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

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Senior Manager
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If x = 3y, is x^2 > y^2? [#permalink]

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08 Oct 2006, 22:14
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Question Stats:

42% (01:45) correct 58% (04:23) wrong based on 466 sessions

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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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Senior Manager
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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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SVP
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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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SVP
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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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Senior Manager
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Re: DS - x, y [#permalink]

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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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Intern
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Concentration: Marketing, Strategy
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Re: If x = 3y, is x^2 > y^2? [#permalink]

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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.

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Director
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Re: If x = 3y, is x^2 > y^2? [#permalink]

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25 Mar 2014, 22:28
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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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_________________

“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

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Re: If x = 3y, is x^2 > y^2? [#permalink]

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30 Jul 2015, 06:54
Question after re arranging becomes is (x+y)(x-y)>0.

So your question becomes is x>y>o?

1) subbing x=3y you know that y>0 and consequently x>0 therefore sufficient.

2) tells you nothing but repeats the stem therefore insufficient.

A

Cheers!

G

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Senior Manager
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If x = 3y, is x^2 > y^2? [#permalink]

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10 Dec 2017, 12:09
$$x = 3y$$

$$x^2 > y^2$$ ?
taking sq root on both sides, then question becoms

$$|x| > |y|$$?
$$|3y| > |y|$$ ?
$$2|y| > 0$$ ?

Modulus is always greater than or equal to zero.

Question is asking is y is not equal to zero ?

Statement 1:
$$y + x < yx$$
Let us assume y = 0, => 0 + x < 0 => x is negative
but question prompt says x = 3y, if y were 0, then x must be zero, but from above, we have x is negative
So our assumption y = 0 is not valid, so y cannot be zero => sufficient to answer the question

Statement 2:
$$x^2 = 9y^2$$ => y can be zero (hence x also) or can be any other number => InSuff

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If x = 3y, is x^2 > y^2?   [#permalink] 10 Dec 2017, 12:09
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