1
Solve for x: 3x − 7 = 2x + 5
Correct answer: D. 12
Move the x terms to one side: 3x − 2x = 5 + 7, so x = 12.
easy
Algebra: Equations, Identities and Quadratics MCQs
Solved algebra MCQs for SSC CGL: linear equations, algebraic identities, x + 1/x problems, factorising quadratics, and sum and product of roots, with step-by-step solutions.
20 MCQsUpdated 27 October 2026
This set covers the algebra asked in SSC and banking quant sections: linear equations, identities such as (a − b)² and a² − b², quick squaring tricks, the sum and product of the roots of a quadratic, and consecutive-number problems.
Many questions are solved faster with an identity than by direct calculation, for example 105² − 95² = (105 + 95)(105 − 95). Every explanation shows the shortest method.
- 2
If 5x + 8 = 43, what is x?
Correct answer: B. 7
5x = 43 − 8 = 35, so x = 7.
easy - 3
If x + y = 9 and x − y = 3, what is x?
Correct answer: B. 6
Add the two equations: 2x = 12, so x = 6 (and y = 3).
easy - 4
If a + b = 10 and ab = 21, what is a² + b²?
Correct answer: D. 58
a² + b² = (a + b)² − 2ab = 100 − 42 = 58.
medium - 5
If a − b = 4 and ab = 12, what is a² + b²?
Correct answer: B. 40
a² + b² = (a − b)² + 2ab = 16 + 24 = 40.
medium - 6
If x + 1/x = 5, what is x² + 1/x²?
Correct answer: C. 23
Square both sides: x² + 2 + 1/x² = 25, so x² + 1/x² = 23.
medium - 7
If x + 1/x = 3, what is x³ + 1/x³?
Correct answer: C. 18
x³ + 1/x³ = (x + 1/x)³ − 3(x + 1/x) = 27 − 9 = 18.
hard - 8
If x − 1/x = 4, what is x² + 1/x²?
Correct answer: B. 18
Square both sides: x² − 2 + 1/x² = 16, so x² + 1/x² = 18.
medium - 9
What is the value of 105² − 95²?
Correct answer: B. 2,000
Use a² − b² = (a + b)(a − b) = 200 × 10 = 2000.
easy - 10
What is the value of 47² + 2 × 47 × 3 + 3²?
Correct answer: A. 2,500
This is (a + b)² with a = 47 and b = 3: (47 + 3)² = 50² = 2500.
medium - 11
What are the roots of x² − 7x + 10 = 0?
Correct answer: A. 2 and 5
Find two numbers that add to 7 and multiply to 10: 2 and 5. So (x − 2)(x − 5) = 0.
medium - 12
What are the roots of x² − x − 12 = 0?
Correct answer: A. 4 and −3
Two numbers that multiply to −12 and add to 1 are 4 and −3, so (x − 4)(x + 3) = 0.
medium - 13
What is the sum of the roots of 2x² − 7x + 3 = 0?
Correct answer: A. 7/2
For ax² + bx + c = 0, the sum of the roots is −b/a = 7/2.
medium - 14
What is the product of the roots of 2x² − 7x + 3 = 0?
Correct answer: C. 3/2
For ax² + bx + c = 0, the product of the roots is c/a = 3/2.
medium - 15
Find the value of 2x² − 3x + 1 when x = 3.
Correct answer: B. 10
2(3)² − 3(3) + 1 = 18 − 9 + 1 = 10.
easy - 16
If y = 2x − 3 and x = 6, what is y?
Correct answer: C. 9
Substitute x = 6 into y = 2x − 3: y = 2 × 6 − 3 = 12 − 3 = 9.
easy - 17
The sum of three consecutive integers is 21. What is the largest of them?
Correct answer: D. 8
Let them be n − 1, n, n + 1. Their sum is 3n = 21, so n = 7 and the largest is 8.
medium - 18
If x/6 = 4/3, what is x?
Correct answer: D. 8
Cross-multiply: 3x = 6 × 4 = 24, so x = 8.
easy - 19
If 2^x = 32, what is x?
Correct answer: B. 5
32 = 2 × 2 × 2 × 2 × 2 = 2⁵, so x = 5.
easy - 20
What is the value of (64)^(1/3)?
Correct answer: D. 4
A cube root: 4 × 4 × 4 = 64, so 64^(1/3) = 4.
easy