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which of the following must be true?

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by [email protected] » Sun Dec 28, 2008 11:22 am
if x and y are different integers and x^2=xy, which of the following must be true?
i. x=0
ii. y=0
iii. x=-y

A) i
B) ii
C) iii
D)i and iii
E) i, ii and iii

A

i usually don't get these kind of questions, this there a concept that i don't know?
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by cramya » Sun Dec 28, 2008 11:28 am
I am not sure on the oa?

x^2 = xy
x^2 - xy = 0

x(x-y) = 0

x does not have to be zero x-y could be 0

x=2 y=2

still the expression above is 0

I would say none but there is no choice like that.
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Re: which of the following must be true?

by aroon7 » Sun Dec 28, 2008 11:31 am
x^2 = xy
(1) when x is 0, above eqn is satisfied regardless of y - true
(2) when x is not zero, the eqn is not satified
eg whn x = 2, 2*2 is not equal to 2 * 0 - false
(3) when x = -y, clearly product xy is negative.
but x^2 is positive - doesnt satify eqn

hence ans is A

Thanks!
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by cramya » Sun Dec 28, 2008 11:34 am
U r correct.

Missed the different intgers part totally.

Well put!
Last edited by cramya on Sun Dec 28, 2008 11:34 am, edited 1 time in total.
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Re: which of the following must be true?

by parallel_chase » Sun Dec 28, 2008 11:34 am
x^2 = xy
x^2-xy = 0
x (x-y) = 0

Therefore, only 2 cases can be true

either x = 0 or x=y

Therefore, answer has to be A.

Hope this helps.
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by aroon7 » Sun Dec 28, 2008 11:34 am
cramya wrote:I am not sure on the oa?

x^2 = xy
x^2 - xy = 0

x(x-y) = 0

x does not have to be zero x-y could be 0

x=2 y=2

still the expression above is 0

I would say none but there is no choice like that.
x(x-y) = 0 implies that x = 0 or x = y
since x and y are diff integers, x = 0 is the solution...
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by Ian Stewart » Sun Dec 28, 2008 11:34 am
cramya wrote:I am not sure on the oa?

x^2 = xy
x^2 - xy = 0

x(x-y) = 0

x does not have to be zero x-y could be 0

x=2 y=2

still the expression above is 0

I would say none but there is no choice like that.
Your analysis is perfect, but it's important to read the question very carefully. It says: "if x and y are different integers "... So certainly x -y cannot be zero, since x and y are different, which means x must be zero.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by cramya » Sun Dec 28, 2008 11:36 am
Thanks Ian!

Missed the different intgers part totally like u said.

Thanksl for pointing it out...

Regards,
Cramya
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by Jeff@TargetTestPrep » Thu Dec 14, 2017 6:02 pm
[email protected] wrote:if x and y are different integers and x^2=xy, which of the following must be true?
i. x=0
ii. y=0
iii. x=-y

A) i
B) ii
C) iii
D)i and iii
E) i, ii and iii
Let's simplify the given equation:

x^2 = xy

x^2 - xy = 0

x(x - y) = 0

x = 0 or x - y = 0

x = 0 or x = y

Notice that it is given in the question that x and y are different integers; therefore x = y is not possible. Thus, it must be true that x = 0. None of the other Roman numerals need to be true, as we can see by letting x = 0 and y = 1.

Answer: A

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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