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

Redeem

Source - GMATprep

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Master | Next Rank: 500 Posts
Posts: 110
Joined: Thu Apr 05, 2012 8:48 am
Thanked: 3 times
Followed by:1 members

Source - GMATprep

by shanice » Fri Aug 10, 2012 7:34 am
If y=4+(x-3)^2, then y is least when x

A)14
B)13
C)0
D)3
E)4

Answer is D.

I don't understand what the question is asking. Can someone explain, please?
Top
Source: — Problem Solving |

GMAT/MBA Expert

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

by Brent@GMATPrepNow » Fri Aug 10, 2012 8:42 am
shanice wrote:If y=4+(x-3)^2, then y is least when x

A)14
B)13
C)0
D)3
E)4

Answer is D.

I don't understand what the question is asking. Can someone explain, please?
We want to minimize the value of 4+(x-3)^2
To do this, we need to minimize the value of (x-3)^2
Notice that (any number)^2 > 0
So, the smallest value possible of (any number)^2 is 0

(x-3)^2 = 0 when x=3.
So, the value of 4+(x-3)^2 is minimized when x=3.

Answer = D

Cheers,
Brent

PS: Be sure to use the Spoiler function to hide the correct answer so that others can try answering the question without seeing the answer.
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pm
Location: New York, NY
Thanked: 13060 times
Followed by:1906 members
GMAT Score:790

by GMATGuruNY » Fri Aug 10, 2012 8:48 am
shanice wrote:If y=4+(x-3)^2, then y is least when x

A)14
B)13
C)0
D)3
E)4

Answer is D.

I don't understand what the question is asking. Can someone explain, please?
To MINIMIZE y, we must MINIMIZE the value of 4 + (x-3)².
Since the square of a value cannot be negative, the least possible value of (x-3)² is 0.
(x-3)² = 0 when x=3.
Thus, y will be its least possible value when x=3:
y = 4 + (x-3)² = 4 + (3-3)² = 4.
If x is any value other than 3, the value of y will INCREASE.

The correct answer is D.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Master | Next Rank: 500 Posts
Posts: 392
Joined: Thu Jan 15, 2009 12:52 pm
Location: New Jersey
Thanked: 76 times

by truplayer256 » Fri Aug 10, 2012 9:37 am
y = 4 + (x - 3)^2

Note that y is always going to increase or stay the same no matter what since (x - 3)^2 is ALWAYS going to be positive. Therefore, the only obvious choice for the least value of y is 4 and this occurs when x = 3.

If you have taken calculus before, you can also use differentiation to come up with your answer:

dy/dx = 2(x - 3) = 0 => x = 3
This means that a minimum occurs when x = 3.

The best choice is D.
Top
Post new topic Post Reply
• Page 1 of 1