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joemama142000
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inequality ds x 16 Jan 2006, 02:19
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is x^2 + y ^2 >6?

1) (x+y )^2 >6

2) xy=2



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inequality ds x 16 Jan 2006, 02:40
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Who knows how to factorise x^2 + y^2 ?

Without this knowledge I say it's E

1) probably insufficient
2) insufficient

1+2)

x^2 + 2xy + y^2 > 6

x^2 + y^2 > 2

Thus it may be greater than 6 but has not to be.
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inequality ds x 16 Jan 2006, 03:01
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E

1. (x+y)^2 > 6 i.e x+y > 2.44

Considering st1 true, Minimum value of x^2 + y^2 will be when both x and y are equal i.e x = 1.23 and y = 1.23. In this case x^2 + y^2 = 3.0258 i.e main stem is FALSE

When x = 5.44 and y = -3 then x^2 + y^2 is certanly greater than 6 i.e main stem is TRUE

So INSUFF

2. xy = 2 Clearly INSUFF

Combined:

x^2 + y^2 > 6 - 4 i.e x^2 + y^2 > 2 INSUFF
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inequality ds x 16 Jan 2006, 03:52
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joemama142000
is x^2 + y ^2 >6?

1) (x+y )^2 >6

2) xy=2
Show more



1)we have: x^2+ y^2 > [(x+y)^2 ]/ 2 > 6/2= 3 ---> not sufficient enough to answer the question

2) we have: x^2+ y^2> 2xy = 2*2=4 ---> also not sufficient enough to answer the question.

1 and 2)

(x+y)^2 > 6 --> x^2+y^2 + 2xy > 6
2xy= 4 ---> x^2+y^2 > 6-4= 2 ---> also not sufficient enough to answer the question

E it is.
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inequality ds x 16 Jan 2006, 03:57
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allabout
Who knows how to factorise x^2 + y^2 ?

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we can't factorize x^2+y^2 , the same with x^4+ y^4

Generally speaking, x^n + y^n can't be factorize in case n is a power of 2, for example: 2, 4, 8, 16, etc....

@allabout: buddy, i don't know what link can provide all the formulas :? ..but i guess GMAT won't test that far like asking you to factorize x^9+y^9. I'll let you know if i can find such a link for next post( soon), i'll provide you with general formula, okie?!! :wink:
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inequality ds x 16 Jan 2006, 05:04
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ps_dahiya
E

1. (x+y)^2 > 6 i.e x+y > 2.44

Considering st1 true, Minimum value of x^2 + y^2 will be when both x and y are equal i.e x = 1.23 and y = 1.23. In this case x^2 + y^2 = 3.0258 i.e main stem is FALSE

When x = 5.44 and y = -3 then x^2 + y^2 is certanly greater than 6 i.e main stem is TRUE

So INSUFF

2. xy = 2 Clearly INSUFF

Combined:

x^2 + y^2 > 6 - 4 i.e x^2 + y^2 > 2 INSUFF
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the oa is E

ps_dahiya how do you know this?
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inequality ds x 16 Jan 2006, 08:22
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clearly E.

1. insuff.

2. insfuff

1 and 2 insuff as (x, y ) can be (2,1), (-2, -1), (1/2, 4) (1/8,16) any of these..
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inequality ds x 16 Jan 2006, 09:09
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x^2 + y^2 = (x+y)^2 -2xy.
Thats how I came to soln..

(x+y )^2 > 6, -2xy = -4

> 2?

We still dont know i f>6
Hence E
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inequality ds x 16 Jan 2006, 22:21
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1) (x+y)^2 = x^2 + 2xy + y^. We do not know the value of 2xy. If it's positive, then x^2 + y^2 could be less than six. Insufficient.

2) xy = 2. x could be 10, y = 1/5 then x^2 + y^2 > 6. However, x could be 2 and y is 1 then x^2 + y^2 < 6

Using (1) and (2), we know x^2 + 4 + y^2 > 6 --> x^2 + y^2 > 4. Not conclusive again.

Ans: E
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inequality ds x 17 Jan 2006, 01:40
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joemama142000
ps_dahiya
E

1. (x+y)^2 > 6 i.e x+y > 2.44

Considering st1 true, Minimum value of x^2 + y^2 will be when both x and y are equal i.e x = 1.23 and y = 1.23. In this case x^2 + y^2 = 3.0258 i.e main stem is FALSE

When x = 5.44 and y = -3 then x^2 + y^2 is certanly greater than 6 i.e main stem is TRUE

So INSUFF

2. xy = 2 Clearly INSUFF

Combined:

x^2 + y^2 > 6 - 4 i.e x^2 + y^2 > 2 INSUFF

the oa is E

ps_dahiya how do you know this?
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To find minimum value we have to take x + y minimum possible. When x increases then y decreases (because x+y > 2.44) so x^2 + y^2 will increases thats why when both are equal then x^2 + y^2 will be minimum.

Example x = 1.23 and y = 1.23 Then x^2 + y^2 = 3.0258
x = 1.3 and y = 1.16 then x^2 + y^2 = 3.0356
x = 2 and y = 0.44 then x^2 + y^2 = 4.1936 and so on......



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Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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