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# GMAT Diagnostic Test Question 42

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Founder
Affiliations: AS - Gold, HH-Diamond
Joined: 04 Dec 2002
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Location: United States (WA)
GMAT 1: 750 Q49 V42
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GMAT Diagnostic Test Question 42 [#permalink]  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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Founder
Affiliations: AS - Gold, HH-Diamond
Joined: 04 Dec 2002
Posts: 13022
Location: United States (WA)
GMAT 1: 750 Q49 V42
GPA: 3.5
Followers: 2919

Kudos [?]: 15199 [2] , given: 3940

Re: GMAT Diagnostic Test Question 42 [#permalink]  29 Sep 2013, 21:01
2
KUDOS
Expert's post
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This post was
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Explanation

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 $$x_{max}-x_{min}=9-(-9)=18$$.

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Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 133
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
Followers: 3

Kudos [?]: 59 [0], given: 68

Re: GMAT Diagnostic Test Question 42 [#permalink]  18 Aug 2014, 20:38
bb wrote:
Explanation

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 $$x_{max}-x_{min}=9-(-9)=18$$.

Can you explain how Xmin = (-9). IMO Xmin = (-2). Where did i go wrong ???
Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 133
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
Followers: 3

Kudos [?]: 59 [0], given: 68

Re: GMAT Diagnostic Test Question 42 [#permalink]  18 Aug 2014, 20:45
Ashishmathew01081987 wrote:
bb wrote:
Explanation

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 $$x_{max}-x_{min}=9-(-9)=18$$.

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]  19 Aug 2014, 01:49
Expert's post
Ashishmathew01081987 wrote:
Ashishmathew01081987 wrote:
bb wrote:
Explanation

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 $$x_{max}-x_{min}=9-(-9)=18$$.

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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# GMAT Diagnostic Test Question 42

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