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If x = 3y, is x^2 > y^2?

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If x = 3y, is x^2 > y^2? [#permalink] New post 08 Oct 2006, 22:14
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If x = 3y, is x^2 > y^2?

(1) y+x < yx

(2) x^2 = 9y^2
[Reveal] Spoiler: OA
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 [#permalink] New post 09 Oct 2006, 00:16
x=3y

Stat1 : x+y<x*y

4y<3y^2

4<3y

4<x

x>4

therfore x is Positive and >4

Therefore x^2>y^2

Stat2 : is neway given in the question itself

Statement 1 is enough in itself to arrive at the anwser.

choice A

Not sure if this is the rite way to do it. It's just an attempt
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 [#permalink] New post 09 Oct 2006, 01:26
(D) for me.

No need statments :)

x = 3*y
=> x^2 = 9*y^2 Thus, x^2 > y^2
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 [#permalink] New post 09 Oct 2006, 06:34
iced_tea wrote:
Fig wrote:
(D) for me.

No need statments :)

x = 3*y
=> x^2 = 9*y^2 Thus, x^2 > y^2


what if y = 0 ?


Yes :D :)... U are right :).... always this case of y=0 or x=0, the one to keep in mind ;)

Thus, it turns to be (A) :)
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Re: DS - x, y [#permalink] New post 09 Oct 2006, 07:22
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if x^2>y^2
implies 9y^2>y^2
implies 8y^2>0 whic is always true for all values of y except zero.
so whichever option can let me know that either x or y are not zero.i'm through.

1. x+y<y*x
so 4y<3y^2
so y(y-4/3)<0
solving which we get either y>4/3 or <zero.
hence y cant be zero.hence x cant be zero.
so this choice helpsme ensure that y ,x cant assume zero value.

2. in this x=y=0 is a posiblity.

hence choice A should be the answer.

iced_tea wrote:
If x=3y, is x^2>y^2?

1). y+x<y*x

2). x^2=9y^2
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Re: If x=3y, is x^2>y^2? 1). y+x<y*x 2). x^2=9y^2 [#permalink] New post 27 Feb 2014, 08:56
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Re: If x = 3y, is x^2 > y^2? [#permalink] New post 25 Mar 2014, 20:31
iced_tea wrote:
If x = 3y, is x^2 > y^2?

(1) y+x < yx

(2) x^2 = 9y^2



1) As x=3y --> 4y<3y^2 --> y>(4/3) and x > 4
Number sub. If y=5/3 --> x=5 --> x^2>y^2
If y=2 --> x=6 --> x^2>y^2
So, 1 alone is sufficient.
2) x = 3y --> x^2=9y^2. So, not sufficient.

Therefore, A is the answer
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Re: If x = 3y, is x^2 > y^2? [#permalink] New post 25 Mar 2014, 22:28
iced_tea wrote:
If x = 3y, is x^2 > y^2?

(1) y+x < yx
(2) x^2 = 9y^2

Sol: Subsitute for x and we need to know whether 8y^2> 0
Or whether y is equal to zero or not

From st 1 we see that 4y<3y^2 or y*(3y-4) >0
We see that either y>0 and y>4/3 or y<0 or y< 4/3

This implies y not equal to zero hence thenl statement is suff.

St2 is same info as given in the question stem

So and is A

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Re: If x = 3y, is x^2 > y^2?   [#permalink] 25 Mar 2014, 22:28
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