Quantitative Reasoning — Practice

Question 1

A train covers 240 km in 4 hours at a constant speed. How far will it travel in 6 hours at the same speed?

Accepted Answer

Speed $=240\div4=60$ km/h (direct proportion). Distance in 6 hours $=60	imes6=360$ km.

Answer: 360 km.

Question 2

10 identical taps fill a tank in 6 hours. How long will 15 identical taps take, at the same individual rate?

Accepted Answer

Total tap-hours $=10	imes6=60$ (a fixed quantity of work). With 15 taps: $60\div15=4$ hours.

Answer: 4 hours.

Question 3

Find the 15th triangular number.

Accepted Answer

Using $\frac{n(n+1)}{2}$ with $n=15$: $\frac{15	imes16}{2}=120$.

Answer: 120.

Question 4

₹2,600 is divided among A, B and C in the ratio 3 : 4 : 6. Find B's share.

Accepted Answer

Total parts $=3+4+6=13$. One part $=2600\div13=₹200$. B's share $=4	imes200=₹800$.

Answer: ₹800.

Question 5

P is currently 4 times as old as Q. In 6 years, P will be 2.5 times as old as Q. Find their current ages.

Accepted Answer

Let Q's age be $x$, so P's is $4x$. In 6 years: $4x+6=2.5(x+6) \Rightarrow 4x+6=2.5x+15 \Rightarrow 1.5x=9 \Rightarrow x=6$. So Q is 6 and P is 24. Check: in 6 years, P is 30, Q is 12, and $30=2.5	imes12$.

Answer: Q = 6 years, P = 24 years.

Question 6

Find the angle between the hour and minute hands at 8:20.

Accepted Answer

$|30(8)-5.5(20)|=|240-110|=130$. Since 130 is smaller than $360-130=230$, the angle is 130°.

Answer: 130°.

Question 7

A sequence begins $5, 15, 45, 135, \ldots$. Find the next term.

Accepted Answer

Each term is 3 times the previous one (a constant ratio, so geometric): $135	imes3=405$.

Answer: 405.

Question 8

Two numbers have a sum of 150 and a difference of 30. Find both numbers.

Accepted Answer

Larger $=\frac{150+30}{2}=90$. Smaller $=\frac{150-30}{2}=60$. Check: $90+60=150$, $90-60=30$.

Answer: 90 and 60.

Question 9

The sum of three consecutive EVEN integers is 90. Find the three integers.

Accepted Answer

Let the integers be $x, x+2, x+4$. Sum: $3x+6=90 \Rightarrow x=28$. The three integers are $28, 30, 32$. Check: $28+30+32=90$.

Answer: 28, 30, 32.

Question 10

A can complete a job in 12 days and B can complete the same job in 18 days. Working together at their own constant rates, how many days will they take?

Accepted Answer

A's rate $=\frac{1}{12}$ per day; B's rate $=\frac{1}{18}$ per day. Combined rate $=\frac{1}{12}+\frac{1}{18}=\frac{3}{36}+\frac{2}{36}=\frac{5}{36}$ per day. Time together $=\frac{36}{5}=7.2$ days.

Answer: 7.2 days.

Question 11

Find the angle between the hour and minute hands at 5:50.

Accepted Answer

$|30(5)-5.5(50)|=|150-275|=125$. Since 125 is smaller than $360-125=235$, the angle is 125°.

Answer: 125°.

Practice — Quantitative Reasoning

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