Problem Solving

BTGModeratorVI wrote: ↑

Thu Jul 23, 2020 6:34 am

If xy = 7 and x – y = 7, then x² + y² =

(A) 35
(B) 42
(C) 49
(D) 56
(E) 63

Answer: E
Source: GMAT Prep Now

We know that (x – y)^2 = x ^2 + y^2 – 2xy

Thus, 7^2 = (x ^2 + y^2) – 2*7

=> x ^2 + y^2 = 63

Correct answer: [spoiler][/spoiler]

Hope this helps!

-Jay
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BTGModeratorVI wrote: ↑

Thu Jul 23, 2020 6:34 am

If xy = 7 and x – y = 7, then x² + y² =

(A) 35
(B) 42
(C) 49
(D) 56
(E) 63

Answer: E
Source: GMAT Prep Now

The important thing to recognize here is that if we square (x - y), we get a x² term and a y² term. We also get an extra xy term, but that's okay, because we're given some information about the product xy.

So, take: x – y = 7 and...
Square both sides: (x - y)² = 7²
Expand: x² - 2xy + y² = 49
Since we're told xy = 7, we'll replace xy with 7 to get: x² - 2(7) + y² = 49
Simplify: x² - 14 + y² = 49
Add 14 to both sides: x² + y² = 63

Answer: E