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11 Jul 2024, 07:06
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Difficulty:
75%
(hard)
Question Stats:
56% (02:01) correct
44%
(02:04)
wrong
based on 163
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H distributed a and b candy to M and Q, respectively. Both a and b can be expressed as a product of two distinct prime numbers. If a and b do not have any common factors, and their values are smaller than 100, what is the maximum difference in the number of candy distributed to both of them?
A. 85
B. 80
C. 93
D. 89
E. 95
A. 85
B. 80
C. 93
D. 89
E. 95
Updated on: 20 Jul 2025, 22:14
Originally posted by HarshavardhanR on 11 Jul 2024, 07:45.
Last edited by HarshavardhanR on 20 Jul 2025, 22:14, edited 1 time in total.
Last edited by HarshavardhanR on 20 Jul 2025, 22:14, edited 1 time in total.
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- To maximize the difference/gap between a and b, we need to pick these numbers as far apart as possible. This would happen if we pick a and b such that one is the largest possible number given the constraints and the other is the smallest possible number given the constraints.
- Largest number less than 100 which is a product of 2 distinct prime numbers = 95 i.e., (5 x 19).
- Smallest number less than 100 which is a product of 2 distinct prime numbers = 6 i.e., (2 x 3).
Required Answer: 95 - 6 = 89.
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Harsha
- Largest number less than 100 which is a product of 2 distinct prime numbers = 95 i.e., (5 x 19).
- Smallest number less than 100 which is a product of 2 distinct prime numbers = 6 i.e., (2 x 3).
Required Answer: 95 - 6 = 89.
___
Harsha
12 Jul 2024, 10:52
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sahilsah456
I think the question needs an edit -
If a and b do not have any common factors other than 1.
Cheers!
