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GMAT Diagnostic Test Question 42

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GMAT Diagnostic Test Question 42 [#permalink] New post 29 Sep 2013, 21:00
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GMAT Diagnostic Test Question 42

Field: Algebra
Difficulty: 700


If x is an integer and 9<x^2<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
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Expert Post
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Re: GMAT Diagnostic Test Question 42 [#permalink] New post 29 Sep 2013, 21:01
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Explanation
Official Answer: D

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

Answer: D.
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Re: GMAT Diagnostic Test Question 42 [#permalink] New post 18 Aug 2014, 20:38
bb wrote:
Explanation
Official Answer: D

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

Answer: D.



Can you explain how Xmin = (-9). IMO Xmin = (-2). Where did i go wrong ???
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Re: GMAT Diagnostic Test Question 42 [#permalink] New post 18 Aug 2014, 20:45
Ashishmathew01081987 wrote:
bb wrote:
Explanation
Official Answer: D

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

Answer: D.



Can you explain how Xmin = (-9). IMO Xmin = (-2). Where did i go wrong ???



My understanding is that since 9 < x^2, it implies that (+/-) 3 < x and since x has to be an integer x = (+/-) 2.
Also, since X^2 < 99, it implies that x < (+/-) 9 but x cannot be less than (-9) since (-3) < x

So Xmax = 9 and Xmin = -2
therefore Xmax - Xmin = 9 -(-2) = 11
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Re: GMAT Diagnostic Test Question 42 [#permalink] New post 19 Aug 2014, 01:49
Expert's post
Ashishmathew01081987 wrote:
Ashishmathew01081987 wrote:
bb wrote:
Explanation
Official Answer: D

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

Answer: D.



Can you explain how Xmin = (-9). IMO Xmin = (-2). Where did i go wrong ???



My understanding is that since 9 < x^2, it implies that (+/-) 3 < x and since x has to be an integer x = (+/-) 2.
Also, since X^2 < 99, it implies that x < (+/-) 9 but x cannot be less than (-9) since (-3) < x

So Xmax = 9 and Xmin = -2
therefore Xmax - Xmin = 9 -(-2) = 11


The easiest way to check your reasoning is to plug -9 there and see whether the inequality holds: (-9)^2=81 < 99, (x cannot be -10 because 10^2=100>99). So, the least value is -9 not -2 (notice that -9 is less than -2).

Also:
9 < x^2 means that x < -3 or x > 3.
x^2 < 99 means that -\sqrt{99}<x<\sqrt{99}

It seems that you need to brush up fundamentals on inequalities:


Hope this helps.
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Re: GMAT Diagnostic Test Question 42   [#permalink] 19 Aug 2014, 01:49
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