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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Expert's post

1

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 _________________

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.

Re: GMAT Diagnostic Test Question 42 [#permalink]
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 ???

Re: GMAT Diagnostic Test Question 42 [#permalink]
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

Re: GMAT Diagnostic Test Question 42 [#permalink]
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: