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If both x and y are nonzero numbers, what is the value of y/x? (1) x

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If both x and y are nonzero numbers, what is the value of y/x? (1) x [#permalink]

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If both x and y are nonzero numbers, what is the value of y/x?

(1) x = 6
(2) y^2 = x^2

[Reveal] Spoiler:
Why isn’t ‘C’ the correct answer? (E is the correct answer here)

If we know that x =6 and
y squared is = square root ( 6 squared) = absolute value (6)
Then absolute value (6)/6 = 1


OPEN DISCUSSION OF THIS QUESTION IS HERE: if-both-x-and-y-are-nonzero-numbers-what-is-the-value-of-y-165767.html
[Reveal] Spoiler: OA
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If both x and y are nonzero numbers, what is the value of y/x? (1) x [#permalink]

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New post 19 Nov 2010, 05:50
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shash wrote:
If both x and y are non zero numbers , what is the value of (y/x)

1) x = 6
2) y square = x square

Why isn’t ‘C’ the correct answer? (E is the correct answer here)

If we know that x =6 and
y squared is = square root ( 6 squared) = absolute value (6)
Then absolute value (6)/6 = 1


If both x and y are nonzero numbers, what is the value of x/y?

Note that \(\sqrt{x^2}=|x|\).

(1) x = 6. Not sufficient.

(2) y^2 = x^2 --> \(|x|=|y|\) --> if \(x\) and \(y\) have the same sign then \(\frac{x}{y}=1\) (for example \(x=y=6\)) but if \(x\) and \(y\) have the opposite signs then \(\frac{x}{y}=-1\) (for example \(x=6\) and \(y=-6\)). Not sufficient.

(1)+(2) We still don't know whether \(x\) and \(y\) have the same sign or not. Not sufficient.

Answer: E.

About \(\sqrt{x^2}=|x|\).

The point here is that as square root function cannot give negative result then \(\sqrt{some \ expression}\geq{0}\).

So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to?

Let's consider following examples:
If \(x=5\) --> \(\sqrt{x^2}=\sqrt{25}=5=x=positive\);
If \(x=-5\) --> \(\sqrt{x^2}=\sqrt{25}=5=-x=positive\).

So we got that:
\(\sqrt{x^2}=x\), if \(x\geq{0}\);
\(\sqrt{x^2}=-x\), if \(x<0\).

What function does exactly the same thing? The absolute value function: \(|x|=x\), if \(x\geq{0}\) and \(|x|=-x\), if \(x<0\). That is why \(\sqrt{x^2}=|x|\).
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Re: If both x and y are nonzero numbers, what is the value of y/x? (1) x [#permalink]

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New post 19 Nov 2010, 07:03
shash wrote:

If we know that x =6 and
y squared is = square root ( 6 squared) = absolute value (6)
Then absolute value (6)/6 = 1


If we know that \(y^2 = 36\), then y can be 6 or -6.
On the other hand, if it is given that y = \(\sqrt{36}\), we only consider the positive value i.e. 6. Here y can only be 6.

It is all in the notation!
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If both x and y are nonzero numbers, what is the value of [#permalink]

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New post 20 Feb 2011, 11:15
If both x and y are nonzero numbers, what is the value of x/y?

(1) x = 6
(2) y^2 = x^2

I did wrong doing following:
√y^2 = √x^2
so, y=x
and answer c
What wrong did i do.
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Re: QR. 30 Number [#permalink]

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New post 20 Feb 2011, 11:21
Baten80 wrote:
QR. 30 Number
If both x and y are nonzero numbers, what is the value of x/y?
(1) x = 6
(2) y^2 = x^2

I did wrong doing following:
√y^2 = √x^2
so, y=x
and answer c
What wrong did i do.


Note that \(\sqrt{x^2}=|x|\).

If both x and y are nonzero numbers, what is the value of x/y?

(1) x = 6. Not sufficient.

(2) y^2 = x^2 --> \(|x|=|y|\) --> if \(x\) and \(y\) have the same sign then \(\frac{x}{y}=1\) (for example \(x=y=6\)) but if \(x\) and \(y\) have the opposite signs then \(\frac{x}{y}=-1\) (for example \(x=6\) and \(y=-6\)). Not sufficient.

(1)+(2) We still don't know whether \(x\) and \(y\) have the same sign or not. Not sufficient.

Answer: E.

About \(\sqrt{x^2}=|x|\).

The point here is that as square root function can not give negative result then \(\sqrt{some \ expression}\geq{0}\).

So \(\sqrt{x^2}\geq{0}\). But what does \(\sqrt{x^2}\) equal to?

Let's consider following examples:
If \(x=5\) --> \(\sqrt{x^2}=\sqrt{25}=5=x=positive\);
If \(x=-5\) --> \(\sqrt{x^2}=\sqrt{25}=5=-x=positive\).

So we got that:
\(\sqrt{x^2}=x\), if \(x\geq{0}\);
\(\sqrt{x^2}=-x\), if \(x<0\).

What function does exactly the same thing? The absolute value function: \(|x|=x\), if \(x\geq{0}\) and \(|x|=-x\), if \(x<0\). That is why \(\sqrt{x^2}=|x|\).
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Re: QR. 30 Number [#permalink]

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New post 20 Feb 2011, 11:24
Baten80 wrote:
QR. 30 Number
If both x and y are nonzero numbers, what is the value of x/y?
(1) x = 6
(2) y^2 = x^2

I did wrong doing following:
√y^2 = √x^2
so, y=x
and answer c
What wrong did i do.


\(sqrt(y^2)=\sqrt(x^2)\) may not always mean - y=x

Say
x=6; y=-6; x^2=36, y=36; but x and y are different.
x=6; y=6; x^2=36, y=36; and here x and y are same.

(1) x=6; Nothing about y. Not sufficient.
(2) (y-x) (y+x) = 0
y-x=0 or y+x=0
If former; y=x
Latter; y=-x
Not sufficient.

Combining both;
x=6
y can be 6 or -6.

Ans: "E"
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Re: QR. 30 Number [#permalink]

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New post 20 Feb 2011, 11:43
fluke wrote:
Baten80 wrote:
QR. 30 Number
If both x and y are nonzero numbers, what is the value of x/y?
(1) x = 6
(2) y^2 = x^2

I did wrong doing following:
√y^2 = √x^2
so, y=x
and answer c
What wrong did i do.


\(sqrt(y^2)=\sqrt(x^2)\) may not always mean - y=x

Say
x=6; y=-6; x^2=36, y=36; but x and y are different.
x=6; y=6; x^2=36, y=36; and here x and y are same.

(1) x=6; Nothing about y. Not sufficient.
(2) (y-x) (y+x) = 0
y-x=0 or y+x=0
If former; y=x
Latter; y=-x
Not sufficient.

Combining both;
x=6
y can be 6 or -6.

Ans: "E"


But as x= 6 (positive) so why i will consider √y^2 i.e., √36=-6 other than 6. [for ans c.] please help.
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Re: QR. 30 Number [#permalink]

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New post 20 Feb 2011, 11:49
Baten80 wrote:
But as x= 6 (positive) so why i will consider √y^2 i.e., √36=-6 other than 6. [for ans c.] please help.


Read my post above: \(\sqrt{x^2}=|x|\).

\(x^2=y^2\) means \(|x|=|y|\) as from (1) \(x=6\) then \(|y|=6\) --> \(y=6\) or \(y=-6\).
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Re: QR. 30 Number [#permalink]

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if both x and y are non-zero numbers, what is the value of [#permalink]

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New post 25 Jun 2011, 23:02
if both x and y are non-zero numbers, what is the value of y/x?
1. x=6
2. ysquare = xsquare
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New post 25 Jun 2011, 23:04
initially i had selected B as the answer...

now i realize

1. x=6
this does not give any information about the value of y. hence no

2. ysquare=xsquare

ysquare
--------- = 1
xsquare

taking square-roots on both sides

+or- y/x = +or-1

hence No

Taking together, it does not give better answer either as

+or- y/6 = +or-1

is my understanding correct about the right answer?
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Re: Prep Test DS-9 [#permalink]

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New post 26 Jun 2011, 00:26
Value of y/x?

Stmt1: x=6. Not sufficient.
Stmt2: \(y^2 = x^2\)
x can be +6
y can be +6
Value \(y/x = 6/6 =1\)
OR
x can be -6
y can be +6
Value of \(y/x=-1\) Not sufficient.

Take (1) and (2) together, x=+6. y can be +6 or -6, giving value of y/x as 1 or -1 respectively.
Hence not sufficient together.

OA E.
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Re: If both x and y are nonzero numbers, what is the value of [#permalink]

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New post 18 May 2014, 11:00
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st(1) no info about y Insuff
st(2) |x|=|y| Insuff
combined st(1&2): |6|=|6| Insuff
Hence E
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If both x and y are nonzero numbers, what is the value of [#permalink]

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New post 17 Sep 2016, 06:27
Bunuel -

I'm confused on why B isn't the correct answer. The problem says at the beginning ..."If both x and y are nonzero numbers..."

So when I went to set up (2), it eliminated the negative root possibility on either side of the eq and I arrived at y = x. This makes the main statement = 1

Did I misread the question?

Thank you in advance for your help!
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Re: If both x and y are nonzero numbers, what is the value of [#permalink]

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New post 17 Sep 2016, 06:35
lawiniecke wrote:
Bunuel -

I'm confused on why B isn't the correct answer. The problem says at the beginning ..."If both x and y are nonzero numbers..."

So when I went to set up (2), it eliminated the negative root possibility on either side of the eq and I arrived at y = x. This makes the main statement = 1

Did I misread the question?

Thank you in advance for your help!


I think you are missing something here. Note that Non Zero means either positive or negative but not Zero.

So, \(y^2 = x^2\) means y is + or - x. Hence x/y will be either 1 or -1. Hence, B is insufficient.

What do you mean by Negative root possibility. Note that we are not given sqrt(y)=sqrt(x). So, you need to be very careful while solving such type of questions.
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If both x and y are nonzero numbers, what is the value of [#permalink]

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New post 17 Sep 2016, 06:43
Hi abhimahna -

I misread the question. I was under the impression we were dealing with non-negative integers. Problem resolved.

Thank you!
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Re: If both x and y are nonzero numbers, what is the value of y/x? (1) x [#permalink]

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Re: If both x and y are nonzero numbers, what is the value of y/x? (1) x   [#permalink] 04 Dec 2017, 10:27
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