Roots

This topic has expert replies
Legendary Member
Posts: 882
Joined: Fri Feb 20, 2009 2:57 pm
Thanked: 15 times
Followed by:1 members
GMAT Score:690

Roots

by crackgmat007 » Fri Oct 02, 2009 7:48 pm
How many roots does this equation have? A*X+A=B

A does not equal 0
B does not equal 0

OA - A

What does roots mean?
Source: — Data Sufficiency |

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

Re: Roots

by Brent@GMATPrepNow » Sat Oct 03, 2009 7:08 am
crackgmat007 wrote:How many roots does this equation have? A*X+A=B

A does not equal 0
B does not equal 0

OA - A

What does roots mean?
"roots" = "solutions"
So, x=3 is a root (solution) to the equation 2x+1=7

This is a misleading question, and it's certainly not an official question.
Based on the solution, it is assumed that x is the only variable that we are solving for but this is not stated (i.e., are we solving for x or solving for x and B?). For example, if A=1, we get the equation x+1=B. Well, here are a few solutions to this equation:
x=1, B=2
x=2, B=3
x=3, B=4 etc
However, an "official answer" of A tells me that B is meant to be a constant and we are merely solving for x (rather than for 2 variables). So, if A doesn't equal zero (statement 1) and B is some constant (although not stated), then we have a linear equation and linear equations have one one solution (thus an OA of A).
Brent Hanneson - Creator of GMATPrepNow.com
Image