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# If x and y are positive, which is greater between A and B?

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Math Expert
Joined: 02 Sep 2009
Posts: 60647
If x and y are positive, which is greater between A and B?  [#permalink]

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11 Nov 2019, 03:46
00:00

Difficulty:

75% (hard)

Question Stats:

43% (01:35) correct 57% (01:26) wrong based on 58 sessions

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If x and y are positive, which is greater between A and B?

(1) A = $$(x^3+y^3)^\frac{1}{3}$$

(2) B = $$(x^2+y^2)^\frac{1}{2}$$

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Joined: 02 Aug 2009
Posts: 8337
Re: If x and y are positive, which is greater between A and B?  [#permalink]

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13 Nov 2019, 00:38
Bunuel wrote:
If x and y are positive, which is greater between A and B?

(1) A = $$(x^3+y^3)^\frac{1}{3}$$

(2) B = $$(x^2+y^2)^\frac{1}{2}$$

Are You Up For the Challenge: 700 Level Questions

We have to look at the two statements combined..

take the sixth power..

(1) $$A^6=((x^3+y^3)^\frac{1}{3})^6=(x^3+y^3)^2=x^6+y^6+2x^3y^3$$

(2) $$B^6=((x^2+y^2)^\frac{1}{2})^6=(x^2+y^2)^3=x^6+y^6+3x^2y^4+3x^4y^2$$

when we check the two, we have to compare $$2x^3y^3$$ and $$3x^2y^4+3x^4y^2$$.....Now at least one of the term $$3x^2y^4$$ or $$3x^4y^2$$ will surely be greater than $$2x^3y^3$$.
Thus B>A

C
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Joined: 02 Aug 2009
Posts: 8337
Re: If x and y are positive, which is greater between A and B?  [#permalink]

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02 Jan 2020, 02:40
1
ShankSouljaBoi wrote:
chetan2u wrote:
Bunuel wrote:
If x and y are positive, which is greater between A and B?

(1) A = $$(x^3+y^3)^\frac{1}{3}$$

(2) B = $$(x^2+y^2)^\frac{1}{2}$$

Are You Up For the Challenge: 700 Level Questions

We have to look at the two statements combined..

take the sixth power..

(1) $$A^6=((x^3+y^3)^\frac{1}{3})^6=(x^3+y^3)^2=x^6+y^6+2x^3y^3$$

(2) $$B^6=((x^2+y^2)^\frac{1}{2})^6=(x^2+y^2)^3=x^6+y^6+3x^2y^4+3x^4y^2$$

when we check the two, we have to compare $$2x^3y^3$$ and $$3x^2y^4+3x^4y^2$$.....Now at least one of the term $$3x^2y^4$$ or $$3x^4y^2$$ will surely be greater than $$2x^3y^3$$.
Thus B>A

C

Hi chetan2u ,

When we put x=y=1 . A becomes equal to B . So the answer to the question is B > A ? Becomes No. hence, insufficient.

Kindly guide

Regards

No, they are different
A=(1^3+1^3)^(1/3)=2^(1/3)
B=(1^2+1^2)^(1/2)=2^(1/2)
B>A
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If x and y are positive, which is greater between A and B?  [#permalink]

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02 Jan 2020, 06:57
Hi chetan2u ,

i have realized my mistake. Thank you

Regards
If x and y are positive, which is greater between A and B?   [#permalink] 02 Jan 2020, 06:57
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