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

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Current Student
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If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x [#permalink]

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01 Feb 2014, 15:05
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If x·y≠0, what is the value of x/y?

(1) −|x|=y

(2) −|y|=x
[Reveal] Spoiler: OA
Current Student
Joined: 06 Sep 2013
Posts: 2005
Concentration: Finance
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Kudos [?]: 643 [0], given: 355

Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x [#permalink]

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01 Feb 2014, 15:08
What I did was

Statement 1

y + |x| = 0, since x and y are different from zero then it means that x = -y

So the value of -y/y = -1

Sufficient

Statement 2

x+|y|=0, means that y= -x

So the value of -x/x = -1

Sufficient

Hence D

Must be something wrong with this approach, or I may be overlooking something

Cheers
J
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Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x [#permalink]

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02 Feb 2014, 02:50
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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.

Hope it's clear.
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Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x [#permalink]

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15 May 2014, 02:47
Bunuel wrote:
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.

Hope it's clear.

Hi Bunuel

I could not really understand how the values of 'x' were obtained in the 1st highlighted text.
From Statement 1, 'y' has to be a negative number. Then, are the values for 'x' to be obtained only by having 'y' as a negative number?

In the 2nd highlighted text, don't we have to consider the value of 'y' too?

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Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x [#permalink]

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15 May 2014, 03:13
1
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Bunuel wrote:
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.

Hope it's clear.

Hi Bunuel

I could not really understand how the values of 'x' were obtained in the 1st highlighted text.
From Statement 1, 'y' has to be a negative number. Then, are the values for 'x' to be obtained only by having 'y' as a negative number?

In the 2nd highlighted text, don't we have to consider the value of 'y' too?

If you look at St 1 we are given that −|x|=y or y+|x|=0 -----------> 1

When $$x\leq{0}$$ then $$|x|=-x$$, or more generally when $$some \ expression\leq{0}$$ then $$|some \ expression|={-(some \ expression)}$$. For example: $$|-5|=5=-(-5)$$;

When $$x\geq{0}$$ then $$|x|=x$$, or more generally when $$some \ expression\geq{0}$$ then $$|some \ expression|={some \ expression}$$. For example: $$|5|=5$$;

Also note that $$|X|\geq{0}$$

So from St 1 we have y + (Some positive no. x)= 0 -----> y is a negative no.

Now we need to find $$x/y$$ and not $$|x|/y$$ and therefore you need to know x to calculate value of y. What you know from St 1 is that y is a negative no but you don't know whether x is a negative or positive no.

Similarly St 2 −|y|=x means x+|y|=0 ------> This means x is a negative no. but we don't know anything about y. It can be positive or negative

Now when you combine the 2 statements you get both x and y are negative and x=y and thus x/y= 1

Hope it helps
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Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x [#permalink]

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19 Apr 2016, 20:57
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Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x [#permalink]

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01 May 2016, 13:04
Hi bunuel
I got how answer choice a & b can not deliver single option.
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Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x [#permalink]

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02 May 2016, 04:02
hatemnag wrote:
Hi bunuel
I got how answer choice a & b can not deliver single option.

Absolute value properties:

When $$x\leq{0}$$ then $$|x|=-x$$, or more generally when $$some \ expression\leq{0}$$ then $$|some \ expression|={-(some \ expression)}$$. For example: $$|-5|=5=-(-5)$$;

When $$x\geq{0}$$ then $$|x|=x$$, or more generally when $$some \ expression\geq{0}$$ then $$|some \ expression|={some \ expression}$$. For example: $$|5|=5$$
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Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x   [#permalink] 02 May 2016, 04:02
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