BTGmoderatorDC wrote:If each of the two digits X and Y is distinct, is the two digit integer XY prime?
(1) Each of the digits X and Y is the sum of 2 distinct single digit prime numbers.
(2) The sum of digits X and Y is 16.

Target question: Is the two-digit integer xy prime?

Given: Each of the two digits x and y is distinct

Statement 1: Each of the digits x and y is the sum of 2 distinct single digit prime numbers.
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 3 + 5 = 8 and y = 2 + 7 = 9. So, xy = 89. In this case, the answer to the target question is YES, xy IS prime
Case b: x = 2 + 7 = 9 and y = 3 + 5 = 8. So, xy = 98. In this case, the answer to the target question is NO, xy is NOT prime
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The sum of digits x and y is 16
Since x and y are DISTINCT DIGITS, there are only 2 possible ways to get a sum of 16. Let's examine each possible case:
Case a: x = 7 and y = 9. So, xy = 79. In this case, the answer to the target question is YES, xy IS prime
Case b: x = 9 and y = 7. So, xy = 97. In this case, the answer to the target question is YES, xy IS prime
Since each possible case yields the SAME answer to the target question, it MUST be the case that xy IS prime
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent

Hi All,

We're told that each of the two DIGITS X and Y is distinct. We're asked if the two-digit integer XY is PRIME. This is a YES/NO question and can be solved by TESTing VALUES.

1) Each of the digits X and Y is the sum of 2 distinct single digit prime numbers.

The single-digit prime numbers are 2, 3, 5 and 7. This means that X and Y could each be any of the following 4 numbers (keep in mind, they must be DISTINCT though - meaning different).
(2+3) = 5
(2+5) = 7
(2+7) = 9
(3+5) = 8

IF....
XY = 75 --> 75 is evenly divisible by 5, so it is NOT prime and the answer to the question is NO.
XY = 79 --> 79 IS prime (trying dividing by 2 through 9 and you'll see) and the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) The sum of digits X and Y is 16.

Since the sum of the digits is 16, the only possible combination of digits is 7 and 9 (remember, the digits have to be DISTINCT, so XY cannot be 88).
XY = 79 --> 79 IS prime (trying dividing by 2 through 9 and you'll see) and the answer to the question is YES.
XY = 97 --> 97 IS prime (trying dividing by 2 through 9 and you'll see) and the answer to the question is YES.
Fact 2 is SUFFICIENT

Final Answer: B

GMAT assassins aren't born, they're made,
Rich