Baten80 wrote:

If x and y are positive integers, what is the value of (x+y)²

(1) x = y - 3

(2) x and y are prime numbers.

Target question: What is the value of (x+y)²? Given: x and y are positive integers Statement 1: x = y - 3 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 = 1 and y = 4, in which case

(x+y)² = (1+4)² = 5² = 25Case b: x = 2 and y = 5, in which case

(x+y)² = (2+5)² = 7² = 49Since we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: http://www.gmatprepnow.com/articles/dat ... lug-values Statement 2: x and y are prime numbers This statement doesn't FEEL sufficient either, so I'll TEST some values.

There are several values of x and y that satisfy statement 2. Here are two:

Case a: x = 2 and y = 2, in which case

(x+y)² = (2+2)² = 4² = 16Case b: x = 2 and y = 3, in which case

(x+y)² = (2+3)² = 5² = 25Since we cannot answer the

target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined Statement 1 tells us that x = y - 3

In other words, x + 3 = y

Or we can say that x + ODD = y

This means that one of the two values (x or y) is EVEN and one is ODD

Statement 2 tells us that x and y are prime numbers

If one of the values is EVEN and also PRIME, then one value must equal 2.

Since x is smaller than y, we can conclude that x = 2, which means y = 5

Now that we know the values of x and y, we can see that

(x+y)² = (2+5)² = 7² = 49Since we can answer the

target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,

Brent

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