Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible ?

(UPSC CSAT – 2023)

1. 10
2. 11
3. 12
4. Infinitely many

Solution: Ans.(3)

If (7x + 96) is divisible by x, then 96 is also divisible by x. Therefore the possible values of x are the factors of 96.

Number of factors of 96 :

96 = 3¹×2⁵

Number of factors of 96 = (1+1)×(5+1) = 2×6 = 12

Hence, 12 values of x are possible.

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