BTGModeratorVI wrote: ↑

Mon Apr 13, 2020 3:48 pm

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.

Answer: C
Source: GMAT paper tests

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 = 25
Case b: x = 2 and y = 5, in which case (x+y)² = (2+5)² = 7² = 49
Since 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: https://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 = 16
Case b: x = 2 and y = 3, in which case (x+y)² = (2+3)² = 5² = 25
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 = 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 = 49

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent