BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

Please help in this question

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 107
Joined: Sat May 23, 2009 9:53 pmFollowed by: 1 member
Location: United States
Thanked: 5 times
by vivecan2005 » Sun Jun 07, 2009 6:01 pm
The longevity of a certain metal construction is determined by the following formula:
l = (7.5 – x)4 + 8.97c, where l is the longevity of the construction, in years, x is the density of the underlying material, in g/cm3, and c is a positive constant equal to 1.05 for this type of metal constructions. For what value of density, x, expressed in g/cm3, will the metal construction have minimal longevity?

A. -7.5
B. 0
C. 7.5
D. 15

E. 75
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Master | Next Rank: 500 Posts
Posts: 472
Joined: Sun Mar 29, 2009 6:54 pm
Thanked: 56 times

by ssmiles08 » Sun Jun 07, 2009 6:32 pm
IMO C?

The greatest value x can be is 7.5 which will give the least value of l.

I don't think it can be d or e b/c otherwise longevity will be a negative value and I don't think that is possible.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Senior | Next Rank: 100 Posts
Posts: 59
Joined: Tue May 05, 2009 1:58 am
Thanked: 1 times

by Pranay » Mon Jun 08, 2009 3:34 am
Yep .. agree with smiles.. :)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Master | Next Rank: 500 Posts
Posts: 235
Joined: Wed Oct 26, 2016 9:21 pmFollowed by: 5 members
Thanked: 3 times

by Anaira Mitch » Sun Jan 15, 2017 8:38 pm
To answer this question, we need to minimize the value of l = (7.5 - x)^4 + (8.97)^1.05. Since we do not need to determine the actual minimum longevity, we do not need to find the value of the second component in our formula, (8.97)^1.05, which will remain constant for any level of x. Therefore, to minimize longevity, we need to minimize the value of the first component in our formula,
i.e. (7.5 - x)^4. Since we are raising the expression (7.5 - x) to an even exponent, 4, the value of
(7.5 - x)4 will always be non-negative, i.e. positive or zero. Thus, to minimize this outcome, we need to find the value of x for which (7.5 - x)^4 = 0.
(7.5 - x)^4 = 0
7.5 - x = 0
x = 7.5

Therefore, the metal construction will have minimal longevity for the value of x = 7.5, i.e. when the density of the underlying material will be equal to 7.5 g/cm3.

The correct answer is C.
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Mon Jan 16, 2017 9:12 am
vivecan2005 wrote:The longevity of a certain metal construction is determined by the following formula:
L = (7.5 - x)� + 8.97c, where l is the longevity of the construction, in years, x is the density of the underlying material, in g/cm3, and c is a positive constant equal to 1.05 for this type of metal constructions. For what value of density, x, expressed in g/cm3, will the metal construction have minimal longevity?

A. -7.5
B. 0
C. 7.5
D. 15
E. 75


Plug in c = 1.05 to get: L = (7.5 - x)� + 8.97(1.05)
Simplify: L = (7.5 - x)� + some positive number

Our goal is to MINIMIZE the value of L
To do this, we must MINIMIZE the value of (7.5 - x)�

Since we exponent is EVEN, we know that (7.5 - x)� will be greater than or equal to zero for all values of x.
So, the MINIMUM value of (7.5 - x)� is ZERO
This occurs when x = 7.5

Answer: C
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1