If √x+√y=7 and √x-√y=5, what is the value of xy?

This topic has expert replies
User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

[GMAT math practice question]

If √x+√y=7 and √x-√y=5, what is the value of xy?

A. 16
B. 25
C. 36
D. 49
E. 64

User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Thu Mar 14, 2019 2:32 am
Max@Math Revolution wrote:[GMAT math practice question]

If √x+√y=7 and √x-√y=5, what is the value of xy?

A. 16
B. 25
C. 36
D. 49
E. 64
Adding the two equations, we get:
2√x = 12
√x = 6
x = 36

Substituting √x = 6 into √x+√y=7, we get:
6 + √y = 7
√y = 1
y = 1

Thus:
xy = 36*1 = 36

The correct answer is C.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3

User avatar
Elite Legendary Member
Posts: 3991
Joined: Fri Jul 24, 2015 2:28 am
Location: Las Vegas, USA
Thanked: 19 times
Followed by:37 members

by Max@Math Revolution » Sun Mar 17, 2019 5:00 pm
=>

Adding the two equations yields 2√x = 12, so x = 36.
Subtracting the two equations yields 2√y = 2, so y = 1.
Therefore, xy = 36.

Therefore, the answer is C.
Answer: C

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 7223
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Mon Mar 18, 2019 5:33 pm
Max@Math Revolution wrote:[GMAT math practice question]

If √x+√y=7 and √x-√y=5, what is the value of xy?

A. 16
B. 25
C. 36
D. 49
E. 64
If we add the two equations, we have 2√x = 12, so √x = 6 and hence x = 36. Similarly, if we subtract the two equations, we have 2√y = 2, so √y = 1 and hence y = 1. Therefore, xy = (36)(1) = 36.

Answer: C

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage

Legendary Member
Posts: 2214
Joined: Fri Mar 02, 2018 2:22 pm
Followed by:5 members

by deloitte247 » Tue Mar 19, 2019 2:51 am
$$\sqrt{x}+\sqrt{y}=7................eqn\ 1$$
$$\sqrt{x}-\sqrt{y}=7................eqn\ 2$$
subtracting eqn 2 from eqn 1
$$2\sqrt{y}=2$$
$$\sqrt{y}=1$$
$$y=1$$
from eqn 1
$$\sqrt{x}+\sqrt{y}=7$$
$$\sqrt{x}+\sqrt{y}=7$$
$$\sqrt{x}+\sqrt{1}=7$$
$$\sqrt{x}=7-1$$
$$\sqrt{x}=6$$
take the square of both sides
$$\left(\sqrt{x}\right)^2=6^2$$
$$x=36$$
$$xy=36\cdot1$$

$$answer\ is\ Option\ C$$