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

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

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New post 19 Aug 2015, 02:47
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Question Stats:

55% (01:40) correct 45% (01:24) wrong based on 133 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 = \((x^2+y^2)^\frac{1}{2}\)

Source : Aristotle Prep

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Re: If x and y are positive, which is greater between A and B?  [#permalink]

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New post 19 Aug 2015, 04:25
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Gnpth 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 = \((x^2+y^2)^\frac{1}{2}\)

Source : Aristotle Prep


2 statements are individually not sufficient.

Combining, we need to check 3 cases, when x and y <1, when x=1=y, x=10=y (large number)

Case 1, x=y=0.5,A= \((0.125+0.125)^{1/3} = 0.25^{1/3}\), and B =\((0.25+0.25)^{1/2}\) = \(0.5^{1/2}\). Clearly A<B

Case 2, x=y=1, A = \((2)^{1/3)\), B = \((2)^{1/2)\), again A<B

Case 3, x=y=10, A = \((2000)^{1/3)\) = \(10*(2)^{1/3)\), and B = \((2000)^{1/2)\) = \(10(20)^{1/2)\), again A<B

Thus, we get a consistent A<B for all 3 cases. C is the correct answer.
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Re: If x and y are positive, which is greater between A and B?  [#permalink]

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New post 17 Mar 2016, 04:58
1
Gnpth 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 = \((x^2+y^2)^\frac{1}{2}\)

Source : Aristotle Prep

expanding the terms of A and B after taking power of 6, we get to check only 2*x*y and 3(x^2+y^2)
I just plugged in values x=y=1; x=y=1/2; x=5 and y=10; x=1/2 and y=1/3
In all the cases, we get A<B
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Re: If x and y are positive, which is greater between A and B?  [#permalink]

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New post 27 Apr 2017, 00:16
Engr2012 wrote:
Gnpth 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 = \((x^2+y^2)^\frac{1}{2}\)

Source : Aristotle Prep


2 statements are individually not sufficient.

Combining, we need to check 3 cases, when x and y <1, when x=1=y, x=10=y (large number)

Case 1, x=y=0.5,A= \((0.125+0.125)^{1/3} = 0.25^{1/3}\), and B =\((0.25+0.25)^{1/2}\) = \(0.5^{1/2}\). Clearly A<B

Case 2, x=y=1, A = \((2)^{1/3)\), B = \((2)^{1/2)\), again A<B

Case 3, x=y=10, A = \((2000)^{1/3)\) = \(10*(2)^{1/3)\), and B = \((2000)^{1/2)\) = \(10(20)^{1/2)\), again A<B

Thus, we get a consistent A<B for all 3 cases. C is the correct answer.


I still doubt that the solution is always right.
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Re: If x and y are positive, which is greater between A and B?  [#permalink]

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New post 04 Jul 2017, 00:25
Gnpth 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 = \((x^2+y^2)^\frac{1}{2}\)

Source : Aristotle Prep



If you raise both A & B to the power 6, you can get A = (x^3 + y^3)^2 vs B = (x^2 + y^2)^3.
Following which its given x & y are positive, hence can use substitution of any two numbers for x and y say 3&5 to check for whole numbers and compare fractions as well 1/2 & 1/3, in both cases equation B will be greater than A.
Do note fraction don't bother going all the way, you just need to estimate which would be bigger, if you take x as 1/2 and b as 1/3, A = (35/216)^2 vs B =(13/36)^3.
Would recommend, estimate and arrive at answer instead of fully solving it.

It takes close to 1:46 for me doing it this way.
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Re: If x and y are positive, which is greater between A and B?   [#permalink] 04 Jul 2017, 00:25
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If x and y are positive, which is greater between A and B?

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