If |x| = |y|, is x/y = -1?

Question

(1) x < 0
(2) y > 0

DAllison2016 · Accepted Answer

My method is a little verbose to write out. Could definitely be explained more succinctly as it's trivial to see.

extbf{1) } x<0

y = \pm x

As x is negative, 
if  y = x , then  \frac{x}{y} = 1 
if  y = -x , then  \frac{x}{y} = -1

Not Sufficient

extbf{2) } y>0

x = \pm y

As y is positive, 
if  x = y , then  \frac{x}{y} = 1 
if  x = -y , then  \frac{x}{y} = -1

Not Sufficient

extbf{(1 + 2)}

y = \pm n 
 x = \pm n

We know from (1) that x = -n.
We know from (2) that y = n

\frac{x}{y} = \frac{-n}{n} = \frac{-1}{1} = -1

Sufficient

(C) both statements taken together are sufficient to answer the question, but neither statement alone is sufficient

Konstantin1983 · Answer

Since absolute values are positive numbers i squared both sides and got x=y

If x<0 then y should also be <0 right? Or no? Please explain.

abhimahna · Answer

When you square both sides, you will get x^2 = y^2, but still that doesn't confirm if x = y or x = -y.

for that, you need to know the sign of both x and y to come to a conclusion. Hence C

apoorv2708 · Answer

The distance of x from 0 on the number line is equal to the distance of y from 0 on the number line.
x can be negative or positive
y can also be negative or positive

Statement 1
x<0 i.e. x is negative
y can be negative or positive

x/y =1 or -1
NOT SUFFICIENT

Statement 2
y>0
x can be negative or positive
x/y= 1 or -1
NOT SUFFICIENT

Both the Statements combined
x<0 and y>0
x/y = -1
SUFFICIENT
Ans C

AkshdeepS · Answer

Given : |x| = |y| means we have four cases: 1. x = y 2. x = -y 3. -x = y 4. -x = -y Question : x/y = -1 ? means x = -y or -x = y ? St 1: x < 0 , but we don't know what "y' is. It can be case 3 or case 4. Insufficient St 2: y > 0, but we don't know what "x' is. It can be case 1 or case 3. Insufficient Combining we get case 3: x < 0, y>0 Sufficient (C)

BrentGMATPrepNow · Answer

Target question : Is x/y = -1? Given : |x| = |y| First of all, this tells us that x and y have the same magnitude . So, EITHER x and y are equal, OR one is negative and one is positive Statement 1 : x < 0 There's no information about y, so this statement probably isn't sufficient. let's TEST some values. There are several values of x and y that satisfy statement 1. Here are two: Case a: x = -2 and y = 2. Notice that |x| = |y|. In this case x/y = (-2)/2 = -1 Case b: x = -2 and y = -2. Notice that |x| = |y|. In this case x/y = (-2)/(-2) = 1 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values Statement 2 : y > 0 There's no information about x, so this statement probably isn't sufficient. let's TEST some values. There are several values of x and y that satisfy statement 2. Here are two: Case a: x = -2 and y = 2. Notice that |x| = |y|. In this case x/y = (-2)/2 = -1 Case b: x = 2 and y = 2. Notice that |x| = |y|. In this case x/y = 2/2 = 1 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that x is negative Statement 2 tells us that y is positive The given information tells us that x and y must have the same magnitude. So, we can conclude that x/y = -1 Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer = C Cheers, Brent

Kinshook · Answer

Asked: If |x| = |y|, is x/y = -1? (1) x < 0 since y=x or y=-x NOT SUFFICIENT (2) y > 0 since y=x or y=-x NOT SUFFICIENT (1) + (2) (1) x < 0 (2) y > 0 Since |x| = |y| and their signs are different x = -y x/y = -1 SUFFICIENT IMO C

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If |x| = |y|, is x/y = -1?

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

GMAT Data Sufficiency (DS) Questions

If |x| = |y|, is x/y = -1?

Prep Toolkit

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