Data Sufficiency Q#59 from Algebra and equation solving module in GMAT Prep Now online course
does xy=x2 (x2 is x squares)
1)y2 - xy = 0 (y2 is x squared)
2)x2 - 2xy +y2 = 0 (x2 and y2 are squared)
I said answer was D that both are sufficient but the video said answer is B
but the way I solved statement 1) was as follows
y2 - xy = 0
--> y2 = xy add xy to both sides
--> y2/y = x divide both sides by y
--> y = x therefore xy must equal x2 and statement 1 should be sufficient in my eyes
where am I going wrong?
Does xy=x2 (the 2 is the exponent)
This topic has expert replies
-
- Newbie | Next Rank: 10 Posts
- Posts: 3
- Joined: Thu Feb 14, 2013 2:16 pm
GMAT/MBA Expert
- Brent@GMATPrepNow
- 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
The problem is where you divided both sides by y, because it may be the case that y=0, in which case our conclusion that y = x may not be true.[email protected] wrote:Data Sufficiency Q#59 from Algebra and equation solving module in GMAT Prep Now online course
does xy=x2 (x2 is x squares)
1)y2 - xy = 0 (y2 is x squared)
2)x2 - 2xy +y2 = 0 (x2 and y2 are squared)
I said answer was D that both are sufficient but the video said answer is B
but the way I solved statement 1) was as follows
y2 - xy = 0
--> y2 = xy add xy to both sides
--> y2/y = x divide both sides by y
--> y = x therefore xy must equal x2 and statement 1 should be sufficient in my eyes
where am I going wrong?
Consider this example: (2)(0) = (3)(0)
Divide both sides by 0 to get: 2 = 3
The big takeaway is that it's okay to divide both sides by a variable as long as we are certain that the variable does not equal zero.
Cheers,
Brent
-
- Newbie | Next Rank: 10 Posts
- Posts: 3
- Joined: Thu Feb 14, 2013 2:16 pm
-
- Master | Next Rank: 500 Posts
- Posts: 124
- Joined: Sun Mar 11, 2012 8:48 pm
- Thanked: 9 times
- Followed by:1 members
Hi,
You must have got that right by now.But still I will proceed with the below steps..
Rephrase the question as
xy-y^2=0
y(x-y) = 0
Any statement will be sufficient if we get to know either y is 0 or x-y is 0
1. y^2 - xy = 0
=> y( y-x) = 0
either y can be 0 or (x-y) can be 0 or both can be 0.Not sufficient.
2. x^2 - 2xy + y^2 = 0
=> (x-y)^2 = 0
=> (x-y) = 0.Sufficient
You must have got that right by now.But still I will proceed with the below steps..
Rephrase the question as
xy-y^2=0
y(x-y) = 0
Any statement will be sufficient if we get to know either y is 0 or x-y is 0
1. y^2 - xy = 0
=> y( y-x) = 0
either y can be 0 or (x-y) can be 0 or both can be 0.Not sufficient.
2. x^2 - 2xy + y^2 = 0
=> (x-y)^2 = 0
=> (x-y) = 0.Sufficient
GMAT/MBA Expert
- Anurag@Gurome
- GMAT Instructor
- Posts: 3835
- Joined: Fri Apr 02, 2010 10:00 pm
- Location: Milpitas, CA
- Thanked: 1854 times
- Followed by:523 members
- GMAT Score:770
Statement 1: y² - xy = 0 ---> y(x - y) = 0
Now either y = 0 or x = y
For y = 0, xy may not be equal to x²
For x = y, xy is always equal to x²
Not sufficient
Statement 2: x² - 2xy + y² = 0 ---> (x - y)² = 0 ---> x = y
Hence, xy is always equal to x²
Sufficient
The correct answer is B.
Anurag Mairal, Ph.D., MBA
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/
GMAT Expert, Admissions and Career Guidance
Gurome, Inc.
1-800-566-4043 (USA)
Join Our Facebook Groups
GMAT with Gurome
https://www.facebook.com/groups/272466352793633/
Admissions with Gurome
https://www.facebook.com/groups/461459690536574/
Career Advising with Gurome
https://www.facebook.com/groups/360435787349781/