State PSC Exam Preparation — BPSC, UPPSC, MPPSC

Q.41 Easy Simple Interest

Priya invested ₹12000 at 8% simple interest per annum. In how many years will the interest earned be equal to the principal?

A10 years

B11 years

C12 years

D12.5 years

Correct Answer: D. 12.5 years

Explanation:

Step 1: We need SI = P, so SI = ₹12000.

Step 2: Using SI = (P × R × T) / 100, we get 12000 = (12000 × 8 × T) / 100.

Step 3: 12000 = 960T, therefore T = 12000 / 960 = 12.5 years.

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Q.42 Easy Simple Interest

Arun invested some money at 14% simple interest for 5 years and earned ₹2800 as interest. If he had invested the same amount at 10% per annum for the same period, how much interest would he have earned?

A₹1800

B₹2000

C₹2200

D₹2400

Correct Answer: B. ₹2000

Explanation:

Step 1: From first investment, 2800 = (P × 14 × 5) / 100 = 0.7P.

Step 2: P = 2800 / 0.7 = ₹4000.

Step 3: At 10% for 5 years, SI = (4000 × 10 × 5) / 100 = 200000 / 100 = ₹2000.

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Q.43 Easy Numbers

What is the sum of the first 10 natural numbers?

A45

B55

C50

D60

Correct Answer: B. 55

Explanation:

Sum of first n natural numbers = n(n+1)/2.

Here n=10, so sum = 10(11)/2 = 110/2 = 55

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Q.44 Easy Numbers

Find the smallest prime number greater than 20.

A21

B23

C25

D27

Correct Answer: B. 23

Explanation:

Check: 21=3×7 (not prime), 23 is only divisible by 1 and 23 (prime), 25=5×5 (not prime), 27=3×9 (not prime).

So 23 is the smallest prime greater than 20.

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Q.45 Easy Numbers

What is the HCF (Highest Common Factor) of 48 and 64?

A8

B12

C16

D24

Correct Answer: C. 16

Explanation:

Factors of 48: 1,2,3,4,6,8,12,16,24,48.

Factors of 64: 1,2,4,8,16,32,64.

Common factors: 1,2,4,8,16. HCF = 16

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Q.46 Easy Numbers

If a number is divisible by both 3 and 5, by which of these is it always divisible?

A8

B15

C20

D25

Correct Answer: B. 15

Explanation:

If a number is divisible by both 3 and 5, and 3 and 5 are coprime (HCF=1), then the number must be divisible by their product: 3×5 = 15

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Q.47 Easy HCF and LCM

Find the HCF of 48 and 64.

A8

B16

C32

D24

Correct Answer: B. 16

Explanation:

Using prime factorization: 48 = 2⁴ × 3, 64 = 2⁶. HCF = 2⁴ = 16 (taking lowest powers of common prime factors).

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Q.48 Easy HCF and LCM

What is the LCM of 12 and 18?

A36

B24

C54

D72

Correct Answer: A. 36

Explanation:

Prime factorization: 12 = 2² × 3, 18 = 2 × 3². LCM = 2² × 3² = 4 × 9 = 36 (taking highest powers of all prime factors).

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Q.49 Easy HCF and LCM

Find the HCF of 56 and 72.

A4

B8

C12

D16

Correct Answer: B. 8

Explanation:

This question asks us to find the Highest Common Factor (HCF) of two numbers using prime factorization or the Euclidean algorithm.

Step 1: Prime factorization of 56

Express 56 as a product of prime numbers.

56 = 2 \times 2 \times 2 \times 7 = 2^3 \times 7

Step 2: Prime factorization of 72

Express 72 as a product of prime numbers.

72 = 2 \times 2 \times 2 \times 3 \times 3 = 2^3 \times 3^2

Step 3: Find the HCF

The HCF is the product of common prime factors with their lowest powers.

\text{HCF} = 2^3 = 8

The HCF of 56 and 72 is 8, making the correct answer (B).

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Q.50 Easy HCF and LCM

The LCM of 15 and 25 is:

A75

B150

C225

D300

Correct Answer: A. 75

Explanation:

This question asks us to find the Least Common Multiple (LCM) of two numbers using prime factorization.

Step 1: Find prime factorization of 15

Break 15 into its prime factors.

15 = 3 \times 5

Step 2: Find prime factorization of 25

Break 25 into its prime factors.

25 = 5 \times 5 = 5^2

Step 3: Calculate LCM using highest powers of all prime factors

The LCM is found by taking the highest power of each prime that appears in either factorization: 3¹ and 5².

\text{LCM} = 3^1 \times 5^2 = 3 \times 25 = 75

The LCM of 15 and 25 is 75.

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