UPSC Prelims 2023 · CSAT
Question 25: Basic Numeracy
Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible ?
AnswerUPSC’s answer is (c).
If x divides 7x + 96, it must divide 96, because 7x is already a multiple of x. So x is any positive divisor of 96 = 2^5 x 3. The number of divisors is (5 + 1)(1 + 1) = 12. They are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48 and 96, so 12 values are possible.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Wrong: 96 has 12 divisors, not 10.
- (b) Wrong: 96 has 12 divisors, not 11.
- (c) Right: the 12 divisors of 96.
- (d) Wrong: x must divide 96, so only finitely many values.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2023, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.