UPSC Prelims 2024 · CSAT
Question 18: Basic Numeracy
421 and 427, when divided by the same number, leave the same remainder 1. How many numbers can be used as the divisor in order to get the same remainder 1?
AnswerUPSC’s answer is (c).
If both numbers leave remainder 1, the divisor divides 421 − 1 = 420 and 427 − 1 = 426, so it divides their HCF. 426 − 420 = 6, and 420 is a multiple of 6, so the HCF is 6. Divisors of 6 are 1, 2, 3 and 6, but a divisor must be larger than the remainder 1, so 1 is out. Valid divisors: 2, 3 and 6, which is 3 numbers.
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. More than one number works: 2, 3 and 6.
- (b) Wrong. 2 counts only two of the three divisors.
- (c) Right. 2, 3 and 6 each leave remainder 1.
- (d) Wrong. 1 cannot be used, since a remainder must be less than the divisor, so there are only 3.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2024, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.