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

akshata19This 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

insufficientStatement 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

InsufficientCombining 1 & 2 we get \(x=2\), so \(y=0\). Hence \(x\) is not equal to \(-y\).

SufficientOption

Cprima-facie also if you look at the question stem, then \(3x-y=2x-2y\) only if \(x=-y\)