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Is a^3-b^2>0?

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Joined: 19 Jul 2013
Posts: 43

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Updated on: 07 May 2017, 02:34
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Difficulty:

85% (hard)

Question Stats:

42% (01:42) correct 58% (01:29) wrong based on 135 sessions

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$$a^3 - b^2 > 0?$$
1. b > 0
2. a > |b|

Originally posted by rajarshee on 06 May 2017, 21:39.
Last edited by chetan2u on 07 May 2017, 02:34, edited 1 time in total.
updated the OA
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Joined: 02 Aug 2009
Posts: 6810
Re: Is a^3-b^2>0?  [#permalink]

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06 May 2017, 22:39
1
3
rajarshee wrote:
$$a^3 - b^2 > 0?$$
1. b > 0
2. a > |b|

Hi,

I do not think the answer should be B, it has to be E and this is WHY...
$$a^3-b^2>0$$...
Here b^2 will always be POSITIVE, so -b^2 will be NEGATIVE..
a^3 will depend on a...

Let's see the statements..
1) b>0..
We have b^2 which is always POSITIVE, so b >0 really doesn't help much..
Insufficient
2) a>|b|
This tells us that a is positive and also GREATER than numeric value of b..
If a >1, a^3 will be greater than b^2 and so ans will always be YES..
But if a is between 0 and 1, and will vary..
Say a=0.2 and b=0.1.....
Hence a>|b| but a^3=0.2^3=0.008 and b^2=0.1^2=0.01.... 0.01>0.008 or b^2>a^3
Now if a=0.9 and b=0.1 ....... a>|b| and a^3>b^2
Insufficient..

Combined nothing new ..
Insufficient

E
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Re: Is a^3-b^2>0?  [#permalink]

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06 May 2017, 22:42
IMHO B
Statement 1: b>0 doesn't tell anything about a. So insufficient.

Statement 2: a>|b| tells us a is positive and its value greater than absolute value of b.

Therefore a^2 >b^2 and since a is positive a^3>b^2
a^3-b^2>0
Sufficient
Ans B

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Re: Is a^3-b^2>0?  [#permalink]

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06 May 2017, 22:45
1
Clearly missed the a<1 scenario.
E is right

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Re: Is a^3-b^2>0?  [#permalink]

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07 May 2017, 20:46
1
Sorry folks, as you pointed out the answer provided was incorrect. Picked it up from a compiled set of questions in a pdf and so not a very reliable source for an answer.
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Re: Is a^3-b^2>0?  [#permalink]

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26 May 2018, 23:23
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Re: Is a^3-b^2>0? &nbs [#permalink] 26 May 2018, 23:23
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