Question 1

1. Find the sum of the first 50 natural numbers.

A) 1225B) 1250C) 1275D) 1300

Answer

✓ Correct Answer: Option C

Explanation: Sum of first n natural numbers $= \frac{n(n+1)}{2}$. For n = 50: $\frac{50 \times 51}{2} = 25 \times 51 = 1275$.

Question 2

2. What is the place value of 7 in the number 87,654?

A) 700B) 7,000C) 70D) 7

Question 3

3. Which of the following is the smallest prime number?

A) 1B) 2C) 3D) 0

Answer

✓ Correct Answer: Option B

Explanation: A prime number is a natural number greater than 1. The smallest prime number is 2. Note: 1 is neither prime nor composite.

Question 4

4. If the number 45x1 is divisible by 3, what is the smallest non-negative integer value for x?

A) 2B) 1C) 0D) 3

Answer

✓ Correct Answer: Option A

Explanation: A number is divisible by 3 if the sum of its digits is divisible by 3. Sum = 4 + 5 + x + 1 = 10 + x. The smallest x that makes 10+x divisible by 3 is x=2 (since 12 is divisible by 3).

Question 5

5. Find the LCM of 12 and 15.

A) 30B) 45C) 180D) 60

Answer

✓ Correct Answer: Option D

Explanation: Multiples of 12: 12, 24, 36, 48, 60... Multiples of 15: 15, 30, 45, 60... The least common multiple is 60.

Question 6

6. Find the HCF of 24 and 36.

A) 12B) 6C) 8D) 4

Answer

✓ Correct Answer: Option A

Explanation: Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36 The highest common factor is 12.

Question 7

7. The HCF of two numbers is 5 and their LCM is 30. If one number is 10, find the other number.

A) 20B) 15C) 25D) 5

Answer

✓ Correct Answer: Option B

Explanation: Formula: $Product of numbers = HCF \times LCM$. $10 \times x = 5 \times 30 ⇒ 10x = 150 ⇒ x = 15$.

Question 8

8. Find the LCM of 8, 12, and 16.

A) 32B) 24C) 48D) 96

Answer

✓ Correct Answer: Option C

Explanation: $8 = 2^3, 12 = 2^2 \times 3, 16 = 2^4$. LCM $= 2^4 \times 3 = 16 \times 3 = 48$.

Question 9

9. Simplify: $25 \times 4 - 10 + 5$

A) 85B) 95C) 105D) 75

Answer

✓ Correct Answer: Option B

Explanation: Using BODMAS: Step 1: Multiplication: $25 \times 4 = 100$. Step 2: 100 - 10 + 5 = 90 + 5 = 95.

Question 10

10. Simplify: 0.5 + 0.25 - 0.125

A) 0.625B) 0.375C) 0.875D) 0.5

Answer

✓ Correct Answer: Option A

Explanation: 0.500 + 0.250 = 0.750. 0.750 - 0.125 = 0.625.

Question 11

11. Calculate: $\sqrt{625} + \sqrt{144}$

A) 25B) 12C) 49D) 37

Answer

✓ Correct Answer: Option D

Explanation: $\sqrt{625} = 25$ and $\sqrt{144} = 12$. Sum = 25 + 12 = 37.

Question 12

12. Simplify: $120 \div 3 \times 2$

A) 20B) 80C) 40D) 60

Answer

✓ Correct Answer: Option B

Explanation: Follow BODMAS (Division before Multiplication): $120 \div 3 = 40$. $40 \times 2 = 80$.

Question 13

13. What is 20% of 500?

A) 100B) 50C) 200D) 150

Answer

✓ Correct Answer: Option A

Explanation: $20% of 500 = \frac{20}{100} \times 500 = 20 \times 5 = 100$.

Question 14

14. Express the fraction $\frac{3}{4}$ as a percentage.

A) 25%B) 50%C) 75%D) 80%

Answer

✓ Correct Answer: Option C

Explanation: To convert a fraction to percentage, multiply by 100: $\frac{3}{4} \times 100 = 3 \times 25 = 75%$.

Question 15

15. If a number is increased by 10% and becomes 110, find the original number.

A) 90B) 100C) 110D) 105

Answer

✓ Correct Answer: Option B

Explanation: Let the number be x. $x + 0.10x = 110 ⇒ 1.1x = 110 ⇒ x = \frac{110}{1.1} = 100$.

Question 16

16. What is 5% of 10% of 1000?

A) 5B) 10C) 50D) 1

Answer

✓ Correct Answer: Option A

Explanation: 10% of 1000 = 100. $5% of 100 = \frac{5}{100} \times 100 = 5$.

Question 17

17. An item is bought for ₹100 and sold for ₹120. Find the profit percentage.

A) 10%B) 15%C) 20%D) 25%

Answer

✓ Correct Answer: Option C

Explanation: Profit = SP - CP = 120 - 100 = ₹20. Profit % $= \frac{Profit}{CP} \times 100 = \frac{20}{100} \times 100 = 20%$.

Question 18

18. The cost price of a chair is ₹500. If it is sold at a loss of 10%, what is the selling price?

A) ₹400B) ₹450C) ₹550D) ₹490

Answer

✓ Correct Answer: Option B

Explanation: Loss = 10% of 500 = ₹50. SP = CP - Loss = 500 - 50 = ₹450.

Question 19

19. Which formula correctly represents Profit?

A) SP - CPB) CP - SPC) SP + CPD) CP / SP

Answer

✓ Correct Answer: Option A

Explanation: Profit occurs when the Selling Price (SP) is greater than the Cost Price (CP). Hence, Profit = SP - CP.

Question 20

20. If the cost price of 10 pens is equal to the selling price of 8 pens, find the profit percentage.

A) 20%B) 15%C) 25%D) 30%

Answer

✓ Correct Answer: Option C

Explanation: Let CP of 1 pen be x. Total CP = 10x. SP of 8 pens = 10x ⇒ SP of 1 pen $= \frac{10x}{8} = 1.25x$. Profit per pen = 1.25x - x = 0.25x. Profit % $= \frac{0.25x}{x} \times 100 = 25%$.

Competitive Exams : Quantitative Aptitude - Mix (Set 3)

1. Find the sum of the first 50 natural numbers.

2. What is the place value of 7 in the number 87,654?

3. Which of the following is the smallest prime number?

4. If the number 45x1 is divisible by 3, what is the smallest non-negative integer value for x?

5. Find the LCM of 12 and 15.

6. Find the HCF of 24 and 36.

7. The HCF of two numbers is 5 and their LCM is 30. If one number is 10, find the other number.

8. Find the LCM of 8, 12, and 16.

9. Simplify: $25 \times 4 - 10 + 5$

10. Simplify: 0.5 + 0.25 - 0.125

11. Calculate: $\sqrt{625} + \sqrt{144}$

12. Simplify: $120 \div 3 \times 2$

13. What is 20% of 500?

14. Express the fraction $\frac{3}{4}$ as a percentage.

15. If a number is increased by 10% and becomes 110, find the original number.

16. What is 5% of 10% of 1000?

17. An item is bought for ₹100 and sold for ₹120. Find the profit percentage.

18. The cost price of a chair is ₹500. If it is sold at a loss of 10%, what is the selling price?

19. Which formula correctly represents Profit?

20. If the cost price of 10 pens is equal to the selling price of 8 pens, find the profit percentage.