Numerical Ability — Practice

Question 1

Evaluate: $36 \div (6 + 2 	imes 3) - 1$.

Accepted Answer

Bracket first: $2	imes3=6$, so $6+6=12$. Then $36\div12=3$. Finally $3-1=2$.

Answer: 2.

Question 2

Add: $\frac{2}{3} + \frac{1}{6}$.

Accepted Answer

LCM of 3 and 6 is 6. Converting: $\frac{4}{6}+\frac{1}{6}=\frac{5}{6}$.

Answer: $\frac{5}{6}$.

Question 3

Find the HCF and LCM of 36 and 60.

Accepted Answer

$36=2^2	imes3^2$, $60=2^2	imes3	imes5$. HCF $=2^2	imes3=12$. LCM $=2^2	imes3^2	imes5=180$. Check: $12	imes180=2160=36	imes60$.

Answer: HCF = 12, LCM = 180.

Question 4

15 men can finish a job in 20 days. How many days will 25 men take, working at the same constant rate?

Accepted Answer

Total work $=15	imes20=300$ man-days. With 25 men: $300\div25=12$ days.

Answer: 12 days.

Question 5

Find $62^2 - 58^2$ without directly squaring either number.

Accepted Answer

Using $a^2-b^2=(a-b)(a+b)$: $(62-58)(62+58)=4	imes120=480$.

Answer: 480.

Question 6

Find the square root of 2,025 by prime factorisation.

Accepted Answer

$2025=3^4	imes5^2$. Pairing: $3^2	imes5=45$.

Answer: 45 (check: $45^2=2025$).

Question 7

Simplify the ratio 42 : 56 : 70 to its lowest terms.

Accepted Answer

The HCF of 42, 56 and 70 is 14. Dividing every term by 14: $3:4:5$.

Answer: 3 : 4 : 5.

Question 8

After a 25% price increase, an item costs ₹750. What was its original price?

Accepted Answer

₹750 represents $1.25$ times the original price. Original price $=750\div1.25=₹600$.

Answer: ₹600.

Question 9

Solve for $x$: $5x + 12 = 2x + 39$.

Accepted Answer

Collecting terms: $5x-2x=39-12$, so $3x=27$, giving $x=9$. Check: $5(9)+12=57$ and $2(9)+39=57$.

Answer: $x=9$.

Question 10

A trader raises a product's price by 30% and then offers a 20% discount on the new price. What is the net percentage change from the original price?

Accepted Answer

Net multiplier $=1.30	imes0.80=1.04$, a 4% net increase — not a 10% net change, since the discount applies to the already-raised price, not the original.

Answer: 4% net increase.

Question 11

The average of 6 numbers is 18. When one number is removed, the average of the remaining 5 numbers becomes 20. Find the removed number.

Accepted Answer

Sum of 6 numbers $=6	imes18=108$. Sum of remaining 5 $=5	imes20=100$. Removed number $=108-100=8$.

Answer: 8.

Question 12

Without a calculator, determine which is larger: $12^3$ or $25^2$.

Accepted Answer

$12^3=12	imes12	imes12=1728$. $25^2=625$. Since $1728>625$, the cube of 12 is larger.

Answer: $12^3=1728 > 25^2=625$.

Practice — Numerical Ability

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