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

Math and Mental Ability Number System

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

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Complete-Test, Previous year (2023)

Infinitely many

- We have the expression \( 7x + 96 \), which must be divisible by \( x \).

- This means that \( \frac{7x + 96}{x} = 7 + \frac{96}{x} \) must be an integer.

- Therefore, \( \frac{96}{x} \) must be an integer, implying \( x \) must be a divisor of 96.

- The positive divisors of 96 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, and 96.

- Hence, there are 12 possible values for \( x \).

Option 3—12 is the correct answer.

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