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

Redeem

For all real numbers x and y, let x# y = (xy)^2 − x + y^2

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
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 » Wed Aug 15, 2018 5:13 am
BTGmoderatorDC wrote:For all real numbers x and y, let x# y = (xy)² − x + y² . What is the value of y that makes x # y equal to -x for all values of x ?

(A) 0
(B) 2
(C) 5
(D) 7
(E) 10
APPROACH #1
We want the following equation to hold true: x # y = -x
Replace x # y with its equivalent to get: (xy)² − x + y² = -x
Add x to both sides to get: (xy)² + y² = 0
Simplify (xy)² to get: x²y² + y² = 0
Factor out the y² to get: y²(x² + 1) = 0
So, the equation will hold true when EITHER y² = 0 OR x² + 1 = 0
If y² = 0, then y =0

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

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 » Wed Aug 15, 2018 5:16 am
BTGmoderatorDC wrote:For all real numbers x and y, let x#y = (xy)^2 − x + y^2 . What is the value of y that makes x # y equal to -x for all values of x ?

(A) 0
(B) 2
(C) 5
(D) 7
(E) 10
APPROACH #2 - Test the answer choices

A) 0
Take x#y = (xy)² − x + y², and replace y with 0
We get: [(x)(0)]² − x + 0² = [0]² − x + 0
= -x
So, when y = 0, x#y = -x
PERFECT!

Answer: A

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8085
Joined: Sat Apr 25, 2015 10:56 am
Location: Los Angeles, CA
Thanked: 43 times
Followed by:29 members

by Scott@TargetTestPrep » Fri Apr 19, 2019 9:15 am
BTGmoderatorDC wrote:For all real numbers x and y, let x# y = (xy)^2 − x + y^2 . What is the value of y that makes x # y equal to -x for all values of x ?

(A) 0
(B) 2
(C) 5
(D) 7
(E) 10

OA A

Source: Princeton Review
If y = 0, then x # 0 is:

0 - x + 0 = -x

Alternate solution:

We want x # y = -x, i.e.,

(xy)^2 - x + y^2 = -x

x^2y^2 + y^2 = 0

y^2(x^2 + 1) = 0

Since x^2 + 1 can't be 0, y^2 must be 0, and hence y must be 0.


Answer: A

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Post new topic Post Reply
• Page 1 of 1