mgm wrote:What is the value of the two-digit positive integer n?
(1) When n is divided by 5, the remainder is equal to the tens digit of n.
(2) When n is divided by 9, the remainder is equal to the tens digit of n.
OA C
I guess this can be solved by listing out possible values but is there a better approach ?
I don't believe there's an approach that doesn't involve listing. But, as Rich demonstrates, we can apply some logic.
Target question:
What is the value of the two-digit positive integer n?
Statement 1: When n is divided by 5, the remainder is equal to the tens digit of n
If the tens digit of n is 1, then n could be 11 or 15
If the tens digit of n is 2, then n could be 22 or 27
If the tens digit of n is 3, then n could be 33 or 38
Etc.
So,
n could equal 11, 16, 22, 27, 33, 38, 44, or 49
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: When n is divided by 9, the remainder is equal to the tens digit of n
If the tens digit of n is 1, then n could be 10 or 19
If the tens digit of n is 2, then n could be 20 or 29
If the tens digit of n is 3, then n could be 30 or 39
Etc.
So,
n could equal 10, 19, 20, 29, 30, 39, 40, 49, 50, 59 . . . 90 or 99
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined:
There's only one value of n that both lists have in common.
So
n must = 49
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer =
C
Cheers,
Brent
