All Free Quantitative Methods MCQs with Answers

• A. x = 6
• B. x = 10
• C. x = 8
• D. x = 12

Explanation: Expanding gives 5x − 10 − 2x − 2 = x + 4, so 3x − 12 = x + 4. Therefore, 2x = 16 and x = 8.

• A. x = 10
• B. x = 12
• C. x = 16
• D. x = 14

Explanation: Multiplying the equation by 6 gives 4x − 2 − 3x − 6 = 6. Hence x − 8 = 6, so x = 14.

• A. k = 1 or 9
• B. k = 9 only
• C. k = 1 only
• D. k = −1 or −9

Explanation: Equal roots require the discriminant to be zero. Here, (k − 3)² − 4k = k² − 10k + 9 = (k − 1)(k − 9), giving k = 1 or k = 9.

• A. −4
• B. −2
• C. 2
• D. 4

Explanation: For ax² + bx + c = 0, the product of the roots is c/a. Thus, the product is −4/2 = −2.

• A. x = 2
• B. x = 4
• C. x = 3
• D. x = 6

Explanation: For y = ax² + bx + c, the vertex occurs at x = −b/(2a). Therefore, x = −6/(2 × −1) = 3, where the downward-opening parabola reaches its…

• A. x < −1/2 or x > 2
• B. −2 < x < 1/2
• C. x ≤ −1/2 or x ≥ 2
• D. −1/2 < x < 2

Explanation: The expression factors as (2x + 1)(x − 2). Since the parabola opens upward, it is negative strictly between its roots, so −1/2 < x < 2.

• A. x ≤ −8 or x ≥ 2
• B. −8 ≤ x ≤ 2
• C. x < −8 or x > 2
• D. −2 ≤ x ≤ 8

Explanation: An absolute value of at least 5 means x + 3 ≤ −5 or x + 3 ≥ 5. These conditions give x ≤ −8 or x ≥ 2, including both endpoints.

• A. a = −1
• B. a = 1
• C. a = 0
• D. a = 4

Explanation: When a = 1, the equation becomes 0x = 4, which is impossible and therefore has no solution.

• A. 9 cm
• B. 12 cm
• C. 15 cm
• D. 18 cm

Explanation: Let the width be w, so the length is w + 3. The perimeter equation is 2w + 2(w + 3) = 54, which gives 4w = 48 and w = 12 cm.

• A. x = 3 only
• B. x = −3 only
• C. x = −1 or 1
• D. x = −3 or 3

Explanation: Set t = |x|, where t is nonnegative. Then t² − 2t − 3 = (t − 3)(t + 1) = 0, so t = 3 and therefore x = −3 or x = 3.

• A. Rs. 1,200
• B. Rs. 1,000
• C. Rs. 1,240
• D. Rs. 1,400

Explanation: Simple interest is calculated as P × r × t. Thus, Rs. 5,000 × 0.08 × 3 equals Rs.

• A. Rs. 12,000
• B. Rs. 12,100
• C. Rs. 12,200
• D. Rs. 12,210

Explanation: The amount is 10,000 × (1.10)², which equals Rs. 12,100. Rs. 12,000 results from applying simple interest instead of annual compounding.

• A. Rs. 40,500.00
• B. Rs. 45,454.55
• C. Rs. 45,000.00
• D. Rs. 41,322.31

Explanation: Present value equals future value divided by (1 + r)ⁿ. Therefore, Rs. 50,000 ÷ (1.10)² equals approximately Rs. 41,322.31; Rs.

• A. Rs. 3,310
• B. Rs. 3,100
• C. Rs. 3,000
• D. Rs. 3,641

Explanation: For an ordinary annuity, payments occur at the end of each period. The value is 1,000[(1.10)³ − 1] ÷ 0.10, giving Rs. 3,310; Rs.

• A. Rs. 2,700.00
• B. Rs. 2,486.85
• C. Rs. 2,735.54
• D. Rs. 3,000.00

Explanation: The present value is 1,000[1 − (1.10)⁻³] ÷ 0.10, which is approximately Rs. 2,486.85.

• A. Rs. 96,000
• B. Rs. 120,000
• C. Rs. 150,000
• D. Rs. 160,000

Explanation: The present value of a level perpetuity is annual payment divided by the discount rate. Thus, Rs. 12,000 ÷ 0.08 equals Rs.

• A. 12.00%
• B. 12.36%
• C. 12.68%
• D. 13.20%

Explanation: The effective annual rate is (1 + 0.12/12)¹² − 1. This equals approximately 12.68%, which is higher than the nominal rate because interest…

• A. A level ordinary annuity
• B. A level annuity due
• C. A perpetuity payment
• D. A simple-interest payment

Explanation: The present value of three end-of-year payments of Rs. 4,021.15 at 10% is approximately Rs. 10,000.

• A. Rs. 3,310
• B. Rs. 3,410
• C. Rs. 3,641
• D. Rs. 3,900

Explanation: Beginning-of-year payments form an annuity due. Its value is the ordinary annuity value multiplied by 1.10, so Rs. 3,310 × 1.10 equals Rs.

• A. Rs. 9,200
• B. Rs. 9,600
• C. Rs. 9,425
• D. Rs. 9,400

Explanation: Under simple bank discount, discount equals F × d × t. The discount is Rs. 10,000 × 0.08 × 9/12, or Rs. 600, so the proceeds are Rs. 9,400.