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

It is currently 14 Nov 2019, 12:30

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

A and B are non zero real numbers. Is A/B > B/A? (1) A^2 > B^2 (2)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Retired Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1417
Location: India
A and B are non zero real numbers. Is A/B > B/A? (1) A^2 > B^2 (2)  [#permalink]

Show Tags

New post 21 Jan 2019, 22:15
1
4
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

24% (01:43) correct 76% (01:57) wrong based on 73 sessions

HideShow timer Statistics

A and B are non zero real numbers. Is A/B > B/A?

(1) A^2 > B^2

(2) A^3 > B^3
Chat Moderator
User avatar
S
Joined: 07 Mar 2016
Posts: 49
Re: A and B are non zero real numbers. Is A/B > B/A? (1) A^2 > B^2 (2)  [#permalink]

Show Tags

New post 22 Jan 2019, 14:12
2
ocelot22 wrote:
amanvermagmat wrote:
A and B are non zero real numbers. Is A/B > B/A?

(1) A^2 > B^2

(2) A^3 > B^3


We can rewrite the question by cross multiplying as A^2>B^2? Yes/NO

(1) A^2>B^2 Suff

(2) A^3 >B>^3 Let A =-1, B=-2. Then A^3 >B^3, but A^2 not >B^2 --- NO

Let A=2 B=1 Then A^3>B^3, and A^2 >B^2 --- Yes

The answer is A


Mate, what if A and/or B have a negative value?
_________________
...once in a while you get shown the light, in the strangest of places if you look at it right...
Director
Director
avatar
G
Joined: 09 Mar 2018
Posts: 994
Location: India
A and B are non zero real numbers. Is A/B > B/A? (1) A^2 > B^2 (2)  [#permalink]

Show Tags

New post Updated on: 23 Jan 2019, 08:57
1
amanvermagmat wrote:
A and B are non zero real numbers. Is A/B > B/A?

(1) A^2 > B^2

(2) A^3 > B^3


non zero real numbers, can be anything from +ive integers , -ive integers to fraction, rational numbers

Question Is A/B > B/A ??

(1) A^2 > B^2

Will take some examples here
A = -2, B = - 1, 4 > 1, Question will be 2/1 > 1/2, Yes
A = -2, B = 1, 4 > 1, Question will be -2 > - 0.5, No

(2) A^3 > B^3

Will take some examples here
A = -1, B = - 2, -1 > -8, Question will be 1/2 > 2/1, No
A = 1/2, B = 1/4, 1/8 > 1/64, Question will be 2 > 1/2 , Yes

Combine both the statements
A^2 > B^2 and A^3 > B^3

We have to choose a value which will satisfy both of them( i thought x will always be greater than y, for both the inequalities to be true and they cannot be both -ive as it will not satisfy the first statement)

Now A and B, both will be +ive
A = 2 and B = 1, 4> 1 and 8 > 1, Question will be 2/1 > 1/2, Yes

A = 1/2, B = 1/4, 1/4 > 1/16 and 1/8 > 1/64, Question will be 2 > 1/2 , Yes

IMO C
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Originally posted by KanishkM on 22 Jan 2019, 04:51.
Last edited by KanishkM on 23 Jan 2019, 08:57, edited 1 time in total.
Manager
Manager
avatar
G
Joined: 16 Oct 2011
Posts: 109
GMAT 1: 570 Q39 V41
GMAT 2: 640 Q38 V31
GMAT 3: 650 Q42 V38
GMAT 4: 650 Q44 V36
GMAT 5: 570 Q31 V38
GPA: 3.75
Reviews Badge CAT Tests
A and B are non zero real numbers. Is A/B > B/A? (1) A^2 > B^2 (2)  [#permalink]

Show Tags

New post Updated on: 22 Jan 2019, 14:26
1
We are not told if A and B are positive real numbers, so avoid the temptation to cross multiply

(1) A^2 > B^2

Let A =-2 B =-1 Then -2/-1 >? -1/-2 --? 2 > 1/2 Yes

Let A =2 B =1 Then 2/1 > 1/2 No

NS

(2) A^3 > B^3

Let A =2 B =1 Then 2/1 > 1/2 Yes

Let A =-1 B =-2 Then -1/-2 >? -2/-1 --? 1/2 > 2 ? NO

NS

(1) and (2)

Dividing 2 by 1 give A> B

Let A = -1 B = -2 Then -1/-2 >? -2/-1 1/2 > 2? No

Let A =2 B =1 Then 2/1 >? 1/2 2 > 1/2? Yes

NS

Answer is E

Originally posted by ocelot22 on 22 Jan 2019, 14:02.
Last edited by ocelot22 on 22 Jan 2019, 14:26, edited 3 times in total.
Manager
Manager
avatar
S
Joined: 11 Jun 2018
Posts: 100
Schools: DeGroote "22 (S)
GMAT 1: 500 Q39 V21
Re: A and B are non zero real numbers. Is A/B > B/A? (1) A^2 > B^2 (2)  [#permalink]

Show Tags

New post 22 Jan 2019, 10:25
@KanishkM:- Isn't A sufficient,

The question asks A/B>B/A

If you cross multiply the question is

Is A^2>B^2
Director
Director
avatar
G
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: A and B are non zero real numbers. Is A/B > B/A? (1) A^2 > B^2 (2)  [#permalink]

Show Tags

New post 22 Jan 2019, 10:28
Manat wrote:
@KanishkM:- Isn't A sufficient,

The question asks A/B>B/A

If you cross multiply the question is

Is A^2>B^2


Hi Manat

But we dont know the magnitude of A and B, if they are not having same signs then ??

(1) A^2 > B^2

Will take some examples here
A = -2, B = - 1, 4 > 1, Question will be 2/1 > 1/2, Yes
A = -2, B = 1, 4 > 1, Question will be -2 > - 0.5, No

Kindly let me know if those cases are apt.
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Chat Moderator
User avatar
S
Joined: 07 Mar 2016
Posts: 49
Re: A and B are non zero real numbers. Is A/B > B/A? (1) A^2 > B^2 (2)  [#permalink]

Show Tags

New post 22 Jan 2019, 13:53
KanishkM wrote:
amanvermagmat wrote:
A and B are non zero real numbers. Is A/B > B/A?

(1) A^2 > B^2

(2) A^3 > B^3


non zero real numbers, can be anything from +ive integers , -ive integers to fraction, rational numbers

Question Is A/B > B/A ??

(1) A^2 > B^2

Will take some examples here
A = -2, B = - 1, 4 > 1, Question will be 2/1 > 1/2, Yes
A = -2, B = 1, 4 > 1, Question will be -2 > - 0.5, No

(2) A^3 > B^3

Will take some examples here
A = -1, B = - 2, -1 > -8, Question will be 1/2 > 2/1, No
A = 1/2, B = 1/4, 1/8 > 1/64, Question will be 2 > 1/2 , Yes

Combine both the statements
A^2 > B^2 and A^3 > B^3

Now A and B, both will be +ive
A = 2 and B = 1, 4> 1 and 8 > 1, Question will be 2/1 > 1/2, Yes

A = 1/2, B = 1/4, 1/4 > 1/16 and 1/8 > 1/64, Question will be 2 > 1/2 , Yes

IMO C


What about if B=2 and A=1? Then A/B < B/A!

Since we only know the +'ve/-'ve nature of the variables and do not know the value of either A or B - I think the answer is E!
_________________
...once in a while you get shown the light, in the strangest of places if you look at it right...
Manager
Manager
avatar
G
Joined: 16 Oct 2011
Posts: 109
GMAT 1: 570 Q39 V41
GMAT 2: 640 Q38 V31
GMAT 3: 650 Q42 V38
GMAT 4: 650 Q44 V36
GMAT 5: 570 Q31 V38
GPA: 3.75
Reviews Badge CAT Tests
Re: A and B are non zero real numbers. Is A/B > B/A? (1) A^2 > B^2 (2)  [#permalink]

Show Tags

New post 22 Jan 2019, 14:13
1
emockus wrote:
ocelot22 wrote:
amanvermagmat wrote:
A and B are non zero real numbers. Is A/B > B/A?

(1) A^2 > B^2

(2) A^3 > B^3


We can rewrite the question by cross multiplying as A^2>B^2? Yes/NO

(1) A^2>B^2 Suff

(2) A^3 >B>^3 Let A =-1, B=-2. Then A^3 >B^3, but A^2 not >B^2 --- NO

Let A=2 B=1 Then A^3>B^3, and A^2 >B^2 --- Yes

The answer is A


Mate, what if A and/or B have a negative value?


I just caught it bro, editing my post as we speak. ;)
Director
Director
avatar
G
Joined: 09 Mar 2018
Posts: 994
Location: India
A and B are non zero real numbers. Is A/B > B/A? (1) A^2 > B^2 (2)  [#permalink]

Show Tags

New post 22 Jan 2019, 18:43
ocelot22 wrote:
We are not told if A and B are positive real numbers, so avoid the temptation to cross multiply

(1) A^2 > B^2

Let A =-2 B =-1 Then -2/-1 >? -1/-2 --? 2 > 1/2 Yes

Let A =2 B =1 Then 2/1 > 1/2 No

NS

(2) A^3 > B^3

Let A =2 B =1 Then 2/1 > 1/2 Yes

Let A =-1 B =-2 Then -1/-2 >? -2/-1 --? 1/2 > 2 ? NO

NS

(1) and (2)

Dividing 2 by 1 give A> B

Let A = -1 B = -2 Then -1/-2 >? -2/-1 1/2 > 2? No

Let A =2 B =1 Then 2/1 >? 1/2 2 > 1/2? Yes

NS

Answer is E


Why is it that when i use the values
A=-1 & B =-2, i am unable to satisfy both the statements

A^2 > B^2 and A^3 > B^3

We have to choose a value which will satisfy both of them( i thought x will always be greater than y, for both the inequalities to be true and they cannot be both -ive as it will not satisfy the first statement)

(-1)^2 > (-2)^2 and -1 > -8
1 > 4 and -1 > -8

1 > 4 No and -1 > -8 Yes
This value cannot be used.

Can you please share your thoughts on this, i believe that value is not apt.

Posted from my mobile device
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
GMAT Club Legend
GMAT Club Legend
User avatar
D
Joined: 18 Aug 2017
Posts: 5265
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: A and B are non zero real numbers. Is A/B > B/A? (1) A^2 > B^2 (2)  [#permalink]

Show Tags

New post 23 Jan 2019, 03:58
amanvermagmat wrote:
A and B are non zero real numbers. Is A/B > B/A?

(1) A^2 > B^2

(2) A^3 > B^3


given
A/B>B/A
#1
A^>B^2

check with a=-2 & b=-1 and at a=-1 & b = -1/2

not sufficient
#2:
a^3>b^3

at a= 3/2 & b =1/2
and a= -1 & b= -2
not sufficeint

from 1 & 2
divide 2 by1
we get
a>b

so at a=2 and b=1
sufficient

IMO C
Manager
Manager
avatar
G
Joined: 16 Oct 2011
Posts: 109
GMAT 1: 570 Q39 V41
GMAT 2: 640 Q38 V31
GMAT 3: 650 Q42 V38
GMAT 4: 650 Q44 V36
GMAT 5: 570 Q31 V38
GPA: 3.75
Reviews Badge CAT Tests
Re: A and B are non zero real numbers. Is A/B > B/A? (1) A^2 > B^2 (2)  [#permalink]

Show Tags

New post 23 Jan 2019, 08:36
KanishkM wrote:
ocelot22 wrote:
We are not told if A and B are positive real numbers, so avoid the temptation to cross multiply

(1) A^2 > B^2

Let A =-2 B =-1 Then -2/-1 >? -1/-2 --? 2 > 1/2 Yes

Let A =2 B =1 Then 2/1 > 1/2 No

NS

(2) A^3 > B^3

Let A =2 B =1 Then 2/1 > 1/2 Yes

Let A =-1 B =-2 Then -1/-2 >? -2/-1 --? 1/2 > 2 ? NO

NS

(1) and (2)

Dividing 2 by 1 give A> B

Let A = -1 B = -2 Then -1/-2 >? -2/-1 1/2 > 2? No

Let A =2 B =1 Then 2/1 >? 1/2 2 > 1/2? Yes

NS

Answer is E


Why is it that when i use the values
A=-1 & B =-2, i am unable to satisfy both the statements

A^2 > B^2 and A^3 > B^3

We have to choose a value which will satisfy both of them( i thought x will always be greater than y, for both the inequalities to be true and they cannot be both -ive as it will not satisfy the first statement)

(-1)^2 > (-2)^2 and -1 > -8
1 > 4 and -1 > -8

1 > 4 No and -1 > -8 Yes
This value cannot be used.

Can you please share your thoughts on this, i believe that value is not apt.

Posted from my mobile device


I believe that what happened, is that by dividing A^3>B^3 by A^2>B^2 to get A>B, I buried one of the constraints of the problem. I am gonna make a note not to do this. Can anybody weigh in if this is the case?
Manager
Manager
avatar
G
Joined: 16 Oct 2011
Posts: 109
GMAT 1: 570 Q39 V41
GMAT 2: 640 Q38 V31
GMAT 3: 650 Q42 V38
GMAT 4: 650 Q44 V36
GMAT 5: 570 Q31 V38
GPA: 3.75
Reviews Badge CAT Tests
Re: A and B are non zero real numbers. Is A/B > B/A? (1) A^2 > B^2 (2)  [#permalink]

Show Tags

New post 23 Jan 2019, 08:56
amanvermagmat wrote:
A and B are non zero real numbers. Is A/B > B/A?

(1) A^2 > B^2

(2) A^3 > B^3


Very high quality question - It is a great example of questions where you have to use attention to detail to not miss a case.
GMAT Club Bot
Re: A and B are non zero real numbers. Is A/B > B/A? (1) A^2 > B^2 (2)   [#permalink] 23 Jan 2019, 08:56
Display posts from previous: Sort by

A and B are non zero real numbers. Is A/B > B/A? (1) A^2 > B^2 (2)

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne