SSC CGL Quant – Number System – Level 2 · Exam Level · Tier I Sprint

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SSC CGL Quant – Number System – 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.  
Three bells ring at intervals of 8, 12 and 18 minutes. They ring together at 10:00 a.m. When will they next ring together?

Correct Answer: D [11:12 a.m.]

Explanation:

LCM(8, 12, 18) = 72 minutes = 1 h 12 min → 11:12 a.m.

2.  
A floor 4.8 m long and 6 m wide is to be paved with identical square tiles, without cutting any. What is the side of the largest such tile?

Correct Answer: B [1.2 m]

Explanation:

HCF(480 cm, 600 cm) = 120 cm = 1.2 m.

3.  
The greatest number that divides 422, 522 and 601 leaving remainders 4, 9 and 12 respectively is:

Correct Answer: A [19]

Explanation:

HCF(418, 513, 589) = 19 (418 = 2 × 11 × 19, 513 = 27 × 19, 589 = 31 × 19).

4.  
The smallest number which leaves remainder 3 when divided by 5, 6 or 8, and is exactly divisible by 7, is:

Correct Answer: C [483]

Explanation:

LCM = 120 → numbers 120k + 3; 120 leaves 1 on ÷ 7, so k + 3 must be a multiple of 7 → k = 4 → 483.

5.  
How many factors does 600 have?

Correct Answer: C [24]

Explanation:

600 = 2³ × 3 × 5² → 4 × 2 × 3 = 24.

6.  
Two-quantity comparison
Quantity I: HCF of 48 and 72
Quantity II: LCM of 6 and 8

Correct Answer: C [Quantity I = Quantity II]

Explanation:

Both equal 24.

7.  
Match the following
P. 0 Q. −7 R. √3
1. irrational 2. whole number 3. integer but not whole

Correct Answer: D [P-2, Q-3, R-1]

Explanation:

0 is whole; −7 is a negative integer; √3 is irrational.

8.  
What is the remainder when 2³¹ is divided by 5?

Correct Answer: A [3]

Explanation:

Remainders of 2ᵏ ÷ 5: 2, 4, 3, 1 (cycle 4); 31 = 4 × 7 + 3 → 3rd place → 3.

9.  
How many zeros are there at the end of 150!?

Correct Answer: B [37]

Explanation:

150 ÷ 5 = 30, 150 ÷ 25 = 6, 150 ÷ 125 = 1 → 37.

10.  
Trick SpotterThe quickest way to find the remainder of 21²⁷ ÷ 22 is:

Correct Answer: D [21 = 22 − 1, so (−1)²⁷ = −1 → remainder 21]

Explanation:

Minus-One Remainder; the unit digit says nothing about division by 22.

11.  
Spot My Mistake“HCF(6, 10, 15) = 1 and LCM = 30, so 6 × 10 × 15 = 1 × 30 = 30.” What is wrong?

Correct Answer: A [HCF × LCM = product holds only for two numbers]

Explanation:

6 × 10 × 15 = 900; the rule is only for pairs.

12.  
Arrange in orderArrange in ascending order: 2⁴⁰, 3³⁰, 5²⁰

Correct Answer: B [2⁴⁰ < 5²⁰ < 3³⁰]

Explanation:

Write as tenth powers: (2⁴)¹⁰ = 16¹⁰, (3³)¹⁰ = 27¹⁰, (5²)¹⁰ = 25¹⁰ → 16 < 25 < 27.

13.  
Assertion–Reason
A: 49 has exactly three factors.
R: If N = pᵃ × qᵇ × … (p, q, … distinct primes), N has (a + 1)(b + 1)… factors.

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

Explanation:

49 = 7² → 2 + 1 = 3 factors (1, 7, 49), exactly as R predicts.

14.  
The LCM of two numbers is 14 times their HCF, and the sum of the HCF and LCM is 600. If one number is 280, the other is:

Correct Answer: D [80]

Explanation:

15 × HCF = 600 → HCF 40, LCM 560 → other = 40 × 560 ÷ 280 = 80.

15.  
Odd one out91, 87, 51, 61

Correct Answer: C [61]

Explanation:

61 is prime; 91 = 7 × 13, 87 = 3 × 29, 51 = 3 × 17.

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