Last visit was: 03 Aug 2024, 09:38 It is currently 03 Aug 2024, 09:38
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# For what value of x between − 4 and 4, inclusive, is the value of x^2

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94778
Own Kudos [?]: 646317 [51]
Given Kudos: 86852
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11502
Own Kudos [?]: 34847 [22]
Given Kudos: 329
Retired Moderator
Joined: 08 Dec 2013
Status:Greatness begins beyond your comfort zone
Posts: 2090
Own Kudos [?]: 9019 [14]
Given Kudos: 171
Location: India
Concentration: General Management, Strategy
GPA: 3.2
WE:Information Technology (Consulting)
General Discussion
Intern
Joined: 26 Jul 2014
Posts: 5
Own Kudos [?]: 1 [1]
Given Kudos: 34
Re: For what value of x between − 4 and 4, inclusive, is the value of x^2 [#permalink]
1
Kudos
IMO

x^2 − 10x + 16
= x^2 − 10x + 25 – 9
=(x-5)^2 – 9

=>( x^2 − 10x + 16)max
<=> (x-5)^2 max
<=> x = -4
*with value of x between − 4 and 4, inclusive
Manager
Joined: 03 Jul 2017
Status:IF YOU CAN DREAM IT, YOU CAN DO IT
Posts: 145
Own Kudos [?]: 33 [0]
Given Kudos: 27
Location: India
Concentration: Finance, International Business
Re: For what value of x between − 4 and 4, inclusive, is the value of x^2 [#permalink]
So here we can just substitute the values from the options and check for which one does the value of x the greatest. But why is the method in the official guide showing all the values from -4 to 4 inclusive and then finding out the greatest value .Isn't that method simply lengthy??
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19249
Own Kudos [?]: 22785 [5]
Given Kudos: 286
Location: United States (CA)
Re: For what value of x between − 4 and 4, inclusive, is the value of x^2 [#permalink]
5
Kudos
Bunuel wrote:
For what value of x between − 4 and 4, inclusive, is the value of x^2 − 10x + 16 the greatest?

(A) − 4
(B) − 2
(C) 0
(D) 2
(E) 4

Let’s first factor the given quadratic.

x^2 − 10x + 16

(x - 8)(x - 2)

In order to make the expression the greatest, we need (x - 8) and (x - 2) to be either both positive or both negative.

Looking at the answer choices, we see that when x is -4, we have the largest possible product:

-12 x -6 = 96

Senior Manager
Joined: 19 Oct 2013
Posts: 411
Own Kudos [?]: 312 [0]
Given Kudos: 117
Location: Kuwait
GPA: 3.2
WE:Engineering (Real Estate)
Re: For what value of x between − 4 and 4, inclusive, is the value of x^2 [#permalink]
It tells us the numbers between -4 and 4 inclusive.

From the question stem we have $$x^2 -10x + 16$$

$$x^2$$ will always be positive

-10x, if x is negative will provide a positive integer.

From the above we can just directly substitute in the equation with -4 giving the greatest value.

Intern
Joined: 01 May 2017
Posts: 24
Own Kudos [?]: 1 [0]
Given Kudos: 86
Re: For what value of x between − 4 and 4, inclusive, is the value of x^2 [#permalink]
Put the options values in the quadratic and try you will get maximum value.

remember square of negative no. always positive and multiplication of negative numbers always positive.
VP
Joined: 28 Jul 2016
Posts: 1197
Own Kudos [?]: 1759 [0]
Given Kudos: 67
Location: India
Concentration: Finance, Human Resources
Schools: ISB '18 (D)
GPA: 3.97
WE:Project Management (Investment Banking)
Re: For what value of x between −4 and 4, inclusive, is the value of x2 − [#permalink]
The answer should be A
You can create facors (x-8)(x-2)
substitute x= -12*-6= 96
or simple the value of
$$x^2$$ − 10x + 16 will be max when all terms are positive.
so we are left with -4 and -2 from choices
-4 will yield better results.
Hence ans A
Can you put this in a better format. Follow thsi to post your result
https://gmatclub.com/forum/11-rules-for- ... 33935.html
Senior Manager
Joined: 10 Oct 2018
Status:Whatever it takes!
Posts: 323
Own Kudos [?]: 529 [0]
Given Kudos: 185
GPA: 4
Re: For what value of x between −4 and 4, inclusive, is the value of x2 − [#permalink]
Nums99 wrote:
For what value of x between −4 and 4, inclusive, is the value of x2 − 10x + 16 the greatest?
(A) −4 (B) −2 (C) 0 (D) 2 (E) 4

For such questions, put in the values given in solution into the given equation- $$x^2$$-10x+16

Option (1) putting in -4 will give 72
Option (2) putting in -2 will give 40
Option (3) putting in 0 will give 16
Option (4) putting in 2 will give 0
Option (5) putting in 4 will give 8

the greatest number obtained is in option A (72) when x=-4

Hope it helps!
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11811 [2]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: For what value of x between −4 and 4, inclusive, is the value of x2 − [#permalink]
2
Kudos
Hi Nums99,

For future reference, you should post your subject-specific questions in their respective sub-forums. For example, the PS Forum can be found here:

https://gmatclub.com/forum/problem-solving-ps-140/

In addition, there's a pretty good chance that many of the practice questions that you might be interested in have already been posted, so you can search them out (for example, through Google). Here is a post discussing the question you are asking about:

https://gmatclub.com/forum/for-what-val ... 11639.html

GMAT assassins aren't born, they're made,
Rich
VP
Joined: 12 Feb 2015
Posts: 1060
Own Kudos [?]: 2173 [0]
Given Kudos: 77
Re: For what value of x between −4 and 4, inclusive, is the value of x2 − [#permalink]
Nums99 wrote:
For what value of x between −4 and 4, inclusive, is the value of x2 − 10x + 16 the greatest?
(A) −4 (B) −2 (C) 0 (D) 2 (E) 4

Solve this question conceptually. I am assuming x2 is actually x^2, which is always non-negative for any value of x. 16 is always positive. Hence we need to worry about only -10x. We can convert this part into a positive number if we have x as negative. Therefore we can rule of option C to E. We are left with -4 and -2. -4 will not only convert -10x to a positive number but also increase its magnitude. Hence Option A is the correct answer.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19249
Own Kudos [?]: 22785 [0]
Given Kudos: 286
Location: United States (CA)
Re: For what value of x between −4 and 4, inclusive, is the value of x2 − [#permalink]
Nums99 wrote:
For what value of x between −4 and 4, inclusive, is the value of x2 − 10x + 16 the greatest?
(A) −4 (B) −2 (C) 0 (D) 2 (E) 4

We see that y = x^2 – 10x + 16 is the graph of an up-opening parabola. We can find the x-intercepts by setting the function equal to 0 and factoring:

x^2 – 10x + 16 = 0

(x – 8)(x - 2) = 0

x = 8 or x = 2

Since the x-intercepts are at 2 and 8, we know that the x-coordinate of the vertex of the parabola (which is a minimum value) is halfway between 2 and 8, which is at x = 5.
For an up-opening parabola, the farther an x-value is from the x-value of the vertex, the greater the value of the function. Thus, from the answer choices given, we see that the x-value that is farthest from x = 5 is -4, and so choice A is correct.

Intern
Joined: 28 Aug 2017
Posts: 7
Own Kudos [?]: 1 [0]
Given Kudos: 55
Location: India
Re: For what value of x between − 4 and 4, inclusive, is the value of x^2 [#permalink]
I tried to apply min ax theory used in differentiation and it doesn’t work in such qns. Just a reminder for Engg students
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5323
Own Kudos [?]: 4269 [1]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Re: For what value of x between − 4 and 4, inclusive, is the value of x^2 [#permalink]
1
Kudos
Asked: For what value of x between − 4 and 4, inclusive, is the value of x^2 − 10x + 16 the greatest?

x^2 − 10x + 16 = (x-5)^2 - 9 = (x-8)(x-2)

The value of x^2 − 10x + 16 is greatest when (x-5)^2 is greatest or |x-5| is greatest.

(A) − 4
x^2 − 10x + 16 = 72
(B) − 2
x^2 − 10x + 16 = 40
(C) 0
x^2 − 10x + 16 = 16
(D) 2
x^2 − 10x + 16 = 0
(E) 4
x^2 − 10x + 16 = -8

IMO A
Director
Joined: 04 Jun 2020
Posts: 542
Own Kudos [?]: 74 [0]
Given Kudos: 623
For what value of x between 4 and 4, inclusive, is the value of x^2 [#permalink]
ScottTargetTestPrep wrote:
Bunuel wrote:
For what value of x between − 4 and 4, inclusive, is the value of x^2 − 10x + 16 the greatest?

(A) − 4
(B) − 2
(C) 0
(D) 2
(E) 4

Let’s first factor the given quadratic.

x^2 − 10x + 16

(x - 8)(x - 2)

Looking at the answer choices, we see that when x is -4, we have the largest possible product:

-12 x -6 = 96

ScottTargetTestPrep
My initial reaction to seeing this problem was just to plug in the answer choices. Do you see that strategy in this case as an inefficient use of time? I thought of factoring, but just directly plugging in seemed more straightforward to me. Thank you!
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11502
Own Kudos [?]: 34847 [1]
Given Kudos: 329
Re: For what value of x between 4 and 4, inclusive, is the value of x^2 [#permalink]
1
Kudos
woohoo921 wrote:
ScottTargetTestPrep wrote:
Bunuel wrote:
For what value of x between − 4 and 4, inclusive, is the value of x^2 − 10x + 16 the greatest?

(A) − 4
(B) − 2
(C) 0
(D) 2
(E) 4

Let’s first factor the given quadratic.

x^2 − 10x + 16

(x - 8)(x - 2)

Looking at the answer choices, we see that when x is -4, we have the largest possible product:

-12 x -6 = 96

ScottTargetTestPrep
My initial reaction to seeing this problem was just to plug in the answer choices. Do you see that strategy in this case as an inefficient use of time? I thought of factoring, but just directly plugging in seemed more straightforward to me. Thank you!

Directly plugging in would also save a lot of time.
You can further save time by realizing that x must be negative.
x^2+16 will always be positive, so we are concerned about -10x. Thus x has to be negative and smaller the x, more will be x^2-10x.
-4 is the least value and our answer.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19249
Own Kudos [?]: 22785 [0]
Given Kudos: 286
Location: United States (CA)
Re: For what value of x between 4 and 4, inclusive, is the value of x^2 [#permalink]
woohoo921 wrote:
ScottTargetTestPrep wrote:
Bunuel wrote:
For what value of x between − 4 and 4, inclusive, is the value of x^2 − 10x + 16 the greatest?

(A) − 4
(B) − 2
(C) 0
(D) 2
(E) 4

Let’s first factor the given quadratic.

x^2 − 10x + 16

(x - 8)(x - 2)

Looking at the answer choices, we see that when x is -4, we have the largest possible product:

-12 x -6 = 96

ScottTargetTestPrep
My initial reaction to seeing this problem was just to plug in the answer choices. Do you see that strategy in this case as an inefficient use of time? I thought of factoring, but just directly plugging in seemed more straightforward to me. Thank you!

Your method works just fine!
Non-Human User
Joined: 09 Sep 2013
Posts: 34224
Own Kudos [?]: 858 [0]
Given Kudos: 0
Re: For what value of x between 4 and 4, inclusive, is the value of x^2 [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: For what value of x between 4 and 4, inclusive, is the value of x^2 [#permalink]
Moderator:
Math Expert
94776 posts