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D01-42

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D01-42 [#permalink]

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If x is an integer and \(9 \lt x^2 \lt 99\), then what is the value of maximum possible value of \(x\) minus minimum possible value of \(x\)?

A. \(5\)
B. \(6\)
C. \(7\)
D. \(18\)
E. \(20\)
[Reveal] Spoiler: OA

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Re D01-42 [#permalink]

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New post 15 Sep 2014, 23:13
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Official Solution:

If x is an integer and \(9 \lt x^2 \lt 99\), then what is the value of maximum possible value of \(x\) minus minimum possible value of \(x\)?

A. \(5\)
B. \(6\)
C. \(7\)
D. \(18\)
E. \(20\)


Notice that \(x\) can take positive, as well as negative values to satisfy \(9 \lt x^2 \lt 99\), hence \(x\) can be: -9, -8, -7, -6, -5, -4, 4, 5, 6, 7, 8, or 9. We are asked to find the value of x(max)-x(min), and since x(max)=9 and x(min)=-9 then x(max)-x(min)=9-(-9)=18.


Answer: D
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Re: D01-42 [#permalink]

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New post 26 Dec 2014, 03:09
Bunuel wrote:
Official Solution:

If x is an integer and \(9 \lt x^2 \lt 99\), then what is the value of maximum possible value of \(x\) minus minimum possible value of \(x\)?

A. \(5\)
B. \(6\)
C. \(7\)
D. \(18\)
E. \(20\)


Notice that \(x\) can take positive, as well as negative values to satisfy \(9 \lt x^2 \lt 99\), hence \(x\) can be: -9, -8, -7, -6, -4, 4, 5, 6, 7, 8, or 9. We are asked to find the value of x(max)-x(min), and since x(max)=9 and x(min)=-9 then x(max)-x(min)=9-(-9)=18.


Answer: D


but the questions is asking about x not x^2 though
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D01-42 [#permalink]

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New post 26 Dec 2014, 07:01
amenon55 wrote:
Bunuel wrote:
Official Solution:

If x is an integer and \(9 \lt x^2 \lt 99\), then what is the value of maximum possible value of \(x\) minus minimum possible value of \(x\)?

A. \(5\)
B. \(6\)
C. \(7\)
D. \(18\)
E. \(20\)


Notice that \(x\) can take positive, as well as negative values to satisfy \(9 \lt x^2 \lt 99\), hence \(x\) can be: -9, -8, -7, -6, -4, 4, 5, 6, 7, 8, or 9. We are asked to find the value of x(max)-x(min), and since x(max)=9 and x(min)=-9 then x(max)-x(min)=9-(-9)=18.


Answer: D


but the questions is asking about x not x^2 though


The question asks what is the value of maximum possible value of \(x\) minus minimum possible value of \(x\)?

x (not x^2) can be: -9, -8, -7, -6, -5, -4, 4, 5, 6, 7, 8, or 9: x(max) - x(min) = 9 - (-9) = 18.
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Re: D01-42 [#permalink]

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New post 02 Dec 2015, 21:39
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amenon55 wrote:
Bunuel wrote:
Official Solution:

If x is an integer and \(9 \lt x^2 \lt 99\), then what is the value of maximum possible value of \(x\) minus minimum possible value of \(x\)?

A. \(5\)
B. \(6\)
C. \(7\)
D. \(18\)
E. \(20\)


Notice that \(x\) can take positive, as well as negative values to satisfy \(9 \lt x^2 \lt 99\), hence \(x\) can be: -9, -8, -7, -6, -4, 4, 5, 6, 7, 8, or 9. We are asked to find the value of x(max)-x(min), and since x(max)=9 and x(min)=-9 then x(max)-x(min)=9-(-9)=18.


Answer: D


but the questions is asking about x not x^2 though


9 < x^2 < 99

Take the square root of all sides. Now when you take the square root of a number you get a positive and a negative root: √9 = ±3 and √99 ≅ ±9.95. This produces two intervals for x:

-9.95 < x < -3 and 3 < x < 9.95

Since x is an integer, its maximum value is x = 9 and its minimum value is x = -9

(Max Value of x) - (Min Value of x) = 9 - (-9) = 9 + 9 = 18
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Re: D01-42 [#permalink]

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New post 10 Dec 2015, 02:48
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. since 9< x^2 < 99 means +/- 3 <x< +/-10 (square root)
therefore max minus min value would be +10 - (-3) which is 10 + 3 = 13.
Please tell me where am i going wrong with my approach.
thank you
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Re: D01-42 [#permalink]

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New post 12 Dec 2015, 07:38
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Bhavanasg wrote:
I think this is a high-quality question and the explanation isn't clear enough, please elaborate. since 9< x^2 < 99 means +/- 3 <x< +/-10 (square root)
therefore max minus min value would be +10 - (-3) which is 10 + 3 = 13.
Please tell me where am i going wrong with my approach.
thank you


Please read the thread above.

Hope it helps.
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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: D01-42 [#permalink]

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New post 26 Apr 2016, 22:58
Good question.
Need to consider the negative values as well...
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Re: D01-42 [#permalink]

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New post 16 Jul 2016, 11:36
x can take positive, as well as negative values

One should always consider all possible cases in mind.
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Re: D01-42 [#permalink]

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New post 22 Aug 2016, 11:48
I think this is a high-quality question and I agree with explanation. GG. Well Played...
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Re: D01-42 [#permalink]

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New post 02 Jan 2017, 03:59
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Since 9<x2 <99 so values of x should range

3,2,1,0,1,2,3,4,5,6,7,8,9
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Re: D01-42 [#permalink]

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New post 02 Jan 2017, 04:18
C3BISHT wrote:
I think this is a poor-quality question and the explanation isn't clear enough, please elaborate. Since 9<x2 <99 so values of x should range

3,2,1,0,1,2,3,4,5,6,7,8,9


I have to disagree. The question is correct and of a good quality.

As for your doubt. If 9 < x^2 < 99 how can x be 3, 2, 1, or 0? The do not satisfy 9 < x^2 < 99. x can be: -9, -8, -7, -6, -4, 4, 5, 6, 7, 8, or 9.
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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: D01-42 [#permalink]

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New post 21 Feb 2017, 17:46
This is a high-quality and "tricky" question.
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Re: D01-42 [#permalink]

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New post 27 May 2017, 11:28
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Is there a reason why you skipped -5 among the possible values of x?
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Re: D01-42 [#permalink]

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Re D01-42 [#permalink]

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New post 06 Feb 2018, 13:03
I think this is a poor-quality question and I agree with explanation.
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Re: D01-42 [#permalink]

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New post 06 Feb 2018, 19:44
Re: D01-42   [#permalink] 06 Feb 2018, 19:44
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