UPSC Prelims 2024 · CSAT
Question 19: Basic Numeracy
A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of litres is an integer. How many different bottle sizes are possible?
AnswerUPSC’s answer is (b).
Whole bottles for both cans mean the bottle size divides both 399 and 532, so it is a common factor. 532 − 399 = 133 and 399 = 3 × 133, so the HCF is 133 = 7 × 19. Its factors are 1, 7, 19 and 133, so four bottle sizes are possible. Remember: sizes that fit both cans exactly are the factors of the HCF.
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. Three counts too few; the HCF 133 has four factors.
- (b) Right. The factors of 133 are 1, 7, 19 and 133.
- (c) Wrong. 133 = 7 × 19 has only 4 factors, not 5.
- (d) Wrong. 6 factors would need an HCF of the form p²q; 133 is not.
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.