It is currently 17 Oct 2017, 19:17

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# GMAT Diagnostic Test Question 42

Author Message
Founder
Joined: 04 Dec 2002
Posts: 15570

Kudos [?]: 28477 [0], given: 5105

Location: United States (WA)
GMAT 1: 750 Q49 V42
GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

29 Sep 2013, 22:00
Expert's post
6
This post was
BOOKMARKED

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
_________________

Founder of GMAT Club

Just starting out with GMAT? Start here... or use our Daily Study Plan

Co-author of the GMAT Club tests

Kudos [?]: 28477 [0], given: 5105

Founder
Joined: 04 Dec 2002
Posts: 15570

Kudos [?]: 28477 [2], given: 5105

Location: United States (WA)
GMAT 1: 750 Q49 V42
Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

29 Sep 2013, 22:01
2
KUDOS
Expert's post
5
This post was
BOOKMARKED
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 $$x_{max}-x_{min}=9-(-9)=18$$.

_________________

Founder of GMAT Club

Just starting out with GMAT? Start here... or use our Daily Study Plan

Co-author of the GMAT Club tests

Kudos [?]: 28477 [2], given: 5105

Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 131

Kudos [?]: 121 [0], given: 68

Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

18 Aug 2014, 21:38
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 ???

Kudos [?]: 121 [0], given: 68

Manager
Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 131

Kudos [?]: 121 [0], given: 68

Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

18 Aug 2014, 21:45
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

Kudos [?]: 121 [0], given: 68

Math Expert
Joined: 02 Sep 2009
Posts: 41873

Kudos [?]: 128619 [0], given: 12180

Re: GMAT Diagnostic Test Question 42 [#permalink]

### Show Tags

19 Aug 2014, 02:49
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.
_________________

Kudos [?]: 128619 [0], given: 12180

Re: GMAT Diagnostic Test Question 42   [#permalink] 19 Aug 2014, 02:49
Display posts from previous: Sort by

# GMAT Diagnostic Test Question 42

Moderator: Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.