SSC CGL Quant – Number System – Tier II Level · Marathon

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SSC CGL Quant – Number System – Tier II Level · Marathon – 13 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 22x − 1 = 8x − 3, then x = ?

Correct Answer: A [8]

Explanation:

8 = 2³ → 2x − 1 = 3x − 9 → x = 8.

2.  
Which is the largest: √2, ∛3, ⁴√5, ⁶√10?

Correct Answer: D [⁴√5]

Explanation:

Raise each to the 12th power: 2⁶ = 64, 3⁴ = 81, 5³ = 125, 10² = 100 → ⁴√5 is the largest.

3.  
642/3 × 32−3/5 = ?

Correct Answer: B [2]

Explanation:

64 2/3 = 4² = 16; 32 −3/5 = 1/2³ = 1/8; 16 × 1/8 = 2.

4.  
The HCF of 3/4, 9/10 and 15/8 is:

Correct Answer: A [3/40]

Explanation:

HCF(3, 9, 15)/LCM(4, 10, 8) = 3/40.

5.  
What is the remainder when 3⁶⁵ is divided by 7?

Correct Answer: D [5]

Explanation:

Remainders of 3ᵏ ÷ 7 cycle in 6: 3, 2, 6, 4, 5, 1; 65 = 6 × 10 + 5 → 5.

6.  
How many zeros are there at the end of 300!?

Correct Answer: B [74]

Explanation:

300/5 + 300/25 + 300/125 = 60 + 12 + 2 = 74.

7.  
What is the remainder when 19²⁵ + 21²⁵ is divided by 40?

Correct Answer: C [0]

Explanation:

aⁿ + bⁿ is divisible by a + b = 40 for odd n.

8.  
If √(2ⁿ) = 64, then n = ?

Correct Answer: A [12]

Explanation:

2 n/2 = 2⁶ → n/2 = 6 → n = 12.

9.  
√12 + √27 − √48 = ?

Correct Answer: D [√3]

Explanation:

2√3 + 3√3 − 4√3 = √3.

10.  
Which of the following is a rational number?

Correct Answer: B [(2 + √3)(2 − √3)]

Explanation:

Conjugates: 2² − (√3)² = 4 − 3 = 1.

11.  
√(10 + 2√21) = ?

Correct Answer: C [√7 + √3]

Explanation:

Find x + y = 10, xy = 21 → 7 and 3 → √7 + √3.

12.  
What is the remainder when 2⁷⁰ is divided by 13?

Correct Answer: C [10]

Explanation:

13 is prime, so 2¹² leaves 1; 70 = 12 × 5 + 10 → 2¹⁰ = 1,024 leaves 10.

13.  
In how many ways can 2,520 be written as a product of two co-prime factors (order ignored)?

Correct Answer: D [8]

Explanation:

2,520 = 2³ × 3² × 5 × 7 has k = 4 different primes → 2 k − 1 = 2³ = 8.

➤ 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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