When 732 is divided by a positive integer x the remainder is 12 How many values of x are there ........

Quantitative Aptitude (CGL) Number System

When 732 is divided by a positive integer x, the remainder is 12. How many values of x are there?

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SSC CGL 4th March 2020 Shift-1

- Let's break it down: When 732 is divided by x, remainder is 12. That means 732 = x*q + 12, so x must divide 732 - 12 = 720.

- x > 12 (remainder always less than divisor)

- So, find all divisors of 720 greater than 12.

- The divisors of 720: 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 72, 80, 90, 120, 144, 180, 240, 360, 720.

- There are 30 total divisors. 10 of these (1,2,3,4,5,6,8,9,10,12) are =12.

- So number of values is 30 - 10 = 20.

- Option 3: 20 is correct.

- Explanation for options:

- Option 1: 19 (Incorrect, less by 1)

- Option 2: 18 (Incorrect, less by 2)

- Option 3: 20 (Correct)

- Option 4: 16 (Incorrect, less by 4)

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