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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: 42249

Kudos [?]: 132595 [0], given: 12326

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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13% (00:51) correct 87% (01:04) wrong based on 14 sessions

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

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

_________________

Kudos [?]: 132595 [0], given: 12326

Intern
Joined: 29 Aug 2017
Posts: 35

Kudos [?]: 2 [0], given: 48

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.

Kudos [?]: 2 [0], given: 48

Re: If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?   [#permalink] 02 Oct 2017, 22:13
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