If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy 0

Question

If xy ≠ 0, is x = y?

(1) |x| = |y|
(2) xy > 0

GMATinsight · Answer

Question : is x = y?

Statement 1 : |x| = |y|

@y=2, x may be 2 or -2 hence
NOT SUFFICIENT

Statement 2 : xy > 0

i.e. signs of both x and y are same because their product is positive but their absolute values may be same or different hence
NOT SUFFICIENT

Combining the two statements

Statement 1 states that absolute values of x and y are same
Statement 2 says that signs of x and y are same
i.e. x = y
SUFFICIENT

Answer: Option C

Chethan92 · Answer

From statement 1:

|x| = |y|.
Squaring on both sides,
x^2 = y^2
x^2-y^2 = 0
(x+y)(x-y) = 0
x = y or x = -y.
 Insufficient .

From statement 2:

xy>0
Either x and y both are positive or both negative.
No extra info.
 Insufficient .

Combining both:

x and y are both positive.
hence x = y.

C is the answer.

Archit3110 · Answer

If xy ≠ 0, is x = y?

(1) |x| = |y|
(2) xy > 0

Stmnt 1= both x & y can be + or - hence not sufficient
stmnt 2= again x& y can be of same sign so not suffcient

combining 1 & 2 suffices the given relation hence C is correct

blanchif · Answer

Hi Guys,

When we speak about x = y do we mean what is inside the bar like |x| and |y| or the outcome of those 2 absolute values ? I can't make the difference of do we need to find |x| and |y| or x and y, which come always +/ve ...

Someone can help please,it is important to understand this basic

Thank you for the help

QuantMadeEasy · Answer

(1) |x| = |y| 
Lets take values to understand
When x = 1, y =1; |x| = |y| and x=y
When x=-1, y=1; |x| = |y| and x≠y
Insufficient

(2) xy > 0 
When product is positive sign of both x and y are same (both either positive or both negative)
when x=1, y =1, xy>0, x=y
when x=1, y =2, xy>0, x≠y
Insufficient

(1)+(2) , Absolute value of x and y are equal and their signs are same (both either positive or both negative)
when x=1, y =1, |x| = |y|, xy>0, x=y
when x=-1, y =-1, |x| = |y|, xy>0, x=y

C is correct

blanchif · Answer

Thank you for your accuracy and detailed answer. However, I might misunderstood something.

In absolute values, the outcome of |X|, wich is x, comes always +/tive. this is why i don't understand why you picked up x=-1 as we know that |X|= x (always positive value) or |-X| = x.
Because if i have x=-1 it can't be |-1| = -1 ? if we have |1| or |-1|, both of them should lead to 1 ...

QuantMadeEasy · Answer

Yes you are correct that there is modulus there are generally two possible values of x When x = 1; |1| = 1 and When x = -1; |-1| = 1 Therefore there are two possible values of x ie 1 and -1, but only one value of |x| ie 1 The question is asking value of x, hence it can be 1 or -1. hope this is clear.

If xy ≠ 0, is x = y? (1) |x| = |y| (2) xy > 0

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