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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Does xy=x2 (the 2 is the exponent)
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Brent@GMATPrepNow
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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
Brent Hanneson - Creator of GMATPrepNow.com
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aaggar7
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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
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Anurag@Gurome
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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
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