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SSC CGL 2020 PYQ — Question 71

SSC CGL - 4th March 2020 Shift 1 • Quantitative Aptitude • Q71

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

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Correct answer: D

Explanation

The correct answer is Option 4 i.e 20.

Understanding/Application

732 is divided by a positive integer x, the remainder is 12.

In order to get 12 as a remainder, the divisor should be greater than 12.

Therefore, x > 12 .

Now

732 = x n + 12
x n  = 720
Now we need to find factors of 720, such that x > 12.

720 = 9 x 4x 5 x 2 x 2 = 24 × 32 × 5
Combinations of these numbers which are greater than 12 ,15, 16, 18, 20, 24, 30, 36, 40, 45, 48, 60, 72, 80, 90, 120, 144, 180, 240, 360 and 720.

The number of values of x are 20