GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 Oct 2018, 22:21

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Is b^2 <= a^2?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 20 Jul 2018
Posts: 40
Location: Poland
Schools: Imperial '21

### Show Tags

Updated on: 07 Oct 2018, 21:57
6
00:00

Difficulty:

65% (hard)

Question Stats:

51% (01:10) correct 49% (00:58) wrong based on 122 sessions

### HideShow timer Statistics

Is $$b^2≤a^2$$

(1) b ≤ a

(2) a+b = a−b

_________________

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.

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.
Math Expert
Joined: 02 Aug 2009
Posts: 6986
Re: Is b^2 <= a^2?  [#permalink]

### Show Tags

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

B
_________________

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

GMAT online Tutor

Manager
Joined: 21 Jun 2017
Posts: 91
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: Is b^2 <= a^2?  [#permalink]

### Show Tags

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.

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

Posted from my mobile device
_________________

Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Math Expert
Joined: 02 Aug 2009
Posts: 6986
Re: Is b^2 <= a^2?  [#permalink]

### Show Tags

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.

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
_________________

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

GMAT online Tutor

Manager
Joined: 21 Jun 2017
Posts: 91
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: Is b^2 <= a^2?  [#permalink]

### Show Tags

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.

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.

_________________

Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Intern
Joined: 20 Jul 2018
Posts: 40
Location: Poland
Schools: Imperial '21
Re: Is b^2 <= a^2?  [#permalink]

### Show Tags

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.
_________________

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.

Manager
Joined: 21 Jun 2017
Posts: 91
Concentration: Finance, Economics
WE: Corporate Finance (Commercial Banking)
Re: Is b^2 <= a^2?  [#permalink]

### Show Tags

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
_________________

Even if it takes me 30 attempts, I am determined enough to score 740+ in my 31st attempt. This is it, this is what I have been waiting for, now is the time to get up and fight, for my life is 100% my responsibility.

Manager
Joined: 10 Sep 2015
Posts: 73
Location: India
Concentration: Finance, Human Resources
GMAT 1: 640 Q47 V31
GPA: 4
Re: Is b^2 <= a^2?  [#permalink]

### Show Tags

14 Oct 2018, 12:13
answer shall be E, not sure how B is marked as OA
Manager
Joined: 10 Sep 2015
Posts: 73
Location: India
Concentration: Finance, Human Resources
GMAT 1: 640 Q47 V31
GPA: 4
Re: Is b^2 <= a^2?  [#permalink]

### Show Tags

14 Oct 2018, 12:14
Hi Bunuel,

please check and update the OA if found wrong.
Intern
Joined: 20 Jul 2018
Posts: 40
Location: Poland
Schools: Imperial '21

### Show Tags

14 Oct 2018, 13:18
asthagupta wrote:
answer shall be E, not sure how B is marked as OA

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

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.

Manager
Joined: 10 Sep 2015
Posts: 73
Location: India
Concentration: Finance, Human Resources
GMAT 1: 640 Q47 V31
GPA: 4
Re: Is b^2 <= a^2?  [#permalink]

### Show Tags

16 Oct 2018, 23:43
Kaczet wrote:
asthagupta wrote:
answer shall be E, not sure how B is marked as OA

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
Intern
Joined: 20 Jul 2018
Posts: 40
Location: Poland
Schools: Imperial '21
Re: Is b^2 <= a^2?  [#permalink]

### Show Tags

17 Oct 2018, 01:06
asthagupta wrote:
Kaczet wrote:
asthagupta wrote:
answer shall be E, not sure how B is marked as OA

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.
_________________

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.

Re: Is b^2 <= a^2? &nbs [#permalink] 17 Oct 2018, 01:06
Display posts from previous: Sort by