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

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

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02 Oct 2017, 00:01
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Difficulty:

55% (hard)

Question Stats:

51% (01:06) correct 49% (01:06) wrong based on 58 sessions

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

(1) x = 2
(2) x – 2 = y

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

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02 Oct 2017, 10:26
(1) x = 2
√6-y = √4-2y)
insufficient , y is unknown

(2) x – 2 = y

i.e x-y =2

√3x-y = √2(x-y)
√3x-y = √2*2
√3x-y = √4
squaring both sides
3x-y =4
split 3x
2x+x-y=4
2x+2=4
x=1

using x-2=y -> y =-1

we have both x and y , can substitute and check , solving this step is not required but we get it to be equal
B is sufficient
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If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?  [#permalink]

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02 Oct 2017, 10:45
akshata19 wrote:
(1) x = 2
√6-y = √4-2y)
insufficient , y is unknown

(2) x – 2 = y

i.e x-y =2

√3x-y = √2(x-y)
√3x-y = √2*2
√3x-y = √4
squaring both sides
3x-y =4
split 3x
2x+x-y=4
2x+2=4
x=1

using x-2=y -> y =-1

we have both x and y , can substitute and check , solving this step is not required but we get it to be equal
B is sufficient

Hi akshata19

This is a "Yes/No" question type where we need to use the statements to prove the question stem is valid or not. However you have used the question stem to find the value of $$x$$ & $$y$$

IMO

Is $$\sqrt{(3x - y)} = \sqrt{(2x - 2y)}$$, square both sides to get
$$3x-y=2x-2y$$, hence the question becomes Is $$x=-y$$?

Statement 1: value of $$x$$ is given but nothing about $$y$$, Hence insufficient

Statement 2: implies $$x=y+2$$, now if $$y=-1$$, then $$x=1$$ and the relation $$x=-y$$ holds true but if $$y=1$$, then $$x=3$$ and the relation $$x=-y$$ is not true. Hence Insufficient

Combining 1 & 2 we get $$x=2$$, so $$y=0$$. Hence $$x$$ is not equal to $$-y$$. Sufficient

Option C

prima-facie also if you look at the question stem, then $$3x-y=2x-2y$$ only if $$x=-y$$
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Re: If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?  [#permalink]

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03 Oct 2017, 10:30
Bunuel wrote:
If x is an integer, is $$\sqrt{3x - y} = \sqrt{2x - 2y}$$ ?

(1) x = 2
(2) x – 2 = y

I think only case is possible when x=-y or y=-x;

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

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03 Oct 2017, 10:42
PK32 wrote:
Bunuel wrote:
If x is an integer, is $$\sqrt{3x - y} = \sqrt{2x - 2y}$$ ?

(1) x = 2
(2) x – 2 = y

I think only case is possible when x=-y or y=-x;

so answer should be E

Hi PK32

Can you explain what is the reason for eliminating option C?
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If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?  [#permalink]

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07 Oct 2017, 10:25
Squaring both LHS and RHS the question becomes is X=(-Y)
From statement 1
X = 2
We don't know the value of Y so this option is not sufficient
From statement 2
X-2 = Y
If x is 1 Then Y is -1 {satisfies the condition X=(-Y)}
But for other values of X it does not satisfy.(for example put X = 0,2,3....)
Hence statement 2 is not sufficient

Combining both statement we have X = 2 And thus Y = 0 (because X-2 = Y)
Sufficient

Hence C

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If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ? &nbs [#permalink] 07 Oct 2017, 10:25
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# If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ?

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