Q&A: practice questions with answers

Concept: Percentage change $=\frac{\text{2021}-\text{2020}}{\text{2020}}\times 100$.

1. Pen $\frac{3}{15}=20\%$, Pencil $\frac{5}{16}=31.25\%$, Notebook $\frac{10}{25}=40\%$
2. Pages $\frac{6}{20}=30\%$, Erasers $\frac{6}{18}=33.3\%$, Charts $\frac{10}{27}=37\%$, Geometry $\frac{12}{32}=37.5\%$
3. Highest = Notebook (40%).

Trick: Geometry has the largest absolute rise (12) but not the largest % rise — divide by the base.

Answer: (B) Notebook

Concept: Volume is conserved: number of pieces = volume of sphere ÷ volume of one hemisphere.

1. Sphere $=\frac{4}{3}\pi (12{)}^3$, hemisphere $=\frac{2}{3}\pi (4{)}^3$
2. $n=\frac{\frac{4}{3}\pi \times 1728}{\frac{2}{3}\pi \times 64}=2\times 27=54$

Trick: $n=2\times {\left(\frac{R}{r}\right)}^3=2\times 3^3=54$; option 27 forgets the factor 2.

Answer: (A) 54

Concept: Hemisphere: $\text{CSA}=2\pi r^2$, $\text{TSA}=3\pi r^2$.

1. $\text{CSA}=2\times \frac{22}{7}\times 49=308{\text{cm}}^2$
2. $\text{TSA}=3\times \frac{22}{7}\times 49=462{\text{cm}}^2$

Trick: With $r=7$: $\pi r^2=154$; CSA $=2\times 154$, TSA $=3\times 154$.

Answer: (D) CSA – $308{\text{cm}}^2$; TSA – $462{\text{cm}}^2$

Concept: Value of a sector $=\frac{\text{angle}}{{360}^{\circ }}\times \text{total}$.

1. UK − Australia $={125}^{\circ }-{75}^{\circ }={50}^{\circ }$
2. $\frac{50}{360}\times 14400=50\times 40=2000$ billion

Trick: $1^{\circ }=\frac{14400}{360}=40$ billion; multiply the angle difference by 40.

Answer: (B) 2,000

Concept: Surface area $=4\pi r^2\propto r^2$.

1. Radius doubled ⇒ area becomes $2^2=4$ times.
2. Increase $=4-1=3$ times $=300\%$

Trick: Increase % $=(k^2-1)\times 100$; 400% is the new area, not the increase.

Answer: (C) $300\%$

Concept: Add the required cells, form the ratio and reduce it.

1. D (Friday + Sunday) = 206 + 326 = 532
2. A (Friday + Saturday) = 350 + 420 = 770
3. $532:770$ — divide by 14 → $38:55$

Trick: Keep the asked order: D first, A second (55 : 38 is the reversed trap).

Answer: (B) 38 : 55

Concept: Third proportional to $a$ and $b$ $=\frac{b^2}{a}$.

1. $a=23$, $b=31$
2. $c=\frac{{31}^2}{23}=\frac{961}{23}$

Trick: Square the second number, divide by the first.

Answer: (B) $\frac{961}{23}$

Concept: Total time $=\frac{d}{B+S}+\frac{d}{B-S}$.

1. $\frac{35}{20+S}+\frac{35}{20-S}=8$
2. Try $S=15$: $\frac{35}{35}+\frac{35}{5}=1+7=8$ ✓
3. (Algebra: $\frac{1400}{400-S^2}=8\Rightarrow S^2=225\Rightarrow S=15$)

Trick: Option testing is fastest; $S$ must be less than 20, which rules out (A).

Answer: (C) $15\text{km/h}$

Concept: HCF = product of the common prime factors with the lowest powers.

1. $12=2^2\times 3$, $18=2\times 3^2$, $42=2\times 3\times 7$
2. $\text{HCF}=2\times 3=6$

Trick: HCF can never exceed the smallest number (12) — and 12 does not divide 18.

Answer: (C) 6

Concept: When only milk is added, the quantity of water stays fixed.

1. Water $=60\%$ of 60 $=36\text{L}$
2. In new mixture water $=40\%$ ⇒ total $=\frac{36}{0.4}=90\text{L}$
3. Milk to add $=90-60=30\text{L}$

Trick: Shortcut: $\text{added}=\frac{60\times (60-40)}{100-60}=30$.

Answer: (A) 30 litres

Concept: To throw dust into someone's eyes means to mislead or deceive a person by hiding the truth.

1. The speaker says nobody can fool him – he sees through tricks.
2. 'Terrify', 'hurt' and 'abuse' do not carry the idea of trickery.
3. Only 'mislead or deceive me' keeps the exact sense.

Trick: Dust in the eyes → you cannot see clearly → you are fooled.

Answer: (D) mislead or deceive me

Concept: Pithy means brief but full of meaning – concise and forcefully expressive.

1. O. Henry's stories are famously short with a twist ending, so 'pithy' praises their brevity and punch.
2. 'Lengthy' contradicts brevity; 'elusive and unreal' and 'exaggerated' are not the meaning.
3. Hence 'concise and expressive'.

Trick: Pith = the essential core; pithy = only the core, no extra words.

Answer: (D) concise and expressive

Concept: A plum job is a very desirable job – easy, pleasant and usually well paid.

1. 'Plum' as an adjective means excellent or most desirable.
2. It says nothing about rarity, difficulty or travel.
3. So the meaning is 'an easy and pleasant job'.

Trick: Plum = sweet fruit → a sweet (pleasant) job.

Answer: (A) An easy and pleasant job

Concept: Prefer takes either a to-infinitive (prefer to watch) or a gerund (prefer watching); 'prefer to watching' mixes both.

1. The sentence is parallel to 'I like to read', so the infinitive fits: 'prefers to watch'.
2. 'In/on watching' are wrong prepositions after prefer.
3. The underlined part must change, so 'No substitution' is wrong.

Trick: prefer + to + V1  or  prefer + V-ing – never 'to + V-ing' here.

Answer: (B) to watch

Concept: Glad means happy or pleased.

1. Opposite of happy = sad.
2. 'Pleased' is a synonym; 'keen' means eager; 'loyal' means faithful.

Trick: Glad ↔ Sad (they even rhyme).

Answer: (C) Sad

Concept: The fixed phrase is people of all ages – 'age' (noun) is needed, not 'aging' (a verb form/gerund meaning growing old).

1. 'tourists of all aging' is ungrammatical.
2. Correct: 'tourists of all ages'.
3. The other segments are fine.

Trick: of all ages / of all sizes / of all kinds – plural noun after 'all'.

Answer: (A) tourists of all aging.

Concept: Imitate means to copy someone's actions, voice or manner.

1. Saurabh copies (mimics) his boss perfectly.
2. 'Admires', 'worships' and 'hates' are feelings, not acts of copying.

Trick: Imitation = copy (an 'imitation' necklace is a copy).

Answer: (C) Copies

Concept: Unequivocal = leaving no doubt; clear and having only one meaning.

1. Equivocal = ambiguous; un- + equivocal = not ambiguous = unambiguous.
2. 'Doubted' is nearly opposite; 'complete' and 'articulate' differ in meaning.

Trick: un-equi-vocal → not 'equal voices' (two meanings) → one clear meaning.

Answer: (C) Unambiguous

Concept: The correct spelling is plagued (to be troubled continually).

1. 'plaged' drops the 'u' of plague.
2. congestion, combustion and uninterruptedly are spelt correctly.

Trick: plague → plagued (keep 'gue', add 'd').

Answer: (A) plaged

Concept: Keep count of means to keep track of a number or total; to remember how many there are.

1. e.g. 'I've lost count of how many times he called.'
2. Deadlines, politeness and invitations are unrelated.

Trick: count → number → total.

Answer: (C) To remember a total