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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 _________________

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

Back to hometown after a short trip to New Delhi for my visa appointment. Whoever tells you that the toughest part gets over once you get an admit is...