SSC CGL Quant – Algebra – Level 2 · Exam Level · Tier I Sprint

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SSC CGL Quant – Algebra – Level 2 · Exam Level · Tier I Sprint – 15 questions, subject: Quantitative Aptitude. Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.

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1.  
If x − 1/x = 3, what is the value of x³ − 1/x³?

Correct Answer: D [36]

Explanation:

m³ + 3m = 27 + 9 = 36.

2.  
If x + 1/x = 3, what is the value of x⁴ + 1/x⁴?

Correct Answer: A [47]

Explanation:

x² + 1/x² = 7 → x⁴ + 1/x⁴ = 49 − 2 = 47.

3.  
If a + b = 5 and ab = 6, what is a³ + b³?

Correct Answer: C [35]

Explanation:

(a + b)³ − 3ab(a + b) = 125 − 90 = 35.

4.  
What is the value of (0.67³ + 0.33³) ÷ (0.67² − 0.67 × 0.33 + 0.33²)?

Correct Answer: B [1]

Explanation:

a³ + b³ = (a + b)(a² − ab + b²), so the quotient is a + b = 1.

5.  

Directions (Q 17–18): The graph shows two straight lines ℓ₁ and ℓ₂. Grid squares are 1 unit.

Diagram-basedAt which point do ℓ₁ and ℓ₂ intersect?

Correct Answer: C [(3, 4)]

Explanation:

ℓ₁: y = x + 1; ℓ₂: 2x + y = 10 → x + 1 = 10 − 2x → x = 3, y = 4.

6.  
(Use the directions above – Q 17–18)
Diagram-basedWhat is the area of the triangle formed by ℓ₁, ℓ₂ and the x-axis?

Correct Answer: D [12 sq units]

Explanation:

x-intercepts −1 and 5 → base 6, height 4 → ½ × 6 × 4 = 12 sq units.

7.  
Two-quantity comparison
Quantity I: a² + b², when a + b = 7 and ab = 12
Quantity II: x⁴ + 1/x⁴, when x + 1/x = √7

Correct Answer: A [Quantity I > Quantity II]

Explanation:

QI = 49 − 24 = 25. QII: x² + 1/x² = 7 − 2 = 5 → 25 − 2 = 23.

8.  
Trick SpotterIf x + 1/x = 5, which is the fastest correct route to x³ + 1/x³?

Correct Answer: B [5³ − 3 × 5]

Explanation:

Ladder: k³ − 3k = 125 − 15 = 110.

9.  
Spot My Mistake“x + 1/x = 6, so x² + 1/x² = 36 + 2 = 38.” What is the correct value?

Correct Answer: A [34]

Explanation:

Squaring gives x² + 2 + 1/x² = 36 → subtract 2: 34.

10.  
If 4x + 5y = 23 and 5x + 4y = 22, what is x + y?

Correct Answer: C [5]

Explanation:

Add: 9x + 9y = 45 → x + y = 5.

11.  
For what value of k does the pair 3x + 2y = 5 and 9x + ky = 15 have infinitely many solutions?

Correct Answer: D [6]

Explanation:

3/9 = 2/k = 5/15 → k = 6.

12.  
For what value of k does the pair 3x + 4y = 5 and 6x + ky = 7 have no solution?

Correct Answer: B [8]

Explanation:

3/6 = 4/k → k = 8, and 5/7 ≠ 1/2, so the lines are parallel.

13.  
Assertion–Reason
A: If x + 1/x = 2, then x¹⁰⁰ + 1/x¹⁰⁰ = 2.
R: The equation x + 1/x = 2 is satisfied only by x = 1.

Correct Answer: A [Both A and R are true and R explains A]

Explanation:

x² − 2x + 1 = 0 → (x − 1)² = 0 → x = 1, so every power gives 1 + 1 = 2.

14.  
Reverse questionIf x² + 1/x² = 23 and x > 0, what is x + 1/x?

Correct Answer: A [5]

Explanation:

(x + 1/x)² = 23 + 2 = 25 → 5.

15.  
What is the remainder when x³ − 2x² + 4x − 5 is divided by (x − 2)?

Correct Answer: C [3]

Explanation:

Remainder theorem: p(2) = 8 − 8 + 8 − 5 = 3.

➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Quantitative Aptitude book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-quantitative-aptitude

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