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Is b^2 <= a^2?

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Is b^2 <= a^2?  [#permalink]

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New post Updated on: 07 Oct 2018, 20:57
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Is \(b^2≤a^2\)

(1) b ≤ a

(2) a+b = a−b

Originally posted by Kaczet on 06 Oct 2018, 09:03.
Last edited by amanvermagmat on 07 Oct 2018, 20:57, edited 2 times in total.
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Re: Is b^2 <= a^2?  [#permalink]

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New post 06 Oct 2018, 18:45
Kaczet wrote:
Is \(a^2≤b^2\)

(1) b ≤ a

(2) a+b = a−b



\(a^2\leq{b^2}......|a|\leq{|b|}\)


(1) b ≤ a
If a>0 and b<0,
say a=10 and b =3 a^2>b^2
but if a=3 and b=-10 a^2<b^2
Insufficient

(2) a+b = a−b
So 2b=0 or b=0
So b^2=0 and whatever be the value of a, a^2 will never be less than 0
Sufficient

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Re: Is b^2 <= a^2?  [#permalink]

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New post 06 Oct 2018, 22:25
chetan2u

Hi

Having issue with statement 2.
If b =o
The stem becomes is a less than or equal to zero ?

Case 1 A is anything but zero.
Answer to stem No

Case 2 A is zero.
Answer to stem Yes a^2 is less than or equal to zero

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Re: Is b^2 <= a^2?  [#permalink]

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New post 06 Oct 2018, 22:28
ShankSouljaBoi wrote:
chetan2u

Hi

Having issue with statement 2.
If b =o
The stem becomes is a less than or equal to zero ?

Case 1 A is anything but zero.
Answer to stem No

Case 2 A is zero.
Answer to stem Yes a^2 is less than or equal to zero

Posted from my mobile device


No it doesn't say anything about a..

a+b=a-b
Say b is 0, then a+0=a-0....a=a
Always true' irrespective of the value of a
So a can be anything
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2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Is b^2 <= a^2?  [#permalink]

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New post 06 Oct 2018, 23:11
chetan2u wrote:
ShankSouljaBoi wrote:
chetan2u

Hi

Having issue with statement 2.
If b =o
The stem becomes is a less than or equal to zero ?

Case 1 A is anything but zero.
Answer to stem No

Case 2 A is zero.
Answer to stem Yes a^2 is less than or equal to zero

Posted from my mobile device


No it doesn't say anything about a..

a+b=a-b
Say b is 0, then a+0=a-0....a=a
Always true' irrespective of the value of a
So a can be anything


Still , not clear.

Rephrasing stem with statement 2.

Is a^2 <=0 ?

Case 1 a=0 . Yes inequality hold true.

Case 2 a is not equal to zero. No inequality is false.

Please guide.
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Re: Is b^2 <= a^2?  [#permalink]

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New post 07 Oct 2018, 05:56
ShankSouljaBoi of course, you are right. That's why I asked the said question on forums. It appeared that way to me during my CAT.
I started scrutinizing the question anew, and corrected it after I had found the typo. Thanks for vigilance.
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Re: Is b^2 <= a^2?  [#permalink]

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New post 07 Oct 2018, 06:02
Kaczet wrote:
ShankSouljaBoi of course, you are right. That's why I asked the said question on forums. It appeared that way to me during my CAT.
I started scrutinizing the question anew, and corrected it after I had found the typo. Thanks for vigilance.


heheh no worries. Im glad i could help
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Re: Is b^2 <= a^2?  [#permalink]

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New post 14 Oct 2018, 11:13
answer shall be E, not sure how B is marked as OA
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Re: Is b^2 <= a^2?  [#permalink]

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New post 14 Oct 2018, 11:14
Hi Bunuel,

please check and update the OA if found wrong.
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Is b^2 <= a^2?  [#permalink]

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New post 14 Oct 2018, 12:18
asthagupta wrote:
answer shall be E, not sure how B is marked as OA


B is the correct answer.

From the statement (2) you have that b=0; no matter what, a^2 can't be less than 0.
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Re: Is b^2 <= a^2?  [#permalink]

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New post 16 Oct 2018, 22:43
Kaczet wrote:
asthagupta wrote:
answer shall be E, not sure how B is marked as OA


B is the correct answer.

From the statement (2) you have that b=0; no matter what, a^2 can't be less than 0.

question is saying less than or EQUAL to,
even if B is 0, A can be zero and hence A=B
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Re: Is b^2 <= a^2?  [#permalink]

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New post 17 Oct 2018, 00:06
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asthagupta wrote:
Kaczet wrote:
asthagupta wrote:
answer shall be E, not sure how B is marked as OA


B is the correct answer.

From the statement (2) you have that b=0; no matter what, a^2 can't be less than 0.

question is saying less than or EQUAL to,
even if B is 0, A can be zero and hence A=B


The statement holds true even if A=B, doesn't it?
From (B) we have that B=0. If A=B=0 then a^2 = b^2. If a≠0 and b=0, then a^2>b^2 no matter what.
You did underscore "equal" yourself, I don't see the problem.
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Re: Is b^2 <= a^2? &nbs [#permalink] 17 Oct 2018, 00:06
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