SSC CGL Quant – Simplification & Approximation – Level 3 · Challenge

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SSC CGL Quant – Simplification & Approximation – Level 3 · Challenge – 11 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.  
(0.64³ + 0.36³) ÷ (0.64² − 0.64 × 0.36 + 0.36²) = ?

Correct Answer: C [1]

Explanation:

a + b = 0.64 + 0.36 = 1.

2.  
1/(3 × 4) + 1/(4 × 5) + … + 1/(19 × 20) = ?

Correct Answer: B [17/60]

Explanation:

Telescoping: 1/3 − 1/20 = 17/60.

3.  
If x = 8 + 3√7, then x + 1/x = ?

Correct Answer: D [16]

Explanation:

1/x = 8 − 3√7 (since 64 − 63 = 1); sum = 16.

4.  
√(30 + √(30 + √(30 + …))) = ?

Correct Answer: A [6]

Explanation:

x = √(30 + x) → x² − x − 30 = 0 → x = 6 (the positive root).

5.  
0.1 + 0.2 + … + 0.8 = ?

Correct Answer: D [4]

Explanation:

(1 + 2 + … + 8)/9 = 36/9 = 4.

6.  
√1,225 × 3.01 + 19.98² ≈ ?

Correct Answer: C [505]

Explanation:

35 × 3 + 20² = 105 + 400 = 505 (exact ≈ 504.6).

7.  
(1 − 1/3)(1 − 1/4)(1 − 1/5) … (1 − 1/30) = ?

Correct Answer: B [1/15]

Explanation:

2/3 × 3/4 × … × 29/30 = 2/30 = 1/15 (telescoping product).

8.  
Assertion–Reason
A: 1/(√9 − √8) = 3 + 2√2.
R: (√a − √b)(√a + √b) = a − b.

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

Explanation:

Multiply by √9 + √8: denominator 9 − 8 = 1, so A = 3 + √8 = 3 + 2√2, using R.

9.  
[5/8 of 64 ÷ {12 − (2 + 6)}] × 3/5 + 1¼ = ?

Correct Answer: C [7 1/4]

Explanation:

( ) 8 → { } 4; 5/8 of 64 = 40; 40 ÷ 4 = 10; 10 × 3/5 = 6; 6 + 1¼ = 7¼.

10.  
2/3 of 3/4 of 1,440 ÷ 4 of 1/2 − (25 − 5 × 3) = ?

Correct Answer: A [350]

Explanation:

Brackets: 25 − 15 = 10. 'Of' first: 2/3 of 3/4 of 1,440 = 720 and 4 of 1/2 = 2.

11.  
Fill in the blank? × 1.5 − 1/4 of 96 = 3² × 4. Find ?

Correct Answer: D [40]

Explanation:

1/4 of 96 = 24 and 3² × 4 = 36; ?

➤ 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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