Bunuel wrote:
If x and y are positive integers, what is the value of \(\sqrt{x} + \sqrt{y}\)?
(1) x + y = 15
(2) \(\sqrt{xy}= 6\)
Kudos for a correct solution.
Target question: What is the value of √x + √y? Statement 1: x + y = 15 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 = 14 and y = 1, in which case
√x + √y = √14 + √1 = √14 + 1Case b: x = 9 and y = 6, in which case
√x + √y = √9 + √6 = 3 + √6Since 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, read my article: https://www.gmatprepnow.com/articles/dat ... lug-values Statement 2: √(xy) = 6 In other words xy = 36
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 = 1 and y = 36, in which case
√x + √y = √1 + √36 = 1 + 6 = 7Case b: x = 4 and y = 9, in which case
√x + √y = √4 + √9 = 2 + 3 = 5Since 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 = 15Statement 2 tells us that
√(xy) = 6Recognize that (√x + √y)² = x + 2√(xy) + y
Rearrange to get: (√x + √y)² =
x + y + 2
√(xy)We get: (√x + √y)² =
15 + 2(
6)
Evaluate: (√x + √y)² = 27
So,
√x + √y = √27 Since we can answer the
target question with certainty, the combined statements are SUFFICIENT
Answer: C
_________________
Brent Hanneson – Creator of gmatprepnow.com
I’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is…
Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing -
Learn more