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

It is currently 13 Nov 2019, 02:23

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

Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59006
Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0  [#permalink]

Show Tags

New post 11 Sep 2019, 21:10
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

73% (01:29) correct 27% (01:25) wrong based on 43 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
User avatar
P
Status: Whatever it takes!
Joined: 10 Oct 2018
Posts: 383
GPA: 4
Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0  [#permalink]

Show Tags

New post Updated on: 11 Sep 2019, 22:08
1
IMO answer is option E

(If the questions mentioned A and B are integers, then answer would have been option B)

Posted from my mobile device
Attachments

IMG_20190912_103415.jpg
IMG_20190912_103415.jpg [ 4.04 MiB | Viewed 556 times ]


_________________
Kudos OK Please!!

ALL ABOUT GMAT- \(https://exampal.com/gmat/blog/gmat-score-explained\)

Originally posted by EncounterGMAT on 11 Sep 2019, 21:23.
Last edited by EncounterGMAT on 11 Sep 2019, 22:08, edited 2 times in total.
Senior Manager
Senior Manager
avatar
P
Joined: 18 May 2019
Posts: 436
GMAT ToolKit User Premium Member CAT Tests
Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0  [#permalink]

Show Tags

New post 11 Sep 2019, 21:46
1
Statement 1 is insufficient since we know nothing about B.
When A=3; and b=-2
(A/B)^3= -27/8 > (AB)^3=216
When A=3 and B=2,
(AB)^3 > (A/B)^3

2 is also insufficient bcos AB>0 means either both A and B are greater than 0 or both A and B are negative.
When A=3 and B=2, (AB)^3 > (A/B)^3
When A=-3 and B=-1/2, (A/B)^3 > (AB)^3
Hence insufficient.

1+2 is still insufficient.
Because we know A and B must be positive in order for both conditions to be satisfied. Meanwhile, when A=3 and B=2, as we saw already, (AB)^3 > (A/B)^3
However when A=3 and B=1/2,
(A/B)^3 > (AB)^3

Hence the answer is E.

Posted from my mobile device
Senior Manager
Senior Manager
User avatar
P
Joined: 31 May 2018
Posts: 451
Location: United States
Concentration: Finance, Marketing
Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0  [#permalink]

Show Tags

New post 11 Sep 2019, 23:56
1
is (A/B)^3 < (AB)^3 ?

STATEMENT (1)- A > 0
but we don't have any information about B
if A = 4 B =\(\frac{1}{4}\) then (A/B)^3 > (AB)^3---is (A/B)^3 < (AB)^3 ? --NO

if A = 4 B = \(\frac{-1}{4}\) then (A/B)^3 < (AB)^3---is (A/B)^3 < (AB)^3 ? --YES

from here we can't get a definite answer
so, INSUFFICIENT

STATEMENT (2)- AB > 0
from here we know A and B are either positive or negative
if A = 4 B = \(\frac{1}{4}\) then (A/B)^3 > (AB)^3---is (A/B)^3 < (AB)^3 ? --NO

if A = 4 B = 2 then (A/B)^3 < (AB)^3---is (A/B)^3 < (AB)^3 ? --YES

from here we can't get a definite answer
so, INSUFFICIENT

combining both statements together
we know AB>0 and A>0 this tells us B>0

if A = 4 B = \(\frac{1}{4}\) then (A/B)^3 > (AB)^3---is (A/B)^3 < (AB)^3 ? --NO

if A = 4 B = 2 then (A/B)^3 < (AB)^3---is (A/B)^3 < (AB)^3 ? --YES

from here we can't get a definite answer
so, INSUFFICIENT

E is the correct answer
Manager
Manager
avatar
S
Joined: 05 Aug 2018
Posts: 72
Location: Thailand
Concentration: Finance, Entrepreneurship
GPA: 3.68
WE: Business Development (Energy and Utilities)
CAT Tests
Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0  [#permalink]

Show Tags

New post 12 Sep 2019, 00:04
(A/B)^3 < (AB)^3 ?


(1) A>0
Let's A = 1, B = -2; insert A,B value, we've got -1/8 < -8. NO
But A = 1, B = 2; 1/8 < 8. Yes

So, A is sufficient

(2) AB>0
Let's A = 1, B = 2; insert A,B value, we've got 1/8 < 8. Yes
But A = 2, B = 1; 8 < 8 No.
So, 2 alone is not suffcient


(1) + (2); A>0 and AB >0, thus both A,B > 0
If A = 1, B =2; 1/8 < 8 Yes.
If A =2 , B =1 ; 8 < 8 No.

Not sufficient. Therefore E is the answer
Senior Manager
Senior Manager
avatar
G
Joined: 07 Mar 2019
Posts: 372
Location: India
GMAT 1: 580 Q43 V27
WE: Sales (Energy and Utilities)
CAT Tests
Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0  [#permalink]

Show Tags

New post 12 Sep 2019, 00:19
Is \((\frac{A}{B})^3 < (AB)^3\) ?

No relation between A and B is given so many possibilities exist.

(1) \(A > 0\)
Here either \(B > A\) for both integer value and non-integer value of positive B.
Example: Let A = 2 & B = 3 then
\((\frac{2}{3})^3 < (2*3)^3\) YES

OR

\(A > B\) for either positive value of B or negative value of B.
Example: Let A = 2 & B = 1 then
\((\frac{2}{1})^3 < (2*1)^3\) NO

INSUFFICIENT.

(2) \(AB > 0\)

Two cases are possible here:

(a) Both A and B are +ve
Take A = 2 & B = 3 then
\((\frac{2}{3})^3 < (2*3)^3\) YES

(b) Both A and B are -ve
Take \(A = \frac{-1}{2}\) & \(B = \frac{-1}{3}\) then
\(((\frac{-1}{2})/(\frac{-1}{3}))^3 < ((\frac{-1}{2})*(\frac{-1}{3}))^3\) NO

INSUFFICIENT.

Together 1) and 2)

We have \(A > 0\) and \(B > 0\)
Again Take A = a2 & B = 3 then
\((\frac{2}{3})^3 < (2*3)^3\) YES

And

Take \(A = \frac{1}{2}\) & \(B = \frac{1}{3}\) then
\(((\frac{1}{2}/\frac{1}{3})^3 < ((\frac{1}{2})*(\frac{1}{3}))^3\) NO

INSUFFICIENT.

Answer (E).
_________________
Ephemeral Epiphany..!

GMATPREP1 590(Q48,V23) March 6, 2019
GMATPREP2 610(Q44,V29) June 10, 2019
GMATPREPSoft1 680(Q48,V35) June 26, 2019
Senior Manager
Senior Manager
avatar
G
Joined: 25 Jul 2018
Posts: 338
Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0  [#permalink]

Show Tags

New post 12 Sep 2019, 00:54
1
Is \((\frac{A}{B})^{3}<(AB)^{3}\)?

\(A^{3}(B^{3}-(\frac{1}{B})^{3}\))>0

\(A^{3}*(B-\frac{1}{B})*(B^{2}+B*\frac{1}{B}+(\frac{1}{B})^{2}\))>0

\((B^{2}+B*\frac{1}{B}+(\frac{1}{B})^{2}\)) is always greater than zero.
--> \(A^{3}*(B-\frac{1}{B})\)>0 ???

(1) A > 0

(2) AB > 0

Statement1:
A > 0
--> (B-\(\frac{1}{B}\))>0 ???

If B=2, then 2-\(\frac{1}{2}\)>0 (Yes)
If B=\(\frac{1}{2}\), then \(\frac{1}{2}\)-2>0 (NO)

Insufficient.

Statement2:
AB > 0
--> Both A and B are Positive or Negative:
\(A^{3}*(B-\frac{1}{B})\)>0

if A=B=2, then --> \(2^{3}(2-\frac{1}{2})\)>0 (yes)
if A=B=\(\frac{1}{2}\), then --> \((\frac{1}{2})^{3}(\frac{1}{2}-2)\)>0 (NO)

Insufficient.

Taken together 1 and 2,
A>0 and AB>0 --> B>0.

\(A^{3}*(B-\frac{1}{B})\)>0 --> (B-\(\frac{1}{B}\))>0 ???

if B=2, then --> (2-\(\frac{1}{2}\))>0 (yes)
if B=\(\frac{1}{2}\), then -->(\(\frac{1}{2}\)-2)>0 (NO)

Insufficient

The answer is E.
GMAT Club Legend
GMAT Club Legend
User avatar
D
Joined: 18 Aug 2017
Posts: 5261
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0  [#permalink]

Show Tags

New post 12 Sep 2019, 02:28
#1
A>0 so A is +ve but no relation of B with A insufficient
#2
AB>0
so either both AB are +ve or -ve also they can be same value /integer/ fraction no given info
insufficient
from 1 &2
we can say that AB are +ve but whether A=B ; A>B or B<A cannot be determined
IMO E


Is(AB)3<(AB)3 ?


(1) A>0

(2) AB>0
Senior Manager
Senior Manager
User avatar
G
Joined: 10 Aug 2018
Posts: 338
Location: India
Concentration: Strategy, Operations
WE: Operations (Energy and Utilities)
Reviews Badge CAT Tests
Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0  [#permalink]

Show Tags

New post 12 Sep 2019, 03:34
IMO it's E.
Because even after combining if we take A=100 and B=1 then NO is the answer.
And if A=100 and B=2 then YES is the answer.

_________________
On the way to get into the B-school and I will not leave it until I win. WHATEVER IT TAKES.

" I CAN AND I WILL"

GMAT:[640 Q44, V34, IR4, AWA5]
Director
Director
avatar
P
Joined: 24 Nov 2016
Posts: 748
Location: United States
Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0  [#permalink]

Show Tags

New post 12 Sep 2019, 04:32
Quote:
Is \((A/B)^3<(AB)^3\)?

(1) A>0
(2) AB>0


rephrase: \((A/B)^3<(AB)^3…A/B<AB…A/B<AB\); Is \(A/B<AB\)?

case 1: \(A,B=(1,2)…A/B<AB…1/2<2:true\)
case 2: \(A,B=(10,1)…A/B<AB…10<10:false\)

(1) A>0: case 1 and 2, insufi.
(2) AB>0: case 1 and 2, insufi.
(1&2) A,B>0: case 1 and 2, insufi.

Answer (E)
Manager
Manager
avatar
S
Joined: 24 Sep 2014
Posts: 51
Concentration: General Management, Technology
Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0  [#permalink]

Show Tags

New post 12 Sep 2019, 07:35
Is (A/B)^3 <(AB)^3 ?

(1) A>0
if A>0, then
\((A/B)^3<(AB)^3\)
\(A^3/B^3<A^3*B^3\)
\(1/B^3<B^3\)
if B = 1, \(1/1^3<1^3\) is not possible
if B = 2, \(1/2^3<2^3\) is possible
so, no unique answer

(2) AB>0
A>0 & B>0 (I) or A<0 & B<0 (II)
condition (I) is same as (1), so no unique answer
we don't have to check condition (II)

(1) & (2)
A>0 (from 1), so B>0
again no unique solution if we take B = 1 or 2
So, answer is E
GMAT Club Bot
Re: Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0   [#permalink] 12 Sep 2019, 07:35
Display posts from previous: Sort by

Is (A/B)^3 < (AB)^3 ? (1) A > 0 (2) AB > 0

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





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