Does xy=x2 (the 2 is the exponent)

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Does xy=x2 (the 2 is the exponent)

by [email protected] » Mon Mar 04, 2013 12:27 pm
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?

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by Brent@GMATPrepNow » Mon Mar 04, 2013 12:33 pm
[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?
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.

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
Brent Hanneson - Creator of GMATPrepNow.com
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by [email protected] » Mon Mar 04, 2013 12:36 pm
Makes perfect sense! thank much - I knew I must have been forgetting one rule or another.

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by aaggar7 » Mon Mar 04, 2013 7:29 pm
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

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by Anurag@Gurome » Mon Mar 04, 2013 9:12 pm
[email protected] wrote:Does xy = x²?
1)y² - xy = 0
2)x² - 2xy + y² = 0
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.
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