If √x+√y=7 and √x-√y=5, what is the value of xy? : Problem Solving (PS)

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

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Math Revolution GMAT Instructor

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

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14 Mar 2019, 01:56

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Question Stats:

82% (01:20) correct

18% (02:28) wrong

based on 33 sessions

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[GMAT math practice question]

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

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

Spoiler: OA

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Re: If √x+√y=7 and √x-√y=5, what is the value of xy? [#permalink]

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14 Mar 2019, 02:20

It's given the system of two linear equations:

$\sqrt{x} + \sqrt{y} = 7$

$\sqrt{x} - \sqrt{y} = 5$

Subtraction method gives: $2\sqrt{y} = 2$

Hence, $y = 1$

Substitute the variable into one of the two linear equations to state the value of $x$.

If we take the first one, $\sqrt{x} + 1 = 7$

$x = 36$

As a result, $xy = 36$

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Re: If √x+√y=7 and √x-√y=5, what is the value of xy? [#permalink]

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14 Mar 2019, 02:22

√x+√y=7...i) and √x-√y=5...ii)

Adding i) & ii), we get

2√x=12
=> √x = 6
=> x = 36

Substituting the value in i) we get,

√y = 1
=> y = 1

So xy = 36

Option C) is the answer

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Re: If √x+√y=7 and √x-√y=5, what is the value of xy? [#permalink]

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14 Mar 2019, 02:57

MathRevolution wrote:

[GMAT math practice question]

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

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

Given,

$√x+√y=7$

$√x-√y=5$

...........................................Adding both equation .
2√x = 12

√x = 6

Substitute the value of √x into equation 1.

6 + √y = 7

√y = 1

Now are looking for the value of xy.

√x√y = 6*1

$\sqrt{xy}$ = 6

xy = 36.

C is the correct answer.

Math Revolution GMAT Instructor

Joined: 16 Aug 2015

Posts: 7230

GMAT 1: 760 Q51 V42

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Re: If √x+√y=7 and √x-√y=5, what is the value of xy? [#permalink]

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17 Mar 2019, 18:18

=>

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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