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655-705 (Hard)|   Algebra|      
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Bunuel
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If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ? 02 Oct 2017, 00:01
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C
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Difficulty:

65% (hard)

Question Stats:

44% (01:48) correct 56% (02:00) wrong based on 83 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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C
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akshata19
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If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ? 02 Oct 2017, 10:26
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(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) ? 02 Oct 2017, 10:45
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akshata19
(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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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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If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ? 03 Oct 2017, 10:30
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Bunuel
If x is an integer, is \(\sqrt{3x - y} = \sqrt{2x - 2y}\) ?

(1) x = 2
(2) x – 2 = y
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I think only case is possible when x=-y or y=-x;

so answer should be E
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If x is an integer, is (3x - y)^(1/2) = (2x - 2y)^(1/2) ? 03 Oct 2017, 10:42
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PK32
Bunuel
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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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) ? 07 Oct 2017, 10:25
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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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