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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which of the following must be true?
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[email protected]
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cramya
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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^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^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!
(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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parallel_chase
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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.
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.
No rest for the Wicked....
x(x-y) = 0 implies that x = 0 or x = ycramya 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.
since x and y are diff integers, x = 0 is the solution...
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Ian Stewart
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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.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.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
ianstewartgmat.com
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Jeff@TargetTestPrep
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Let's simplify the given equation:[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
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
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