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# If (xy)^(1/2) = 3, what is the value of x ?

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Math Expert
Joined: 02 Sep 2009
Posts: 43373
If (xy)^(1/2) = 3, what is the value of x ? [#permalink]

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17 Sep 2017, 02:04
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Difficulty:

45% (medium)

Question Stats:

55% (00:42) correct 45% (00:29) wrong based on 76 sessions

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If $$\sqrt{xy} = 3$$, what is the value of x ?

(1) x = y
(2) y = 3
[Reveal] Spoiler: OA

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Intern
Joined: 26 Jul 2017
Posts: 18
Location: India
Re: If (xy)^(1/2) = 3, what is the value of x ? [#permalink]

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17 Sep 2017, 02:11
Bunuel wrote:
If $$\sqrt{xy} = 3$$, what is the value of x ?

(1) x = y
(2) y = 3

1. x = y gives us \sqrt{x^2} = 3 -----> |x| = 3 ----------> x = +3 or -3. Hence insufficient.

2. y =3 gives us \sqrt{x3} = 3 ---- on squaring both sides we get 3x = 9 --------> hence x=3. Sufficient

Intern
Joined: 25 Apr 2017
Posts: 15
Re: If (xy)^(1/2) = 3, what is the value of x ? [#permalink]

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17 Sep 2017, 02:20
I think the answer is B

1, X=Y-> /x/=3 -> x = 3 or x = -3 -> insufficient
2, y = 3 -> 3x = 9 -> x=3 -> sufficient
Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 233
Re: If (xy)^(1/2) = 3, what is the value of x ? [#permalink]

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24 Sep 2017, 02:45
Bunuel wrote:
If $$\sqrt{xy} = 3$$, what is the value of x ?

(1) x = y
(2) y = 3

hi

√xy = 3
So
| xy | = 9

statement 1 says x = y
x can be -3 or 3
so, -3 = -3 or 3 = 3, not sufficient

statement 2 says
y = 3

| 3x | = 9

x = 3
or

x = -3

not sufficient ...

statement 1 and 2 taken together:

x = 3, sufficient

C

Manager
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Joined: 24 Mar 2015
Posts: 233
Re: If (xy)^(1/2) = 3, what is the value of x ? [#permalink]

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25 Sep 2017, 01:06
Bunuel wrote:
If $$\sqrt{xy} = 3$$, what is the value of x ?

(1) x = y
(2) y = 3

hi Bunuel

looking forward to your solution to the question

thanks
Math Expert
Joined: 02 Sep 2009
Posts: 43373
Re: If (xy)^(1/2) = 3, what is the value of x ? [#permalink]

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25 Sep 2017, 02:00
gmatcracker2017 wrote:
Bunuel wrote:
If $$\sqrt{xy} = 3$$, what is the value of x ?

(1) x = y
(2) y = 3

hi Bunuel

looking forward to your solution to the question

thanks

If $$\sqrt{xy} = 3$$, what is the value of x ?

(1) x = y:

$$\sqrt{x^2} = 3$$;

Square: $$x^2 = 9$$;

x = 3 or x = -3. Not sufficient.

(2) y = 3:

$$\sqrt{3x} = 3$$;

Square: $$3x = 9$$;

x = 3. Sufficient.

P.S. Note that x = -3 is not a valid solution for (2) because in this case $$\sqrt{xy} = \sqrt{-9}$$, which is undefined and not equal to 3 as given in the stem.
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Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 233
Re: If (xy)^(1/2) = 3, what is the value of x ? [#permalink]

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25 Sep 2017, 03:09
Bunuel wrote:
gmatcracker2017 wrote:
Bunuel wrote:
If $$\sqrt{xy} = 3$$, what is the value of x ?

(1) x = y
(2) y = 3

hi Bunuel

looking forward to your solution to the question

thanks

If $$\sqrt{xy} = 3$$, what is the value of x ?

(1) x = y:

$$\sqrt{x^2} = 3$$;

Square: $$x^2 = 9$$;

x = 3 or x = -3. Not sufficient.

(2) y = 3:

$$\sqrt{3x} = 3$$;

Square: $$3x = 9$$;

x = 3. Sufficient.

P.S. Note that x = -3 is not a valid solution for (2) because in this case $$\sqrt{xy} = \sqrt{-9}$$, which is undefined and not equal to 3 as given in the stem.

thanks man
we cannot take square roots over negative numbers
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Joined: 22 Nov 2016
Posts: 251
Location: United States
GPA: 3.4
Re: If (xy)^(1/2) = 3, what is the value of x ? [#permalink]

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26 Sep 2017, 15:48
Can we square the question stem to get xy = 9 and then proceed?
_________________

Kudosity killed the cat but your kudos can save it.

Math Expert
Joined: 02 Sep 2009
Posts: 43373
Re: If (xy)^(1/2) = 3, what is the value of x ? [#permalink]

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26 Sep 2017, 20:11
sasyaharry wrote:
Can we square the question stem to get xy = 9 and then proceed?

__________________
Yes, we can do this.
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Re: If (xy)^(1/2) = 3, what is the value of x ?   [#permalink] 26 Sep 2017, 20:11
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