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

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Manager
Joined: 18 Feb 2015
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If |x| = |y|, is x/y = -1? [#permalink]

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31 Jul 2016, 11:31
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If |x| = |y|, is x/y = -1?

(1) x < 0
(2) y > 0
[Reveal] Spoiler: OA
Manager
Joined: 07 Jul 2016
Posts: 79
GPA: 4
Re: If |x| = |y|, is x/y = -1? [#permalink]

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31 Jul 2016, 16:21
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HarveyKlaus wrote:
If $$\vert x\vert = \vert y\vert$$, is $$\frac{x}{y} = -1$$?

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

$$\textbf{1) } x<0$$

$$y = \pm x$$

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

Not Sufficient

$$\textbf{2) } y>0$$

$$x = \pm y$$

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

Not Sufficient

$$\textbf{(1 + 2)}$$

$$y = \pm n$$
$$x = \pm n$$

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

[Reveal] Spoiler:
(C) both statements taken together are sufficient to answer the question, but neither statement alone is sufficient

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Re: If |x| = |y|, is x/y = -1? [#permalink]

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07 Aug 2016, 07:00
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.
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Re: If |x| = |y|, is x/y = -1? [#permalink]

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07 Aug 2016, 07:16
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Konstantin1983 wrote:
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.

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
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Re: If |x| = |y|, is x/y = -1? [#permalink]

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20 Jul 2017, 22:04
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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
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Re: If |x| = |y|, is x/y = -1? [#permalink]

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10 Mar 2018, 23:01
HarveyKlaus wrote:
If |x| = |y|, is x/y = -1?

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

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)
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Re: If |x| = |y|, is x/y = -1?   [#permalink] 10 Mar 2018, 23:01
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# If |x| = |y|, is x/y = -1?

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