If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x

Question

If x·y≠0, what is the value of x/y?

(1) −|x|=y

(2) −|y|=x

chetan2u · Answer

If x·y≠0, what is the value of x/y?

(1) −|x|=y
We can say that the numerical values without sign of x and y are same, so x/y will be 1 or -1 depending on signs of x and y. 
-|x|=y......|x|=-y
So y<0
Nothing about x
Insufficient

(2) −|y|=x
-|y|=x......|y|=-x
So x<0
Nothing about y
Insufficient

Combined 
Both x an y are negative, so x/y=1
Sufficient

C

sumitkrocks · Answer

If x·y≠0, what is the value of x/y?

Statement:1 −|x|=y
 y is negative
No info about x 
Not sufficient

Statement:2 −|y|=x
x is negative 
No info about y 
Not sufficient

Combined x and y are negative

Hence, Sufficient 
C is the answer

Bunuel · Answer

If x·y≠0, what is the value of x/y?

xy≠0 implies that neither of them is 0.

(1) −|x|=y. Notice that this implies that y must be a negative number.

If \(x>0\), then \(-x=y\) --> \(\frac{x}{y}=-1\), for example, consider \(x=-1\) and \(y=-1\).
If \(x<0\), then \(-(-x)=y\) --> \(\frac{x}{y}=1\), for example, consider \(x=1\) and \(y=-1\).

Not sufficient.

(2) −|y|=x. Notice that this implies that x must be a negative number.

If \(y>0\), then \(-y=x\) --> \(\frac{x}{y}=-1\), for example, consider \(x=-1\) and \(y=1\).
If \(y<0\), then \(-(-y)=x\) --> \(\frac{x}{y}=1\), for example, consider \(x=-1\) and \(y=-1\).

Not sufficient.

(1)+(2) Since from (2) we have that x is a negative number, then from (1) -|x|=y, becomes -(-x)=y --> x=y --> x/y=1. Sufficient.

Answer: C.

Hope it's clear.

TheBipedalHorse · Answer

If x·y≠0, what is the value of x/y?

(1) −|x|=y

Recalling the graph of y = |x|, which is V shaped graph going through (0,0), this statement simply means the graph is an inverted V going through (0,0) and the gradient (y/x) is the same in magnitude (but different in sign) towards the east and west of origin. Therefore this alone is not sufficient

(2) −|y|=x
Recalling the graph of x = |y| which is a < shaped graph bouncing at point (0,0), this statement means the graph is actually a > shaped graph bouncing at (0,0). Again, the gradient (y/x) is the same in magnitude (but different in sign) towards the north and south of origin. This alone is not sufficient

Combining 1 and 2, there is only one common arm from the both graph, and that is the / shape arm at the 3rd quadrant of the cartesian plane. This has a fixed y/x (gradient) value. Hence combined the both statements are sufficient

If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards