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

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If both x and y are nonzero numbers, what is the value of [#permalink] New post 20 Feb 2011, 10:15
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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.
[Reveal] Spoiler: OA

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Re: QR. 30 Number [#permalink] New post 20 Feb 2011, 10:21
Expert's post
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] New post 20 Feb 2011, 10:24
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] New post 20 Feb 2011, 10:43
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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Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
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Re: QR. 30 Number [#permalink] New post 20 Feb 2011, 10:49
Expert's post
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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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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Re: QR. 30 Number [#permalink] New post 20 Feb 2011, 10:53
Expert's post
Baten80 wrote:
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. it is positive or negative?


If x=-5=negative then -x=-negative=positive.
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NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: If both x and y are nonzero numbers, what is the value of [#permalink] New post 18 May 2014, 10:00
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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
Re: If both x and y are nonzero numbers, what is the value of   [#permalink] 18 May 2014, 10:00
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