Q&A: practice questions with answers

Concept: Half-yearly compounding: rate $=\frac{R}{2}$, periods $=2n$.

1. Rate $=5\%$ per half-year, 4 periods.
2. $A=6500\times (1.05{)}^4=6500\times 1.21550625$
3. $A\approx 7900.79$ ⇒ ₹7,900 (integral value)

Trick: Effective CI for 4 periods at 5% $\approx 21.55\%$; $6500\times 21.55\%\approx 1400.8$.

Answer: (D) ₹7,900

Concept: If A takes 2.4 times the time of (B + C), A's rate $=\frac{\text{rate of }(B+C)}{2.4}$.

1. Let B's one-day work $=b$; C $=\frac{1}{75}$.
2. $A=\frac{b+\frac{1}{75}}{2.4}$ and $A+b=\frac{1}{27}$.
3. $b+\frac{1}{75}+2.4b=\frac{2.4}{27}\Rightarrow 3.4b=\frac{8}{90}-\frac{1}{75}=\frac{34}{450}$
4. $b=\frac{1}{45}$ ⇒ B alone takes 45 days.

Trick: Check: B = 45 days, A + B = 27 ⇒ A = $\frac{1}{27}-\frac{1}{45}=\frac{1}{67.5}$; B + C $=\frac{1}{45}+\frac{1}{75}=\frac{1}{28.125}$, and $67.5=2.4\times 28.125$ ✓.

Answer: (C) 45

Concept: If two circles touch externally at C and AB is a direct common tangent, then $\angle ACB={90}^{\circ }$ always.

1. Draw the common tangent at C meeting AB at M: $MA=MC=MB$ (tangents from one point are equal).
2. So $\angle MAC=\angle MCA$ and $\angle MBC=\angle MCB$.
3. Angle sum in $△ACB$: $2(\angle MCA+\angle MCB)={180}^{\circ }\Rightarrow \angle ACB={90}^{\circ }$.

Yaad rakhein: The 55° is extra data – it only gives $\angle CBA={35}^{\circ }$; $\angle ACB$ is always 90°.

Answer: (B) 90°

Concept: Percentage is taken on the total number of boys only.

1. Total boys $=25+20=45$
2. Boys not in Science $=20$
3. $\frac{20}{45}\times 100=\frac{400}{9}\approx 44.44\%$

Trick: $\frac{4}{9}=0.444\dots$; using all 95 students instead of 45 boys is the common mistake.

Answer: (D) 44.44%

Concept: Quantity of a sector = sector % × total.

1. Grapes $=10\%$, Oranges $=15\%$.
2. Difference $=5\%$ of 1200 kg
3. $=\frac{5}{100}\times 1200=60\text{kg}$

Trick: Find the % difference first, then convert once.

Answer: (A) 60

Concept: Add the two organisations for each year, then simplify the ratio.

1. 2019: D + E $=7000+6600=13600$
2. 2021: D + E $=8000+7600=15600$
3. $13600:15600=136:156=34:39$

Trick: 2019 total is smaller, so the first term must be smaller – rules out 39 : 34 and 14 : 9.

Answer: (D) 34 : 39

Concept: $\tan \theta +\frac{1}{\tan \theta }=2\Rightarrow (\tan \theta -1{)}^2=0\Rightarrow \tan \theta =1$, so $\theta ={45}^{\circ }$ and $\cot \theta =1$.

1. Every power of 1 is 1.
2. $2(1)+3(1)+5(1)(1)$
3. $=2+3+5=10$

Trick: $x+\frac{1}{x}=2$ ⇒ $x=1$; then just add the coefficients.

Answer: (C) 10

Concept: Drop the altitude PM; in an equilateral triangle it bisects the base and equals $\frac{\sqrt{3}}{2}a$.

1. $QS=\frac{9}{3}=3$, $QM=4.5$ ⇒ $SM=1.5$
2. $P{M}^2=\frac{3}{4}\times 81=60.75$
3. $P{S}^2=P{M}^2+S{M}^2=60.75+2.25=63$
4. $PS=\sqrt{63}\text{cm}$

Trick: If $QS=\frac{a}{3}$ in an equilateral triangle, $P{S}^2=\frac{7}{9}{a}^2=\frac{7}{9}\times 81=63$.

Answer: (B) $\sqrt{63}$

Concept: $\text{CP}=\frac{\text{SP}}{1-\text{loss}\%}$; new SP $=\text{CP}\times (1+\text{gain}\%)$.

1. $\text{CP}=\frac{1596}{0.76}=$ ₹2,100
2. SP for 24% gain $=2100\times 1.24=$ ₹2,604

Trick: Directly: $1596\times \frac{124}{76}=21\times 124=2604$.

Answer: (D) 2604

Concept: $2n$ must be a common multiple of 12, 14, 16 and 18; least $2n$ = LCM.

1. $12=2^2\times 3$, $14=2\times 7$, $16=2^4$, $18=2\times 3^2$
2. $\text{LCM}=2^4\times 3^2\times 7=1008$
3. $n=\frac{1008}{2}=504$

Trick: Don't stop at the LCM (1008) – the question asks for the number that is doubled.

Answer: (C) 504

Concept: Spurious means false, fake or not what it claims to be. An antonym must mean real or authentic.

1. ‘They drank some spurious drink’ = a fake/adulterated drink, which is why they fainted.
2. Genuine = real, authentic – exact opposite.
3. Artificial is close to spurious (a synonym-type word); curious (eager to know) and nefarious (wicked) are unrelated.

Trick: Spurious = fake ↔ genuine = real. Think ‘spurious liquor’ (नकली शराब).

Answer: (D) genuine

Concept: A ‘-mania’ word names an abnormal, uncontrollable urge. The urge to steal (without need) is kleptomania (Greek kleptein = to steal).

1. Pyromania – compulsion to set things on fire.
2. Dipsomania – uncontrollable craving for alcohol.
3. Megalomania – obsession with power/one’s own greatness.
4. Only Kleptomania = morbid compulsion to steal.

Trick: Klepto = steal (kleptomaniac = one who steals compulsively); pyro = fire; dipso = drink; megalo = great.

Answer: (B) Kleptomania

Concept: (Straight) from the horse’s mouth means getting information directly from the person who knows it first-hand.

1. The underlined part ‘heard the facts directly from him’ = first-hand information from the person involved.
2. Speak of the devil – said when the person being discussed appears.
3. Get something out of your system – get rid of a strong feeling/urge.
4. Pour one’s heart out – share deep feelings, not ‘facts directly’.

Trick: Horse’s mouth = original source. ‘I heard it straight from the horse’s mouth’ = from the person himself.

Answer: (D) Straight from horse’s mouth

Concept: Numismatics is the study or collection of coins, currency and medals (Latin nummus = coin).

1. Philately – collection and study of postage stamps.
2. Antiquary – a person who studies or collects antiques.
3. Apothecary – a person who prepares and sells medicines (old word for pharmacist).
4. So ‘study of coins’ = Numismatics.

Yaad rakhein: Numismatics – ‘N’ for ‘Notes/coiNs’; Philately – ‘P’ for ‘Postage stamps’.

Answer: (C) Numismatics

Concept: Quite (adverb) means ‘fairly/completely’; quiet (adjective) means ‘silent’. After the linking verb be we need an adjective of state – quiet.

1. Meaning required: the students should remain silent in the exam → ‘be quiet’.
2. ‘be quite’ is a spelling-confusion error, so substitution is needed.
3. ‘have quiet’ is unidiomatic; ‘been quiet’ cannot follow ‘to’ (to + base form needed).

Trick: quiet = silent (ends in -et like ‘secret’); quite = very/fairly (ends in -te).

Answer: (B) be quiet

Concept: Insipid means lacking flavour, tasteless; figuratively, dull or uninteresting.

1. The customers refused to pay because the platter was tasteless → ‘lacking taste’.
2. ‘full of flavours’ and ‘full of spices’ are the opposite of insipid.
3. ‘filled with dirt’ means dirty, not tasteless.

Trick: Insipid = in (not) + sapid (tasty) → not tasty.

Answer: (D) lacking taste

Concept: Raise a hue and cry means to make a loud public protest or outcry against something.

1. Doctors are loudly opposing the RTH (Right to Health) bill → they are protesting.
2. ‘Enquire’ = ask; ‘Postpone’ = delay; ‘Abandon’ = give up – none shows loud opposition.

Trick: Hue and cry = shouting/outcry → strong protest.

Answer: (B) Protest

Concept: Part and parcel (of something) means an essential, inseparable part of it.

1. Technology has become an essential element of modern life → ‘an integral part’.
2. ‘an obstacle’, ‘a myth’ and ‘a useless part’ all contradict the positive, essential sense of the idiom.

Trick: Part and parcel = can’t be separated → integral (अभिन्न).

Answer: (D) an integral part

Concept: Major (adjective) means important, large or serious in size/extent.

1. Considerable = large in size, amount or importance – closest in meaning.
2. Diligent = hard-working; Shallow = not deep/superficial (closer to an antonym); Creviced = having cracks.

Trick: Major ≈ considerable/significant; minor ≈ negligible.

Answer: (C) Considerable

Concept: Abstract qualities used in a general sense take no article. Here ‘courteous’ is an adjective directly after the gerund being.

1. ‘Being courteous costs you nothing’ – the blank lies between the adjective and the verb costs.
2. No noun follows the blank, so ‘a/an/the’ has nothing to modify.
3. Hence no article is required.

Trick: An article needs a noun after it; no noun → no article.

Answer: (A) No article required