Competitive Exams : Quantitative Aptitude - Mix (Set 3) | Concept of Maths

Question 1

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

A) 1225

B) 1250

C) 1275

D) 1300

Answer

Correct Answer: C

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) 700

B) 7,000

C) 70

D) 7

Answer

Correct Answer: B

In $87,654$, the digit $7$ is in the thousands place. Therefore, its place value is $7 \times 1000 = 7,000$.

Question 3

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

A) 1

B) 2

C) 3

D) 0

Answer

Correct Answer: B

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) 2

B) 1

C) 0

D) 3

Answer

Correct Answer: A

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) 30

B) 45

C) 180

D) 60

Answer

Correct Answer: D

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) 12

B) 6

C) 8

D) 4

Answer

Correct Answer: A

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) 20

B) 15

C) 25

D) 5

Answer

Correct Answer: B

Formula: $\text{Product of numbers} = \text{HCF} \times \text{LCM}$. $10 \times x = 5 \times 30 \implies 10x = 150 \implies x = 15$.

Question 8

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

A) 32

B) 24

C) 48

D) 96

Answer

Correct Answer: C

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

Question 9

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

A) 85

B) 95

C) 105

D) 75

Answer

Correct Answer: B

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) 0.625

B) 0.375

C) 0.875

D) 0.5

Answer

Correct Answer: A

Question 11

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

A) 25

B) 12

C) 49

D) 37

Answer

Correct Answer: D

Question 12

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

A) 20

B) 80

C) 40

D) 60

Answer

Correct Answer: B

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

Question 13

13. What is $20\%$ of $500$?

A) 100

B) 50

C) 200

D) 150

Answer

Correct Answer: A

Question 14

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

A) 25%

B) 50%

C) 75%

D) 80%

Answer

Correct Answer: C

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) 90

B) 100

C) 110

D) 105

Answer

Correct Answer: B

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

Question 16

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

A) 5

B) 10

C) 50

D) 1

Answer

Correct Answer: A

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

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: C

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

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) ₹400

B) ₹450

C) ₹550

D) ₹490

Answer

Correct Answer: B

Loss $= 10\% \text{ of } 500 = ₹50$. $SP = CP - \text{Loss} = 500 - 50 = ₹450$.

Question 19

19. Which formula correctly represents Profit?

A) SP - CP

B) CP - SP

C) SP + CP

D) CP / SP

Answer

Correct Answer: A

Profit occurs when the Selling Price ($SP$) is greater than the Cost Price ($CP$). Hence, $\text{Profit} = SP - CP$.

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: C

Let $CP$ of 1 pen be $x$. Total $CP = 10x$. $SP$ of 8 pens $= 10x \implies SP$ 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) | Concept of Maths