Q&A: practice questions with answers

Concept: Area of four walls $=2(l+b)h$; total surface area $=2(lb+bh+hl)$.

1. $l=5b$: $2(6b)(8)=720\Rightarrow 96b=720\Rightarrow b=7.5$, $l=37.5$.
2. $lb=281.25$, $bh=60$, $hl=300$.
3. TSA $=2(281.25+60+300)=2\times 641.25=1282.5{\text{m}}^2$.

Trick: TSA = four walls + $2lb$ $=720+562.5=1282.5$.

Answer: (D) $1282.5{\text{m}}^2$

Concept: For equal distances, average speed $=\frac{2xy}{x+y}$.

1. $\frac{2\times 60\times 40}{60+40}=\frac{4800}{100}=48\text{km/h}$.
2. Check: distance $=1800$ km; times 30 h + 45 h; $\frac{3600}{75}=48$.

Trick: The 30 hours given is extra data – not needed.

Answer: (D) $48\text{km/h}$

Concept: Average speed $=\frac{\text{total distance}}{\text{total time}}$; convert $15\text{m/s}$ to km/h by $\times \frac{18}{5}$.

1. $15\times \frac{18}{5}=54\text{km/h}$; lap 2 time $=\frac{162}{54}=3$ h.
2. Total time $=4+3+4=11$ h; total distance $=50\times 11=550$ km.
3. Lap 3 $=550-200-162=188$ km; speed $=\frac{188}{4}=47\text{km/h}$.

Trick: Find total time first – then total distance follows from the average.

Answer: (A) $47\text{km/h}$

Concept: They meet at the starting point after the LCM of the times each takes for one round.

1. Times per round: $\frac{36}{3}=12$ h, $\frac{36}{4}=9$ h, $\frac{36}{6}=6$ h.
2. LCM$(12,9,6)=36$ h.

Trick: Starting-point meeting → LCM of round times (not of speeds).

Answer: (B) 36 hours

Concept: The radius is perpendicular to the tangent at the point of contact, so OA is the hypotenuse.

1. $O{A}^2={12}^2+5^2=144+25=169$.
2. $OA=13\text{cm}$.

Trick: (5, 12, 13) Pythagorean triplet.

Answer: (D) $13\text{cm}$

Concept: Difference of ratio parts corresponds to the difference in prices.

1. $9-5=4$ parts $=₹380$ ⇒ 1 part $=₹95$.
2. Ball $=5\times 95=₹475$.

Trick: Difference in parts ↔ difference in values.

Answer: (C) Rs. $475$

Concept: The required number is the largest 5-digit multiple of LCM(13, 15, 18, 21).

1. LCM $=13\times 5\times 9\times 2\times 7=8190$.
2. $99999÷8190$ gives quotient 12.
3. $12\times 8190=98280$.

Trick: Largest $n$-digit multiple = $99999-(99999mod\text{LCM})$; remainder here is 1719.

Answer: (B) $98280$

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

1. $456-(76+225)=456-301=155$.
2. $\frac{3}{4}\text{ of }\frac{76}{18}=\frac{228}{72}=\frac{19}{6}$.
3. $\frac{19}{6}÷\frac{19}{1728}=\frac{19}{6}\times \frac{1728}{19}=288$.
4. $155+288=443$.

Yaad rakhein: 'of' is done before division.

Answer: (A) $443$

Concept: Volume is conserved: $\frac{4}{3}\pi (r_1^3+r_2^3+r_3^3)=\frac{1}{3}\pi R^{2}h$; then CSA $=\pi Rl$.

1. $\frac{4}{3}\pi (1000+512+216)=\frac{4}{3}\pi \times 1728=2304\pi$.
2. $\frac{1}{3}\pi \times 144\times h=2304\pi \Rightarrow h=48$.
3. $l=\sqrt{{12}^2+{48}^2}=\sqrt{2448}\approx 49.48$.
4. CSA $=3.14\times 12\times 49.48\approx 1864.41{\text{cm}}^2$.

Trick: ${10}^3+8^3+6^3={12}^3$ – the three spheres equal one sphere of radius 12.

Answer: (D) $1864.41{\text{cm}}^2$

Concept: $\text{Required }\%=\frac{\text{first average}}{\text{second average}}\times 100$. Read the values (in thousands) from the graph carefully by year.

1. 2012 sales: B = 18, D = 21 → average $=\frac{18+21}{2}=19.5$
2. 2011 sales: A = 11, E = 18 → average $=\frac{11+18}{2}=14.5$
3. Required percentage $=\frac{19.5}{14.5}\times 100=\frac{39}{29}\times 100\approx 134.48\%$
4. Since the 2012 average (19.5) is larger than the 2011 average (14.5), the answer must be more than $100\%$ – yet every option is below $100\%$.

Trick: "X is what % of Y" → X on top. Bigger on top ⇒ answer above $100\%$. The value $74.36\%$ appears only if the ratio is reversed: $\frac{14.5}{19.5}\times 100\approx 74.36\%$, which answers the opposite question.

Answer: As printed, the required value is $\approx 134.48\%$, which is not among the options, so no option fits the question as asked.

Concept: 'A' is used before a word beginning with a consonant sound and 'an' before a vowel sound; 'a lot of' is a fixed phrase.

1. 'big' starts with a consonant sound, so it takes 'a': a big city.
2. 'lot' also starts with a consonant sound: a lot of rubbish.
3. (A) 'an big' and (D) 'an lot' are wrong; (B) drops the article before 'big city'.

Trick: Choose the article by the first sound, not the letter: a + consonant sound, an + vowel sound.

Answer: (C) In a big city like Mumbai, we see a lot of rubbish being thrown from households and factories.

Concept: Vigorous means strong, healthy and full of energy. Its opposite describes weakness.

1. Frail = weak and delicate – the exact opposite.
2. Sturdy and Robust are synonyms of vigorous.
3. Buoyant = cheerful / able to float – not an opposite.

Trick: Vigorous ↔ Frail is like Strong ↔ Weak.

Answer: (C) Frail

Concept: A slap on the wrist means a very light or mild punishment, much less than the offence deserves.

1. A slap on the wrist hardly hurts – so the punishment is only symbolic.
2. Example: He got away with a slap on the wrist for cheating.
3. (A), (B) and (D) are literal or unrelated guesses.

Trick: Wrist pe halki si thapki = halki saza.

Answer: (C) A very mild punishment.

Concept: The phrasal verb is let oneself go = to stop caring about one's appearance or behaviour. After 'let', the bare infinitive (base form) is used.

1. Pattern: let + object + base verb → let herself go.
2. 'be gone', 'gone' and 'going' are not base forms after 'let'.
3. 'let her go in' changes the meaning completely.

Trick: let / make / help + object + V1 (no 'to', no -ing).

Answer: (A) let herself go

Concept: Resilient describes a person who recovers quickly and becomes strong in spite of difficulties.

1. Resilient = able to bounce back from hardship.
2. Anxious = worried; Triggered = provoked/upset; Safe = protected – none means growing strong through difficulty.

Trick: Resilience = rubber ball – hit it hard and it bounces back.

Answer: (D) Resilient

Concept: Penchant means a strong liking or fondness for something.

1. Example: She has a penchant for classical music.
2. So the synonym is Liking.
3. Disliking is the opposite; Bitterness and Sourness are unrelated.

Trick: Penchant ≈ 'pen-chant' – something you love so much you keep chanting it.

Answer: (B) Liking

Concept: The noun meaning 'the process of food going bad' is spelt spoilage (spoil + age).

1. Correct: spoilage – the 'i' comes before the 'l'.
2. irreversible, modification and inedible are all spelt correctly.

Trick: Think of the root verb: spoil → spoilage, just like pack → package.

Answer: (B) spoliage

Concept: A lot on one's plate means having a lot of work or many responsibilities to deal with.

1. Example: I can't take this project; I already have a lot on my plate.
2. The idiom is figurative – it is not about eating or food (A), (D), nor illness (C).

Trick: Plate full = hands full = too much to do.

Answer: (B) A lot to do

Concept: Intense means very strong, extreme or powerful (intense heat, intense pain).

1. The opposite is Faint = weak, slight, barely felt.
2. Regular, Rough and Stationary are not opposites of 'strong in degree'.

Trick: Intense light ↔ faint light.

Answer: (D) Faint

Concept: To be on thin ice means to be in a risky or dangerous situation where one wrong move can cause trouble.

1. Walking on thin ice may make it crack at any moment – hence 'risk'.
2. Example: After being late thrice, he is on thin ice with his boss.

Trick: Thin ice = it may crack anytime = risky.

Answer: (C) To be in a risky situation