Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
Re: problem solving [#permalink]
08 Feb 2011, 05:33
This post received KUDOS
if x and y ARE different integers and x^2=xy which of the following must be true?
x=0 y=0 x=-y
a. 1 only b. 2 only c. 3 only d. 1 and 3 e. 1,2 and 3
x^2=xy --> x(x-y)=0 --> either x=0 or x=y but as given that x and y are different numbers than the second option is out and we have: x=0. So only I is always true (in fact because of the same reason that x and y are different numbers II and III are never true).
Re: different integers [#permalink]
03 Nov 2011, 22:07
This post received KUDOS
Okay, something is off here for me
What I did is this
X ^ 2 = xy
I took the square root of x ^ 2 so I ended up with
x = square root of (x.y) which means x = square root of (x) * square root of (y)
Therefore, square root of (y) will equal x/square root of (x)
If x is = 0 then it will be undefined. You can't divide by 0.
The same applies to the value of square root of (x) which will equal x/square root of (y). Therefore, y can't equal 0.
Anyone help me here?
First of all, square root of x^2 is |x|, not x. Do not take the square root until and unless you really need to. x^2 = xy You do not divide both sides by x here. You lose out on a solution. What you can very safely do is x^2 - xy = 0 x(x-y) = 0 Now, either x = 0 or x = y or both Since x and y are different, x must be 0.
When x = 0, no matter what the value of y, x^2 is equal to xy since both sides are equal to 0. Since x = 0, you cannot re-write this as y = x^2/x _________________
The question gives you x^2=xy
you can simplify that as x^2-xy=0
x(x-y)=0 the solution will be either x=0 or x=y, since x and y are different integers x cannot equal y, that leaves you x=0 to be the only answer.
Re: If x and y are different integers and x^2 = xy, which of the [#permalink]
19 Jan 2014, 00:07
Hello from the GMAT Club BumpBot!
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________