DS Question - need help

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DS Question - need help

by devgmat » Wed Jan 18, 2012 12:12 pm
Q. If a is a positive integer and 81 is divided by a results in a remainer of 1, what is the value of a?

1)The remainder when a is divided by 40 is 0.
2)The remainder when 40 is divided by a is 40.

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Dev

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by Ian Stewart » Wed Jan 18, 2012 3:30 pm
devgmat wrote:Q. If a is a positive integer and 81 is divided by a results in a remainer of 1, what is the value of a?

1)The remainder when a is divided by 40 is 0.
2)The remainder when 40 is divided by a is 40.

Thanks
Dev
If you know that, say, the remainder is 3 when x is divided by 10, that means that x is 3 more than some multiple of 10. In other words, x - 3 must be divisible by 10. So if the remainder is 1 when 81 is divided by a, that means that 81 is 1 more than some multiple of a, or in other words, 80 is divisible by a. So from the stem, we learn that a is a divisor of 80.

Statement 1 tells us that a is divisible by 40. Since a is a divisor of 80, a can only be equal to 40 or 80. Since we have two possible values for a, the Statement is not sufficient.

From Statement 2, we know that when we divide 40 by a, the remainder is 40. This will happen only when a is greater than 40. For example, if you divide 40 by 53, the quotient is 0, and the remainder is 40. So Statement 2 is just an abstract way of saying a > 40. Since we know from the stem that a is a divisor of 80, the only possible value of a is 80 itself (since 80 has no other divisors greater than 40). So Statement 2 is sufficient and the answer is B.
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by devgmat » Thu Jan 19, 2012 8:12 am
Thanks Ian.

I was not able to interpret statement 2 correctly. I understand it now :-)

80 is divisible by 'a' --> a is divisor of 80. 'a' could be 2,5,8,10,16,20,40,80.

From statement 1 we can say that 'a' can be 40,80,120....

combining Question and statement 1, 'a' can be 40 & 80. -> not sufficient.

from statement 2 we can say that for remainder to be 40 when 40 divided by 'a', it has to be greater than 40.

combining Question and statement 2, 'a' can be only 80.

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by ArunangsuSahu » Thu Jan 19, 2012 8:38 am
81-1=80 has 1,2,4,5,10,16,20,40,80 as factors

Statement 1:
a=40,80 satisfies..SO INSUFFICIENT..Two answers

Statement 2:
Only 40 divided by 80 gives a remainder of 40 in the above case included.. SUFFICIENT

(B)