UPSC Prelims 2019 · CSAT
Question 15: Basic Numeracy
In a school every student is assigned a unique identification number. A student is a football player if and only if the identification number is divisible by 4, whereas a student is a cricketer if and only if the identification number is divisible by 6. If every number from 1 to 100 is assigned to a student, then how many of them play cricket as well as football ?
AnswerUPSC’s answer is (b).
A number that is both a football player's and a cricketer's must be divisible by 4 and by 6, that is by their LCM, 12. The multiples of 12 up to 100 are 12, 24, 36, 48, 60, 72, 84 and 96, so there are 8 such numbers (100 / 12 is 8.33, take the whole part). Do not use 4 × 6 = 24 as the common multiple; 24 is not the smallest one.
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: 4 is the count of multiples of 24, the wrong common multiple.
- (b) Right: multiples of 12 up to 100 number 8.
- (c) Wrong: 10 matches no count of multiples of 12.
- (d) Wrong: 12 is the LCM itself, not the count.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2019, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.