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

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

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[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

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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.

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=>

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

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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

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scott@targettestprep.com



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$$\sqrt{x}+\sqrt{y}=7................eqn\ 1$$
$$\sqrt{x}-\sqrt{y}=7................eqn\ 2$$
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
$$\left(\sqrt{x}\right)^2=6^2$$
$$x=36$$
$$xy=36\cdot1$$

$$answer\ is\ Option\ C$$

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