Q&A: practice questions with answers

Concept: B is common with the same value 4, so A : B : C $=3:4:5$.

1. C − A $=5-3=2$ parts $=30$
2. 1 part $=15$
3. B $=4\times 15=60$

Trick: Equalise the common term first, then use the given difference.

Answer: (B) $60$

Concept: BODMAS: brackets, then 'of', then division, then addition/subtraction.

1. $2\frac{1}{5}-2=\frac{1}{5}$; $\frac{1}{5}\times 5=1$
2. $\frac{2}{5}÷1=\frac{2}{5}$
3. $\frac{2}{3}\text{ of }\frac{3}{5}=\frac{2}{5}$
4. $\frac{1}{4}+\frac{2}{5}-\frac{2}{5}=\frac{1}{4}$

Trick: The two $\frac{2}{5}$ terms cancel.

Answer: (B) $\frac{1}{4}$

Concept: Non-trained $\%=100-$ trained $\%$.

1. College A male: $56\%$ of $225=126$
2. College B female: $75\%$ of $128=96$
3. Total $=126+96=222$

Trick: $\frac{3}{4}\times 128=96$ is quick.

Answer: (A) $222$

Concept: $\cot \theta \sin \theta =\cos \theta$; max of $a\sin \theta +b\cos \theta$ is $\sqrt{a^2+b^2}$.

1. Expression $=19\sin \theta +6\cos \theta$
2. Max $=\sqrt{{19}^2+6^2}=\sqrt{361+36}=\sqrt{397}$

Trick: Simplify $\cot \theta \sin \theta$ first, then apply $\sqrt{a^2+b^2}$.

Answer: (B) $\sqrt{397}$

Concept: Volume of a hollow cylinder $=\pi (R^2-r^2)h$.

1. $R=7$ cm, $r=4$ cm, $h=42$ cm
2. $V=\frac{22}{7}\times (49-16)\times 42$
3. $=22\times 33\times 6=4356{\text{cm}}^3$

Trick: $R^2-r^2=(R+r)(R-r)=11\times 3=33$.

Answer: (C) $4356$

Concept: $\times$ and $÷$ are done left to right, then $+$.

1. $22\times 10=220$
2. $220÷5=44$
3. $44\times 2=88$
4. $88+12=100$

Trick: Do not compute $5\times 2$ first — go strictly left to right.

Answer: (C) $100$

Concept: Compare P + Q with R + S for each year.

1. 1989: 24 vs 25; 1990: 30 vs 23; 1991: 30 vs 26
2. 1992: 29 vs 31
3. 1993: $21+12=33$ and $13+20=33$ ✔

Trick: Check only the option years.

Answer: (C) 1993

Concept: Value of a sector $\propto$ its angle.

1. Savings ${60}^{\circ }=₹8000$
2. Expenditure $={360}^{\circ }-{60}^{\circ }={300}^{\circ }$
3. ${300}^{\circ }=\frac{300}{60}\times 8000=₹40000$

Trick: Expenditure is 5 times savings (${300}^{\circ }:{60}^{\circ }$).

Answer: (B) 40000

Concept: Area $\propto r^2$, volume $\propto r^3$.

1. $r_1:r_2=\sqrt{9}:\sqrt{49}=3:7$
2. Volumes $=3^3:7^3=27:343$

Trick: Square root, then cube.

Answer: (A) $27:343$

Concept: Do all $\times$ and $÷$ first, then $+$ and $-$ from left to right.

1. $81+1-81+9+81-9-81$
2. $=1$

Trick: The $81$s and $9$s cancel in pairs, leaving $9÷9=1$.

Answer: (C) $1$

Concept: The sentence says one must use the present opportunity to make a name; the idiom must mean ‘act at the right moment’.

1. ‘Beat around the bush’ (avoid the main point) does not fit ‘take this opportunity’.
2. Strike while the iron is hot = act quickly while the favourable chance lasts – exactly the sense needed.
3. ‘Fight tooth and claw’ = fight fiercely; ‘pass with flying colours’ = succeed brilliantly; ‘bare the foot’ is not an idiom.

Yaad rakhein: Iron is shaped only while it is hot – so use a chance before it cools off.

Answer: (A) strike while the iron is hot

Concept: ‘Resolve’ (verb) = settle or find an answer to a doubt/problem. Its opposite is to raise doubts or question.

1. In the sentence Nisha has many questions – things not yet resolved.
2. To ‘question’ something = to raise doubt about it, the reverse of resolving it.
3. ‘Satisfied’ is close to ‘resolved’ (similar sense); ‘about’ and ‘knows’ are unrelated.

Yaad rakhein: Resolve = answer a doubt; question = raise a doubt.

Answer: (B) Questions

Concept: Here ‘advance’ is used in the sense ‘advanced, higher level’ (as in advanced knowledge). Its opposite is ‘basic / beginner level’.

1. The sentence speaks of an elementary or intermediate knowledge of the language.
2. Elementary = basic, first-stage – the opposite of advanced.
3. ‘Destination’, ‘believes’ and ‘knowledge’ are not opposite in meaning to ‘advance’.

Yaad rakhein: Levels: elementary → intermediate → advanced.

Answer: (C) Elementary

Concept: Something that cannot be avoided or prevented is inevitable.

1. The underlined phrase: issues ‘that couldn’t be avoided’.
2. Inevitable = certain to happen; unavoidable.
3. Unthinkable = cannot be imagined; unsolvable = cannot be solved; incapable = not able (used for people).

Yaad rakhein: In-evitable = not avoidable (Latin evitare = to avoid).

Answer: (C) inevitable

Concept: The improved phrase must keep the meaning (friend went away when bad men came) in better, standard words.

1. ‘Vanished’ (magically ceased to be visible) is better expressed as disappeared for a person leaving suddenly; ‘goons’ is slang – thugs is standard.
2. ‘Disappeared when the thugs arrived’ keeps the meaning.
3. ‘Mobilised’, ‘condemned’ and ‘attacked’ need an object or change the meaning completely.

Yaad rakhein: Keep the sense, upgrade the words: vanished → disappeared, goons → thugs, came → arrived.

Answer: (B) disappeared when the thugs arrived

Concept: The word means ‘replied to (the phone)’ – past tense of answer.

1. ‘Awnsered’ has the letters w and n swapped.
2. Correct spelling: a-n-s-w-e-r-e-d → answered.
3. ‘awmsered’, ‘ansvered’, ‘answorod’ are all misspelt.

Yaad rakhein: answer = ANS + WER (silent w after s).

Answer: (D) answered

Concept: To decline an invitation politely, hinting you may accept it another time, is ‘to take a rain check’.

1. Rain check: originally a ticket for a later game when a match was rained out.
2. So ‘take a rain check’ = politely refuse now, with a promise to come later – matches the underlined words.
3. ‘Spoil a moment’ = ruin it; ‘call it a day’ = stop working; ‘take with a grain of salt’ = doubt something.

Yaad rakhein: ‘Can I take a rain check?’ = not today, maybe later.

Answer: (B) To take a rain check

Concept: A lively, cheerful, outgoing (sociable) person is an extrovert.

1. Extro- = outward; such a person enjoys company and talks freely.
2. Introvert = shy, inward-looking person; ambivert = mix of both.
3. Orator = a skilled public speaker.

Yaad rakhein: Extro = outside (outgoing), Intro = inside (reserved).

Answer: (C) Extrovert

Concept: ‘Gift of the gab’ = the ability to speak easily, fluently and convincingly.

1. ‘Gab’ is an informal word for talk/chatter.
2. So the ‘gift’ (natural talent) of ‘gab’ = a talent for speaking.
3. It does not refer to a person, lying or singing.

Yaad rakhein: Gab = talk → gift of the gab = gift of talking.

Answer: (B) A talent for speaking

Concept: ‘Fluctuate’ = to rise and fall irregularly, to keep changing. The opposite is to become steady – stabilise.

1. Prices that fluctuate keep changing; prices that stabilise stop changing.
2. ‘Vacillate’ (waver) and ‘fickle’ (changeable) are similar in sense, not opposite.
3. ‘Deflect’ = turn aside – unrelated.

Yaad rakhein: Fluctuate ↔ stabilise; synonyms: waver, vacillate, oscillate.

Answer: (A) Stabilise