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UPSC Prelims

CSAT Year Wise (Temporary Link, This will be removed and no PDFs shall be downloaded here. Please download CSAT subject wise files) / सी सैट

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CSAT 2023

Q25 2023, Number System: Divisibility Rules

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

मान लीजिए, x कोई धन पूर्णांक है, इस प्रकार कि 7x + 96 विभाज्य है x से

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The expression 7x + 96 is divisible by x, which means that 96 is divisible by x, or x is a factor of 96.

96 = 2⁵ × 3

So, x can be 2, 4, 8, 16, 32, 6, 12, 24, 48, and 96. Also x can be 1 and 3.

So, a total of 12 possible values.

Thus, option (c) is the correct answer.

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