M7MBA wrote:If x² - y² = 27 what is the value of (x+y)²?

(1) y = 3

(2) x - y = 3

Target question: What is the value of (x+y)²?

Given: x² - y² = 27

Statement 1: y = 3
Take x² - y² = 27 and replace y with 3 to get: x² - (3)² = 27
Evaluate: x² - 9 = 27
Simplify: x² = 18
So, EITHER x = √18 OR x = -√18
Let's test each case:
Case a: x = √18 and y = 3. So, (x + y)² = (√18 + 3)². So, in this case, the answer to the target question is (√18 + 3)²
Case b: x = -√18 and y = 3. So, (x + y)² = (-√18 + 3)². So, in this case, the answer to the target question is (-√18 + 3)²
NOTE: We need not actually calculate the values of (√18 + 3)² and (-√18 + 3)². We need only see that the two values are DIFFERENT
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x - y = 3
Take x² - y² = 27 and FACTOR the left side to get: (x + y)(x - y) = 27
Replace (x-y) with 3 to get: (x + y)(3) = 27
So, it must be the case that (x+y) = 9
If (x+y) = 9, then (x+y)² = 81
So, the answer to the target question is 81
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent