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SVP  Joined: 06 Sep 2013
Posts: 1647
Concentration: Finance
If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 59% (01:37) correct 41% (01:40) wrong based on 293 sessions

### HideShow timer Statistics If x·y≠0, what is the value of x/y?

(1) −|x|=y

(2) −|y|=x
Math Expert V
Joined: 02 Sep 2009
Posts: 56264
Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x  [#permalink]

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3
5
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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SVP  Joined: 06 Sep 2013
Posts: 1647
Concentration: Finance
Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x  [#permalink]

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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
Intern  Joined: 19 Oct 2013
Posts: 17
Location: India
Concentration: General Management, Operations
WE: Engineering (Other)
Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x  [#permalink]

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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?

Director  Joined: 25 Apr 2012
Posts: 668
Location: India
GPA: 3.21
Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x  [#permalink]

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2
1
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
_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
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Joined: 20 Apr 2014
Posts: 88
Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x  [#permalink]

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Hi bunuel
I got how answer choice a & b can not deliver single option.
Math Expert V
Joined: 02 Sep 2009
Posts: 56264
Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x  [#permalink]

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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]

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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.

I have a little question.
So let's use values for both the statements,
Statement 1: -|x| = y
This means that y is a negative integer, but the magitude is same for both x and y.
Now since x cannot be equal to y, therefore x will be the same number but in positive.
For example, if y= -3, x will have to be +3 because otherwise if it is -3, then x and y will be exactly the saem which shouldn't be.
Thus x/y will definitely be equal to -1.
Thus statement is sufficient.
Similarly, statement 2 is also sufficient.

Please correct me, if I am wrong.

Please give KUDOS, if you like my effort. _________________
Desperately need 'KUDOS' !!
Math Expert V
Joined: 02 Sep 2009
Posts: 56264
Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x  [#permalink]

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rekhabishop wrote:
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.

I have a little question.
So let's use values for both the statements,
Statement 1: -|x| = y
This means that y is a negative integer, but the magitude is same for both x and y.
Now since x cannot be equal to y, therefore x will be the same number but in positive.
For example, if y= -3, x will have to be +3 because otherwise if it is -3, then x and y will be exactly the saem which shouldn't be.
Thus x/y will definitely be equal to -1.
Thus statement is sufficient.
Similarly, statement 2 is also sufficient.

Please correct me, if I am wrong.

Please give KUDOS, if you like my effort. Why cannot x and y be equal? Note here that unless it is explicitly stated otherwise, different variables CAN represent the same number.
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Joined: 22 Sep 2016
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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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Bunuel wrote:
rekhabishop wrote:
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.

I have a little question.
So let's use values for both the statements,
Statement 1: -|x| = y
This means that y is a negative integer, but the magitude is same for both x and y.
Now since x cannot be equal to y, therefore x will be the same number but in positive.
For example, if y= -3, x will have to be +3 because otherwise if it is -3, then x and y will be exactly the saem which shouldn't be.
Thus x/y will definitely be equal to -1.
Thus statement is sufficient.
Similarly, statement 2 is also sufficient.

Please correct me, if I am wrong.

Please give KUDOS, if you like my effort. Why cannot x and y be equal? Note here that unless it is explicitly stated otherwise, different variables CAN represent the same number.

Sorry, my bad. I read X*Y not equal to zero as, X-Y not equal to zero. _________________
Desperately need 'KUDOS' !!
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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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