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

Redeem

Looked like a Quadratic Equation ...?

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Newbie | Next Rank: 10 Posts
Posts: 1
Joined: Wed Dec 18, 2013 8:41 am

Looked like a Quadratic Equation ...?

by Julia W » Sat Jun 14, 2014 1:51 pm
If x and y are positive and x^2+y^2=100, then for which of the following is the value of x+y greatest?

a) x = 10
b) x = 9
c) x = 8
d) x = 7
e) x = 6

The correct answer for this Problem Solving question is D) however, I have reviewed the answer over and over but still do not understand how this was reached.

Please help!
Thank you,
J[/spoiler]
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 » Sat Jun 14, 2014 2:10 pm
Julia W wrote:If x and y are positive and x² + y² = 100, then for which of the following is the value of x+y greatest?

a) x = 10
b) x = 9
c) x = 8
d) x = 7
e) x = 6
To find the y-value for each answer choice, we'll PLUG in the given x-value.

a) x = 10
We get 10² + y² = 100
Evaluate: 100 + y² = 100
Simplify: y² = 0
Solve: y = 0
So x + y = 10 + 0 = 10

b) x = 9
We get 9² + y² = 100
Evaluate: 81 + y² = 100
Simplify: y² = 19
Solve: y = √19
NOTE: We need not find the EXACT value of y here. We need only recognize that √16 = 4 and √25 = 5.
Since 19 is BETWEEN 16 and 25, √19 is BETWEEN 4 and 5. In other words, y = 4.something
So, x + y = 9 + 4.something = 13.something

c) x = 8
We get 8² + y² = 100
Evaluate: 64 + y² = 100
Simplify: y² = 36
Solve: y = 6
So x + y = 8 + 6 = 14

d) x = 7
We get 7² + y² = 100
Evaluate: 49 + y² = 100
Simplify: y² = 51
Solve: y = √51
NOTE: Recognize that √49 = 7 and √64 = 8.
Since 51 is BETWEEN 49 and 64, √51 is BETWEEN 7 and 8. In other words, y = 7.something
So x + y = 7 + 7.something = 14.something

e) x = 6
We get 6² + y² = 100
Evaluate: 36 + y² = 100
Simplify: y² = 64
Solve: y = 8
So x + y = 6 + 8 = 14

Answer: D

Cheers,
Brent
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 » Sun Jun 15, 2014 2:14 am
Julia W wrote:If x and y are positive and x^2+y^2=100, then for which of the following is the value of x+y greatest?

a) x = 10
b) x = 9
c) x = 8
d) x = 7
e) x = 6
Some reasoning behind the OA:

(x+y)² = x² + y² + 2xy.

Since x² + y² = 100, we get:
(x+y)² = 100 + 2xy.
x+y = √(100 + 2xy).

Implication:
To maximize the value of x+y, we must maximize the value of xy.

Given the constraint that x+y = k, where x, y and k are positive, the greatest possible value of xy occurs when x=y.
Example: x+y = 10
If x=5 and y=5, then xy = 5*5 = 25.
If x=6 and y=4, then xy = 6*4 = 24.
If x=7 and y=3, then xy = 7*3 = 21.
As the products above show, the greatest value of xy occurs when x=y.

Here, x² + y² = 100.
Implication:
The greatest possible value of xy occurs when x=y=√50.
Since √49 = 7, the answer choice closest to √50 is D.

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
Post new topic Post Reply
• Page 1 of 1