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M19-20

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Official Solution:

Which of the following always equals \(\sqrt{9 + x^2 - 6x}\) ?

A. \(x - 3\)
B. \(3 + x\)
C. \(|3 - x|\)
D. \(|3 + x|\)
E. \(3 - x\)

\(\sqrt{9 + x^2 - 6x} = \sqrt{(3 - x)^2} = |3 - x|\) (by the definition of a square root).

Answer: C
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M19-20 [#permalink]

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Hi Bunuel,

I got the roots for the equation as (x-3)^2 (reading the equation as x^2 - 6x +9 - We've flipped the values of a and b in the equation a^2 - 2ab + b^2). Based on my approach |x - 3| would be the correct answer and on yours |3 - x| is the correct answer.

Does my above para make any sense? If it does, and if the question has both of these options, which would be the correct answer? If it doesn't please help me understand my mistake.
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joseph0alexander wrote:
Hi Bunuel,

I got the roots for the equation as (x-3)^2 (reading the equation as x^2 - 6x +9 - We've flipped the values of a and b in the equation a^2 - 2ab + b^2). Based on my approach |x - 3| would be the correct answer and on yours |3 - x| is the correct answer.

Does my above para make any sense? If it does, and if the question has both of these options, which would be the correct answer? If it doesn't please help me understand my mistake.


The point is that |x - 3| = |3 - x|. Both indicate the distance between x and 3.
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Re: M19-20 [#permalink]

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New post 21 Nov 2014, 05:05
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Bunuel wrote:
The point is that |x - 3| = |3 - x|. Both indicate the distance between x and 3.


So, I understand that both of our answers are correct and that both these values won't appear as options in a single question.
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joseph0alexander wrote:
Bunuel wrote:
The point is that |x - 3| = |3 - x|. Both indicate the distance between x and 3.


So, I understand that both of our answers are correct and that both these values won't appear as options in a single question.

____________
Yes, that's correct.
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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

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Re: M19-20 [#permalink]

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New post 24 Jul 2015, 07:44
Bunuel wrote:
Official Solution:

Which of the following always equals \(\sqrt{9 + x^2 - 6x}\) ?

A. \(x - 3\)
B. \(3 + x\)
C. \(|3 - x|\)
D. \(|3 + x|\)
E. \(3 - x\)

\(\sqrt{9 + x^2 - 6x} = \sqrt{(3 - x)^2} = |3 - x|\) (by the definition of a square root).

Answer: C


i answered choice a : x-3

i took the the expression as x^2-6x+9 ---> (x-3)^2. no my understanding is that on GMAT when some expression is under root sign, only positive root is considered...? is it correct. if it is so, the we need not take mod value...? pls help

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riyazgilani wrote:
Bunuel wrote:
Official Solution:

Which of the following always equals \(\sqrt{9 + x^2 - 6x}\) ?

A. \(x - 3\)
B. \(3 + x\)
C. \(|3 - x|\)
D. \(|3 + x|\)
E. \(3 - x\)

\(\sqrt{9 + x^2 - 6x} = \sqrt{(3 - x)^2} = |3 - x|\) (by the definition of a square root).

Answer: C


i answered choice a : x-3

i took the the expression as x^2-6x+9 ---> (x-3)^2. no my understanding is that on GMAT when some expression is under root sign, only positive root is considered...? is it correct. if it is so, the we need not take mod value...? pls help


Exactly because the square root function cannot give negative result the answer is |3-x|, an absolute value of 3-x, which also cannot be negative.

MUST KNOW: \(\sqrt{x^2}=|x|\):

The point here is that since 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 \(\sqrt{x^2}=|x|\).

I'd advice to go through basics and only after to practice questions:

Theory on Abolute Values: math-absolute-value-modulus-86462.html
Absolute value tips: absolute-value-tips-and-hints-175002.html

DS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=37
PS Abolute Values Questions to practice: search.php?search_id=tag&tag_id=58

Hard set on Abolute Values: inequality-and-absolute-value-questions-from-my-collection-86939.html

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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

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New post 10 Dec 2015, 03:55
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. please elaborate the explanation.

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I think this is a high-quality question and I agree with explanation.

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After solving this question I got the result as |X-3| and I answered it as X-3, And got this wrong.
Thanks for giving the link which clears the basic of Absolute value including the result:

|A-B| = |B-A|

Which is clearly applicable in this question provided options.

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New post 30 Mar 2017, 20:19
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Bunuel wrote:
riyazgilani wrote:
Bunuel wrote:
Official Solution:

Which of the following always equals \(\sqrt{9 + x^2 - 6x}\) ?

A. \(x - 3\)
B. \(3 + x\)
C. \(|3 - x|\)
D. \(|3 + x|\)
E. \(3 - x\)

\(\sqrt{9 + x^2 - 6x} = \sqrt{(3 - x)^2} = |3 - x|\) (by the definition of a square root).

Answer: C


i answered choice a : x-3

i took the the expression as x^2-6x+9 ---> (x-3)^2. no my understanding is that on GMAT when some expression is under root sign, only positive root is considered...? is it correct. if it is so, the we need not take mod value...? pls help


Exactly because the square root function cannot give negative result the answer is |3-x|, an absolute value of 3-x, which also cannot be negative.

MUST KNOW: \(\sqrt{x^2}=|x|\):

The point here is that since 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 \(\sqrt{x^2}=|x|\).

I'd advice to go through basics and only after to practice questions:




Hello Bunuel, Vyshak
I thought the equation was as follows:
\(\sqrt{x^2}=x\), if \(x>{0}\);
\(\sqrt{x^2}=-x\), if \(x<={0}\).
Am i wrong? Please correct me if so.
Thanks

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Re: M19-20 [#permalink]

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New post 30 Mar 2017, 22:01
manishtank1988 wrote:
Hello Bunuel, Vyshak
I thought the equation was as follows:
\(\sqrt{x^2}=x\), if \(x>{0}\);
\(\sqrt{x^2}=-x\), if \(x<={0}\).
Am i wrong? Please correct me if so.
Thanks


You can put = sign in any of the two because \(\sqrt{0^2}=0=-0\).
_________________

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Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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.


What are GMAT Club Tests?
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Re: M19-20 [#permalink]

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New post 31 Mar 2017, 10:00
Dear Bunuel,

The answer choices CAN"T have the following answers in their list: \(|3 - x|\) and \(|x - 3|\) Because the following rule:

\(|3 - x|\) = \(|x - 3|\)

Am I right?

Thanks in advance

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Re: M19-20 [#permalink]

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New post 31 Mar 2017, 15:07
Bunuel wrote:
manishtank1988 wrote:
Hello Bunuel, Vyshak
I thought the equation was as follows:
\(\sqrt{x^2}=x\), if \(x>{0}\);
\(\sqrt{x^2}=-x\), if \(x<={0}\).
Am i wrong? Please correct me if so.
Thanks


You can put = sign in any of the two because \(\sqrt{0^2}=0=-0\).


Understood thanks...

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Re: M19-20 [#permalink]

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This question is based on the principle of \(\sqrt{x^2}=|x|\)
Hence its \(|x-3|=|3-x|\)
Straight away C.

Press Kudos id this helps! :)

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Re: M19-20   [#permalink] 21 Aug 2017, 05:28
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