to 72.8$.

Answer: (B) $72.8\%$

Concept: $l^2=r^2+h^2$ and curved surface area $=\pi rl$.

1. Let $l=4k,h=3k$; then $r=\sqrt{16k^2-9k^2}=\sqrt{7}k$.
2. CSA $=\pi \times \sqrt{7}k\times 4k=4\sqrt{7}\pi k^2=4\sqrt{7}\pi \Rightarrow k=1$.
3. Radius $=\sqrt{7}$ units.

Trick: Compare directly: $4\sqrt{7}\pi k^2$ with $4\sqrt{7}\pi$ ⇒ $k^2=1$.

Answer: (D) $\sqrt{7}$

Concept: Brackets first, then division, then subtraction.

1. $(5+7)÷3=12÷3=4$.
2. $[4+4]=8$.
3. $16÷8=2$; $15-2=13$.

Trick: Inside the square bracket, division $12÷3$ comes before adding 4.

Answer: (D) $13$

Concept: Brackets, then ÷ and × left to right, then + and − left to right.

1. $16÷2=8$; $7\times 15÷3=35$.
2. $\{(1+4)\times 5\}=25$; $4\times 3=12$.
3. $8-35+25+12-10=0$.

Trick: Group positives and negatives: $(8+25+12)-(35+10)=45-45=0$.

Answer: (B) $0$

Concept: Distance $=$ speed $\times$ time; for the same distance, time ∝ $\frac{1}{\text{speed}}$.

1. $180$ min $=3$ h; distance $=60\times 3=180\text{km}$.
2. New time $=\frac{180}{40}=4.5$ h $=4$ hr $30$ min.

Trick: $3\times \frac{60}{40}=4.5$ h directly.

Answer: (A) 4 hr 30 min

Concept: The rolled edge becomes the circumference $2\pi r$; the other side is the height. $V=\pi r^{2}h=\frac{C^{2}h}{4\pi }$.

1. Along length: $C=60,h=36$ ⇒ $V_1=\frac{{60}^2\times 36}{4\pi }$.
2. Along breadth: $C=36,h=60$ ⇒ $V_2=\frac{{36}^2\times 60}{4\pi }$.
3. $V_1:V_2=\frac{{60}^2\times 36}{{36}^2\times 60}=\frac{60}{36}=5:3$.

Trick: Ratio of volumes = ratio of the rolled sides: $60:36=5:3$.

Answer: (B) 5 : 3

Concept: Make waves means to create trouble or disturbance, to upset the existing situation.

1. Waves disturb calm water; similarly, a person who 'makes waves' causes problems or stirs controversy.
2. Example: The new manager made waves by questioning old rules.
3. (B) 'give up', (C) 'take it easy', (D) 'have patience' all suggest calmness or quitting – the opposite idea.

Trick: Calm water vs. waves – waves = trouble.

Answer: (A) To cause difficulty

Concept: Correct spelling: Admission – only one 'd' after 'A'.

1. The word comes from admit (ad + mit) – a single 'd'.
2. Admit → Admission (double 's' only).
3. Matriculation, Prohibition, Humorous are all correctly spelt.

Yaad rakhein: Admit has one 'd', so Admission also has one 'd'.

Answer: (D) Addmission

Concept: An action continuing from a past point up to now, with 'for the past …', needs the present perfect tense.

1. 'For the past three years' shows a period starting in the past and continuing till now.
2. Simple present 'is' cannot express this; use 'has been'.
3. Correct: For the past three years, my uncle has been away from home.

Trick: 'for/since/for the past' + continuing state → has/have been.

Answer: (C) my uncle is

Concept: Panacea = a remedy for all diseases or problems; a cure-all.

1. Greek pan = all + akos = cure → cure for all.
2. Fanatic = person with extreme zeal; Heretic = one who opposes accepted beliefs; 'Service' is unrelated.
3. So 'a remedy for all the diseases' = panacea.

Trick: Pan = all (Pan-India, Panorama) → Panacea = cure for all.

Answer: (B) Panacea

Concept: Embrace means to hold someone closely in one's arms (hug), or to accept something eagerly and willingly. Its opposite is to reject, discard or throw away.

1. In the sentence, the climbers hugged each other in joy, i.e. they held each other close.
2. Junked = discarded, thrown away as useless – the act of pushing away/rejecting, which is the opposite of holding close and accepting.
3. Cradled = held gently in the arms; Contained = held within – both are close to the meaning of embraced.
4. Limited = restricted; it is not the opposite of holding or accepting.

Trick: embrace ↔ reject / discard / junk; embrace ≈ hug, cradle, welcome.

Answer: (B) Junked

Concept: Correct spelling: Interrogative – double 'r'.

1. The word comes from inter + rogare (to ask) → inter + rogative = interrogative.
2. Auditions, Interference, Greengrocers are correctly spelt.
3. Hence 'Interogative' is misspelt.

Yaad rakhein: Interrogate, Interrupt, Irregular – prefix ends in 'r' and root starts with 'r' → 'rr'.

Answer: (A) Interogative

Concept: Many animals have separate words for male and female; we use those words instead of adding 'male'/'female'. Male dog = dog, female dog = bitch.

1. Standard gender pair: dog – bitch (like horse – mare, lion – lioness).
2. Each noun takes its own article: 'a dog and a bitch'.
3. 'puppy' = young dog, not female; 'lady dog' is not standard English.

Yaad rakhein: Gender pairs: dog–bitch, horse–mare, fox–vixen, drake–duck.

Answer: (B) a dog and a bitch

Concept: Students study in an institute; 'of great importance' is the fixed phrase; 'starting point' is the correct compound noun.

1. 'students of an institute' → better 'students in an educational institute'.
2. 'is of great importance' is correct ('in great importance' is wrong) – so (A) is out.
3. (D) uses 'start point', which is not the standard expression ('starting point').
4. (B) corrects the preposition and keeps everything else right.

Trick: be + of + importance/value/use (of great importance, of no use).

Answer: (B) The quality of students in an educational institute is of great importance and a crucial starting point.

Concept: A singular subject (one organisation's name) takes a singular verb.

1. 'The Centre for Policy Research' is one body – a singular subject.
2. Present tense singular verb needs '-s': estimates.
3. Correct: …the Centre for Policy Research estimates that India has the largest stock…
4. 'Although there is no proven data' and 'India has the largest stock' are correct.

Trick: Name of one organisation = singular → verb + s.

Answer: (B) Centre for Policy Research estimate

Concept: In indirect speech with a past reporting verb ('asked'), the present tense of the reported question shifts to the past.

1. Reporting verb 'asked' is in the past tense.
2. Hence 'is' → was, matching 'worked' in the same sentence.
3. Correct: She asked me where my hometown was and where I worked.
4. 'has been', 'would be', 'were' do not follow the rule here.

Trick: Past reporting verb → is → was, works → worked.

Answer: (D) hometown was