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02 Oct 2017, 00:01
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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
(1) x = 2
(2) x – 2 = y
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
√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
02 Oct 2017, 10:45
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akshata19
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 \(x=-y\)
