Data Sufficiency

theachiever wrote:What is the value of the two-digit number XY, where X represents the tens digit and Y represents the units digit?

(1) The product of the digits is 12.

(2) The sum of the digits is 8.


I felt it should have been C but OA is E

Target question: What is the value of the 2-digit number?

Statement 1: The product of the digits is 12
There are several pairs of digits that meet this condition. Here are two:
Case a: X=2 and Y=6 in which case the 2-digit number is 26
Case b: X=6 and Y=2 in which case the 2-digit number is 62
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The sum of the digits is 8.
There are several pairs of digits that meet this condition. Here are two:
Case a: X=2 and Y=6 in which case the 2-digit number is 26
Case b: X=6 and Y=2 in which case the 2-digit number is 62
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
There are still two pairs of digits that meet this condition. They are
Case a: X=2 and Y=6 in which case the 2-digit number is 26
Case b: X=6 and Y=2 in which case the 2-digit number is 62
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

I thought I should mention that a lot of students will get to the point where they have 2 equations (xy=12 and x+y=8) and assume that, since we have 2 equations with 2 variables the combined statements must be sufficient.

This is a common myth, which is covered in our free video titled "Common GMAT Data Sufficiency Myths - Part II" at https://www.gmatprepnow.com/module/gmat- ... cy?id=1107

Cheers,
Brent