Data Sufficiency

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

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

We need to determine the value of x + y.

Statement One Alone:

x and y are consecutive prime numbers.

Since x and y could be any two consecutive prime numbers, statement one alone is not sufficient to answer the question.

Statement Two Alone:

x - y = 1

This means x and y are two consecutive integers. However, since x and y could be any two consecutive integers, statement two alone is not sufficient to answer the question.

Statements One and Two Together:

Using both statements, we see that x and y are 1 apart and are consecutive prime numbers. The only consecutive prime numbers that are 1 apart are 2 and 3. Thus, x + y = 5.

Answer: C