Vincen wrote:If x are y are positive integers, what is the value of x+y?
(1) x and y are consecutive prime numbers
(2) x - y = 1
Target question: What is the value of x+y?
Given: x are y are positive integers
Statement 1: x and y are consecutive prime numbers
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 2 and y = 3 (two consecutive primes), in which case
x + y = 2 + 3 = 5
Case b: x = 19 and y = 23 (two consecutive primes), in which case
x + y = 19 + 23 = 42
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Aside: For more on this idea of testing values when a statement doesn't feel sufficient, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values
Statement 2: x - y = 1
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 3 and y = 2, in which case
x + y = 3 + 2 = 5
Case b: x = 5 and y = 4, in which case
x + y = 5 + 4 = 9
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
Statement 1 tells us that x and y are consecutive primes
Statement 2 tells us that x and y differ by 1
If x and y differ by 1, then one number is ODD and the other is EVEN
Since there is only one EVEN prime number (2), then it must be the case that y = 2 and x = 3, in which case
x + y = 3 + 2 = 5
Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer:
C
Cheers,
Brent
