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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, 21:57
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Is \(b^2≤a^2\)

(1) b ≤ a

(2) a+b = a−b

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21.07.2018 OG gmat prep 400 (Q26,V20)
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06.10.2018 Economist xxx (Q??, V38) - tested the verbal part only.


Originally posted by Kaczet on 06 Oct 2018, 10:03.
Last edited by amanvermagmat on 07 Oct 2018, 21:57, 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, 19:45
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, 23:25
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

Posted from my mobile device
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Re: Is b^2 <= a^2?  [#permalink]

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New post 06 Oct 2018, 23:28
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
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 07 Oct 2018, 00:11
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, 06:56
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, 07:02
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, 12:13
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, 12:14
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, 13:18
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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12.08.2018 MGMAT 680 (Q49, V33)
06.10.2018 Economist xxx (Q??, V38) - tested the verbal part only.

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Re: Is b^2 <= a^2?  [#permalink]

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New post 16 Oct 2018, 23:43
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, 01:06
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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Going to take the real test in November...

21.07.2018 OG gmat prep 400 (Q26,V20)
28.07.2018 OG gmat prep 550 (Q42,V23)
04.08.2018 MGMAT 680 (Q50,V31)
12.08.2018 MGMAT 680 (Q49, V33)
06.10.2018 Economist xxx (Q??, V38) - tested the verbal part only.

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Re: Is b^2 <= a^2? &nbs [#permalink] 17 Oct 2018, 01:06
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