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27 Oct 2021, 15:14
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B
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Question Stats:
49% (02:02) correct
51%
(02:12)
wrong
based on 87
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If \(a\) is a positive integer, \(r\) is the remainder when \(a\) is divided by 7, and \(s\) is the remainder when \(a\) is divided by 5, is \(rs\) equal to zero?
(1) The least common multiple of \(a\) and 35 is greater than 35.
(2) The greatest common divisor of \(a\) and 35 is greater than 1.
(1) The least common multiple of \(a\) and 35 is greater than 35.
(2) The greatest common divisor of \(a\) and 35 is greater than 1.
27 Oct 2021, 23:57
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IMO B.
We need to find is the remainder = 0. Here we can say it has three scenarios:-
1. r = 0 OR s = 0 OR both R and S = 0. In other words we can say - if a is a multiple of 5 or 7 and certainly 35.
S1 - LCM (a,35) > 35. A > 35. Can be a multiple of 35(70, 105..) and not (36,50..)
S2-
GCD of (a,35)
a = 1, ... , a
35 = 1,5,7,35
But S2 tells us GCD is greater than 1..then it must be true that 'a' is a multiple of (5,7,35) that is it can be either multiple of 5 OR 7 which satisfies the condition
Please feel free to correct me if I am wrong.
Thanks.
sjuniv32
We need to find is the remainder = 0. Here we can say it has three scenarios:-
1. r = 0 OR s = 0 OR both R and S = 0. In other words we can say - if a is a multiple of 5 or 7 and certainly 35.
S1 - LCM (a,35) > 35. A > 35. Can be a multiple of 35(70, 105..) and not (36,50..)
S2-
GCD of (a,35)
a = 1, ... , a
35 = 1,5,7,35
But S2 tells us GCD is greater than 1..then it must be true that 'a' is a multiple of (5,7,35) that is it can be either multiple of 5 OR 7 which satisfies the condition
Please feel free to correct me if I am wrong.
Thanks.
