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# If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?

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Math Expert
Joined: 02 Sep 2009
Posts: 58320
If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?  [#permalink]

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02 Oct 2017, 04:43
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Difficulty:

85% (hard)

Question Stats:

32% (01:36) correct 68% (01:56) wrong based on 85 sessions

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If x is an integer, is $$\sqrt{3x - y} = \sqrt{2x - 2y}$$ ?

(1) x^2 = y
(2) x = y

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Joined: 29 Aug 2017
Posts: 35
Re: If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?  [#permalink]

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02 Oct 2017, 22:13
Bunuel wrote:
If x is an integer, is $$\sqrt{3x - y} = \sqrt{2x - 2y}$$ ?

(1) x^2 = y
(2) x = y

Question: Is $$(3x - y)^2 = (2x - 2y)^2$$
Is $$9x^2 -6xy+ y^2 = 4x^2 -8xy + 4y^2$$
Is $$5x^2 + 2xy -3y^2 = 0$$
Is $$5x^2 + 5xy -3xy - 3y^2 = 0$$
Is $$5x(x+y) -3y(x+y) = 0$$
Is $$(5x - 3y)(x + y) = 0$$
Is 5x= 3y or x = -y
Is x/y = 3/5 or -1

Statement 1: x^2 = y
x/y = 1/x
This is not sufficient to know whether x/y = 5/3 or -1 since 1/x could be anything

Statement 2: x = y
x/y = 1
This statement is sufficient because it proves that x/y is not equal to 5/3 or -1.

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Re: If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?  [#permalink]

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17 Jan 2018, 14:57
1
1
Hi, Bunuel,

How come answer will be D?

From both the statements,

if x = 1, y = 1, answer to $$\sqrt{3x-y}$$ = $$\sqrt{2x-2y}$$ ? is No
if x = 0, y = 0, answer to $$\sqrt{3x-y}$$ = $$\sqrt{2x-2y}$$ ? is Yes

am i missing anything?

Math Expert
Joined: 02 Sep 2009
Posts: 58320
Re: If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?  [#permalink]

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17 Jan 2018, 21:03
hellosanthosh2k2 wrote:
Hi, Bunuel,

How come answer will be D?

From both the statements,

if x = 1, y = 1, answer to $$\sqrt{3x-y}$$ = $$\sqrt{2x-2y}$$ ? is No
if x = 0, y = 0, answer to $$\sqrt{3x-y}$$ = $$\sqrt{2x-2y}$$ ? is Yes

am i missing anything?

Yes, the answer is E, not D. Edited. Thank you.
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Re: If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?   [#permalink] 17 Jan 2018, 21:03
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