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# If A = 2B, is A^4 > B^4?

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Math Expert
Joined: 02 Sep 2009
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If A = 2B, is A^4 > B^4?  [#permalink]

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23 Jun 2016, 01:12
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Difficulty:

65% (hard)

Question Stats:

51% (02:20) correct 49% (02:30) wrong based on 89 sessions

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If A = 2B, is A^4 > B^4?

(1) A^2 = 4B^2.
(2) 2A + B < A/2 + B.

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Joined: 04 Jun 2016
Posts: 571
GMAT 1: 750 Q49 V43
Re: If A = 2B, is A^4 > B^4?  [#permalink]

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23 Jun 2016, 01:43
If A = 2B, is A^4 > B^4?
A and B both can be positive or both can be negative. (Question stem )
(1) A^2 = 4B^2.
YES , If A=2B, squaring will give A^2=4B^2 (since it a square function, it will take care of any negative sign)

(2) 2A + B <A/2+B
2A<A/2
A/2>2A
A>4A => A is negative; so B is also negative.
A has a bigger magnitude than B
so A^4>B^4 (rasing a negative number to a even power will yield a positive number and since A is greater in magnitude its value after ^4 will be more than B)
YES

Bunuel wrote:
If A = 2B, is A^4 > B^4?

(1) A^2 = 4B^2.
(2) 2A + B < A/2 + B.

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Re: If A = 2B, is A^4 > B^4?  [#permalink]

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23 Jun 2016, 03:12
LogicGuru1 wrote:
If A = 2B, is A^4 > B^4?
A and B both can be positive or both can be negative. (Question stem )
(1) A^2 = 4B^2.
YES , If A=2B, squaring will give A^2=4B^2 (since it a square function, it will take care of any negative sign)

(2) 2A + B <A/2+B
2A<A/2
A/2>2A
A>4A => A is negative; so B is also negative.
A has a bigger magnitude than B
so A^4>B^4 (rasing a negative number to a even power will yield a positive number and since A is greater in magnitude its value after ^4 will be more than B)
YES

Bunuel wrote:
If A = 2B, is A^4 > B^4?

(1) A^2 = 4B^2.
(2) 2A + B < A/2 + B.

I think the answer is B. The reason is condition 1 fails for B = 0
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Joined: 02 Aug 2009
Posts: 7108
Re: If A = 2B, is A^4 > B^4?  [#permalink]

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17 Jul 2017, 08:41
4
Bunuel wrote:
If A = 2B, is A^4 > B^4?

(1) A^2 = 4B^2.
(2) 2A + B < A/2 + B.

Hi..
$$A=2B.......A^4=16B^4$$...
is $$A^4 > B^4$$?
if A=B=0 ans is NO, otherwise YES

lets see the statements

(1) $$A^2 = 4B^2$$.
Nothing New .. already given from A=2B
insuff

(2) 2A + B < A/2 + B
$$\frac{3A}{2}<0$$..
so A is NOT equal to 0
suff

B
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Re: If A = 2B, is A^4 > B^4?  [#permalink]

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24 Feb 2018, 14:11
1
A = 2B, then the question is if 16B^4 > B^4?
B^4 is always positive and if B^4 ≠ 0, we can affirm that 16B^4 > B^4. But as B could be equal to Zero, we need to evaluate the statements

Statement 1:
A^2 = 4B^2
Well, the question stem gave the information that A = 2B so A^2 is 4B^2. We know that from the question stem and this statement doesn't help at all.

Statement 2:
2A + B < A/2 + B (rule out the Bs)
2A < A/2
2A - A/2 < 0
3A/2 < 0

So A is a negative number and ≠ than 0.
Statement 2 is sufficient to answer the question and affirm that 16B^4 > B^4!
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Re: If A = 2B, is A^4 > B^4? &nbs [#permalink] 24 Feb 2018, 14:11
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