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.