BTGModeratorVI wrote: ↑Thu Jun 18, 2020 5:43 am
If x^2 - y^2 = 27, what is the value of (x + y)^2 ?
(1) y = 3
(2) x - y = 3
Answer:
B
Source: GMAT Hacks
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 = 36
So, EITHER x = 6 OR x = -6
Let's test each case:
Case a: x = 6 and y = 3. So, (x + y)² = (6 + 3)² = 9² = 81. So, in this case, the answer to the target question is
(x+y)² = 81
Case b: x = -6 and y = 3. So, (x + y)² = (-6 + 3)² = (-3)² = 9. So, in this case, the answer to the target question is
(x+y)² = 9
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
(x+y)² = 81
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: B
Cheers,
Brent
