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If r and s are positive integers, when r+s is divided by 3, what is th

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If r and s are positive integers, when r+s is divided by 3, what is th  [#permalink]

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New post 16 Feb 2016, 01:58
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A
B
C
D
E

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Question Stats:

68% (01:34) correct 32% (01:19) wrong based on 135 sessions

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If r and s are positive integers, when r+s is divided by 3, what is the remainder?

1) rs is divisible by 9
2) s is divisible by 3


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Re: If r and s are positive integers, when r+s is divided by 3, what is th  [#permalink]

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New post 16 Feb 2016, 05:26
r and s are positive integers
from statement 1 rs divisible by 9
r = 9 or s = 9
or r equals 9 s equals 1
or r =3, s=3.

so many possiblities. we can't find value of r and s.

from statement 2

s is divisible by 3. and s is positive integers.

s equals to multiples of 3
s=3,6,9. we don't value of r.

from statment 1 and 2 so many values for s and r . we can't find unique solution.
so option E is correct
E
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Re: If r and s are positive integers, when r+s is divided by 3, what is th  [#permalink]

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New post 17 Feb 2016, 22:59
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

If r and s are positive integers, when r+s is divided by 3, what is the remainder?
1) rs is divisible by 9
2) s is divisible by 3


In the original condition, there are 2 variables(r,s), which should match with the number of equations. So you need 2 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make C the answer.
When 1) & 2), r=s=3 -> yes, r=1, s=9 -> no, which is not sufficient.
Therefore, the answer is E.
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Re: If r and s are positive integers, when r+s is divided by 3, what is th  [#permalink]

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New post 22 Mar 2016, 08:15
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Re: If r and s are positive integers, when r+s is divided by 3, what is th  [#permalink]

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New post 30 Nov 2017, 23:35
(1) rs is divisible by 9, or by 3^2. This means that when we mutliply r and s, we get at least two 3's in the prime factorisation of the product.
Now its possible that both r and s have at least one 3 each in its prime factorisation, in which case each of them will be a multiple of 3, thus their sum will also be a multiple of 3. In that case, the remainder will be 0.
But its also possible that only r has two 3's in its prime factorisation, while s does not have any 3 in its prime factorisation, in which case one of them is a multiple of 9, but other one is not a multiple of 3. In this case their sum will NOT be a multiple of 3, and remainder will NOT be 0 (but either 1 or 2).
So Insufficient.

(2) s is divisible by 3, but we dont know whether r is divisible by 3 or not. Thus we cant say whether their sum will be divisible by 3 or not. So Insufficient.

Combining the two statements, we know s is divisible by 3 (so it has at least one 3 in its prime factorisation) and the product of r and s is divisible by 9 (so at least two 3's in the prime factorisation of product). Here again its possible that both r and s are divisible by 3 (so product divisible by 9) and thus their sum will also be divisible by 3. BUT its also possible that s is divisible by 9 also (any number divisible by 9 is also divisible by 3) while r is not divisible by 3.. in this case product will be divisible by 9 but sum will not be divisible by 3.
Insufficient.

Hence E answer
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Re: If r and s are positive integers, when r+s is divided by 3, what is th &nbs [#permalink] 30 Nov 2017, 23:35
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