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

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

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

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)

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

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

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