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Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x [#permalink]
02 Feb 2014, 01:50

1

This post received KUDOS

Expert's post

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.

Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x [#permalink]
15 May 2014, 01:47

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.

Answer: C.

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?

Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x [#permalink]
15 May 2014, 02:13

1

This post received KUDOS

shaderon 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.

Answer: C.

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?

Thanks in advance.

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

Some important properties about |x|

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.”

gmatclubot

Re: If x·y≠0, what is the value of x/y? (1) −|x|=y (2) −|y|=x
[#permalink]
15 May 2014, 02:13

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