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M22-03

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M22-03  [#permalink]

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New post 16 Sep 2014, 01:15
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What is the value of \(x\) ?


(1) \(x^4 = |x|\)

(2) \(x^2 \gt x\)
Spoiler: OA

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Re M22-03  [#permalink]

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New post 16 Sep 2014, 01:15
1
Official Solution:


(1) \(x^4 = |x|\). This statement implies that \(x=-1\), \(x=0\), or \(x=1\). Not sufficient.

(2) \(x^2 \gt x\). Rearrange and factor out \(x\) to get \(x(x-1) \gt 0\). The roots are \(x=0\) and \(x=1\), "\(\gt\)" sign means that the given inequality holds true for: \(x \lt 0\) and \(x \gt 1\). Not sufficient.

(1)+(2) The only value of \(x\) from (1) which is in the range from (2) is \(x=-1\). Sufficient.


Answer: C
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Re: M22-03  [#permalink]

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New post 09 Nov 2014, 21:42
Thanks for Explanation! I did not understand following part

" The roots are x=0 and x=1, \("\gt"\) sign means that the given inequality holds true for: \(x \lt 0\) and \(x \gt 1\)."

I thought \(x(x-1) \gt 0\) would mean \(x \gt 0\) and \(x \gt 1\)

Please suggest. Also how did we get -1 as final answer. As per statement (2) \(x \gt 1\).

Thanks

Bunuel wrote:
Official Solution:


(1) \(x^4 = |x|\). This statement implies that \(x=-1\), \(x=0\), or \(x=1\). Not sufficient.

(2) \(x^2 \gt x\). Rearrange and factor out \(x\) to get \(x(x-1) \gt 0\). The roots are \(x=0\) and \(x=1\), "\(\gt\)" sign means that the given inequality holds true for: \(x \lt 0\) and \(x \gt 1\). Not sufficient.

(1)+(2) The only value of \(x\) from (1) which is in the range from (2) is \(x=-1\). Sufficient.


Answer: C
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Re: M22-03  [#permalink]

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New post 10 Nov 2014, 02:57
Sky78 wrote:
Thanks for Explanation! I did not understand following part

" The roots are x=0 and x=1, \("\gt"\) sign means that the given inequality holds true for: \(x \lt 0\) and \(x \gt 1\)."

I thought \(x(x-1) \gt 0\) would mean \(x \gt 0\) and \(x \gt 1\)

Please suggest. Also how did we get -1 as final answer. As per statement (2) \(x \gt 1\).

Thanks

Bunuel wrote:
Official Solution:


(1) \(x^4 = |x|\). This statement implies that \(x=-1\), \(x=0\), or \(x=1\). Not sufficient.

(2) \(x^2 \gt x\). Rearrange and factor out \(x\) to get \(x(x-1) \gt 0\). The roots are \(x=0\) and \(x=1\), "\(\gt\)" sign means that the given inequality holds true for: \(x \lt 0\) and \(x \gt 1\). Not sufficient.

(1)+(2) The only value of \(x\) from (1) which is in the range from (2) is \(x=-1\). Sufficient.


Answer: C


Check links below.

Solving Quadratic Inequalities - Graphic Approach: solving-quadratic-inequalities-graphic-approach-170528.html
Inequality tips: tips-and-hints-for-specific-quant-topics-with-examples-172096.html#p1379270
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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

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 M22-03  [#permalink]

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New post 21 Jun 2016, 07:13
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Not able to understand the explanation
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Re: M22-03  [#permalink]

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New post 21 Jun 2016, 07:18
89renegade wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. Not able to understand the explanation


Please check alternate solutions here: what-is-the-value-of-x-147037.html
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Re: M22-03  [#permalink]

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New post 27 Dec 2017, 08:31
+1 for C. From the first statement x=-1,0, or 1. From second statement , x<0 or x>1. Each statement alone is not sufficient. Combine the two, x=-1. Hence option C.
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M22-03  [#permalink]

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New post 16 Feb 2018, 06:51
Bunuel wrote:
Sky78 wrote:
Thanks for Explanation! I did not understand following part

" The roots are x=0 and x=1, \("\gt"\) sign means that the given inequality holds true for: \(x \lt 0\) and \(x \gt 1\)."

I thought \(x(x-1) \gt 0\) would mean \(x \gt 0\) and \(x \gt 1\)

Please suggest. Also how did we get -1 as final answer. As per statement (2) \(x \gt 1\).

Thanks

Bunuel wrote:
Official Solution:


(1) \(x^4 = |x|\). This statement implies that \(x=-1\), \(x=0\), or \(x=1\). Not sufficient.

(2) \(x^2 \gt x\). Rearrange and factor out \(x\) to get \(x(x-1) \gt 0\). The roots are \(x=0\) and \(x=1\), "\(\gt\)" sign means that the given inequality holds true for: \(x \lt 0\) and \(x \gt 1\). Not sufficient.

(1)+(2) The only value of \(x\) from (1) which is in the range from (2) is \(x=-1\). Sufficient.


Answer: C


Check links below.

Solving Quadratic Inequalities - Graphic Approach: http://gmatclub.com/forum/solving-quadr ... 70528.html
Inequality tips: http://gmatclub.com/forum/tips-and-hint ... l#p1379270



Hi Bunuel,

I too have exactly the same question as the previous person...I went through the links provided and still cannot understand why in statement 2, x is not either greater than 0 or greater than 1. I then got confused as to how you got to the answer being x= (-1).

Would really appreciate a breakdown of the above queries please.

Thanks,

Tosin
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M22-03  [#permalink]

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New post 16 Feb 2018, 06:57
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ttaiwo wrote:
Hi Bunuel,

I too have exactly the same question as the previous person...I went through the links provided and still cannot understand why in statement 2, x is not either greater than 0 or greater than 1. I then got confused as to how you got to the answer being x= (-1).

Would really appreciate a breakdown of the above queries please.

Thanks,

Tosin


This is explained in detail in the links provided.

x > 0 or x > 1 doe not make any sense. Is x > 0? So, could it be 0.5? Or is x > 1?

\(x(x-1) \gt 0\) --> x and x - 1 have the same sign.

x > 0 and x - 1 > 0 --> x > 0 and x > 1. Simultaneously to be true x > 1 has to be true.
x < 0 and x - 1 < 0 --> x < 0 and x < 1. Simultaneously to be true x < 0 has to be true.

So, \(x(x-1) \gt 0\) is true for x < 0 and x > 1.
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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

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: M22-03  [#permalink]

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New post 17 Feb 2018, 03:58
Bunuel wrote:
ttaiwo wrote:
Hi Bunuel,

I too have exactly the same question as the previous person...I went through the links provided and still cannot understand why in statement 2, x is not either greater than 0 or greater than 1. I then got confused as to how you got to the answer being x= (-1).

Would really appreciate a breakdown of the above queries please.

Thanks,

Tosin


This is explained in detail in the links provided.

x > 0 or x > 1 doe not make any sense. Is x > 0? So, could it be 0.5? Or is x > 1?

\(x(x-1) \gt 0\) --> x and x - 1 have the same sign.

x > 0 and x - 1 > 0 --> x > 0 and x > 1. Simultaneously to be true x > 1 has to be true.
x < 0 and x - 1 < 0 --> x < 0 and x < 1. Simultaneously to be true x < 0 has to be true.

So, \(x(x-1) \gt 0\) is true for x < 0 and x > 1.


Thanks a lot...now understood.
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Re: M22-03  [#permalink]

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New post 10 Jul 2018, 23:17
is the absolute value of zero, zero?
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Re: M22-03  [#permalink]

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New post 10 Jul 2018, 23:22
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ENEM wrote:
is the absolute value of zero, zero?


Yes, |0| = 0. An absolute value show the distance from 0. For example, |-3| = 3 means that -3 is 3 units from 0. How far is 0 from 0? What is the distance from 0 to 0? It's 0.

Hope it's clear.
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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

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: M22-03 &nbs [#permalink] 10 Jul 2018, 23:22
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