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# Does xy=x^2 ?

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09 Jan 2004, 17:44
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This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Again, I disagree with the OA provided for a question. This one is taken from the 3rd CAT of the PR CD.

Does xy=x^2 ?

(1) xy=y^2
(2) x^2=y^2
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09 Jan 2004, 17:48
Martin is it C by combining both the statements we can say that xy=y^2
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09 Jan 2004, 18:00
rakesh1239 wrote:
Martin is it C by combining both the statements we can say that xy=y^2

Answer is C but I get D. Could you tell me what I'm doing wrong?

(1) xy=y^2 then x=y^2/y then x=y so xx=x^2 suff.

If xy=x^2 then x^2*y^2=x^4

(2) x^2=y^2 substitute above then you get x^2*x^2=x^4
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09 Jan 2004, 18:06
substitute the value of statement 1 in 2 or statement 2 in 1, we can cancel out y^2 and say that xy=x^2
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09 Jan 2004, 18:28
rakesh1239 wrote:
substitute the value of statement 1 in 2 or statement 2 in 1, we can cancel out y^2 and say that xy=x^2

Yeah, I know. I was showing you a way in which each statement by itself is sufficient. If my reasoning is correct then answer should be D instead of C. (D beats C in DS)

Do you see anything wrong in my last post?
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09 Jan 2004, 18:37
in the first statement u derived x=y^2/y , cancelled y with y and said x=y but y can be -ve too, in which case x= -y
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09 Jan 2004, 18:46
rakesh1239 wrote:
in the first statement u derived x=y^2/y , cancelled y with y and said x=y but y can be -ve too, in which case x= -y

But x could no be -y , suppose x=2 and y=-2

then if x*y=y*y we would get 2*(-2)=(-2)*(-2) => -4=4 not possible
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09 Jan 2004, 18:53
that was what i was saying that in ur case in the 1st statement u r getting x= -y which cant be and so we need to combine both the statements
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09 Jan 2004, 20:13
I still don't see how I could get x=-y

All I said was that if we have X*Y=Y*Y then X=Y
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10 Jan 2004, 23:59
Hmmm...i get A

Does xy=xx

For statement 1: xy has to be + since yy is + and xy=yy so either x=y or -x=-y will work.

For statement 2: we agree that x=-1 and y=1 will work since xx & yy will be positive so it doesnt matter what the sign for x or y is but it will for the stem xy=xx

I'm lost...can any explain...or show me my error?
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14 Jan 2004, 08:35
Anybody else wants to try this problem?

We are all getting different answers...
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14 Jan 2004, 08:57
Does xy=x^2 ?

(1) xy=y^2
(2) x^2=y^2

1) consider (1,0). It makes (1) correct, but it does not make the problem correct. (1,1) on the other hand, makes both of them correct. Insufficient.

2) tells us only that the absolute value of X is the absolute value of y. not sufficient, since if x is negative and y is positive, that the equation holds, but if x is positive and y is negative, the equation does not hold. insufficient.

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20 Jan 2004, 20:58
Here is how it should go.

(1) xy = y^2 => y^2 - xy = 0 => y(y-x) = 0

=> y = 0 or y = x
If y = 0 then the question becomes is x^2 = 0? we do not know.

if y= x, then LHS of the question becomes x^2. so the answer is yes.

So the statement 1 insufficient

(2) x^2 = y^2

=> x^2 - y^2 = 0 => (x+y) (x-y) = 0

=> x = -y or x = y

If x = -y => y = -x, the question becomes is -x^2 = x^2, the answer is NO

If x = y then the answer to the question is YES.

sO (2) INSUFFICIENT

TOGETHER

statement (1) gives y = 0 or y = x
statement(2) gives x = -y or x = y

20 Jan 2004, 20:58
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