It is currently 19 Nov 2017, 11:22

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Manager
Joined: 16 Feb 2011
Posts: 240

Kudos [?]: 200 [0], given: 9

Is (A/B)^3<(AB)^3 1) A>0 2) AB>0 [#permalink]

### Show Tags

05 Sep 2011, 02:18
00:00

Difficulty:

45% (medium)

Question Stats:

59% (00:31) correct 41% (00:40) wrong based on 22 sessions

### HideShow timer Statistics

Is (A/B)^3<(AB)^3

1) A>0
2) AB>0
[Reveal] Spoiler: OA

Kudos [?]: 200 [0], given: 9

Intern
Joined: 11 May 2011
Posts: 19

Kudos [?]: 29 [0], given: 1

### Show Tags

05 Sep 2011, 06:33
Hello,

Option E: Both alone are in sufficient and both together are insufficient too.

Consider 1)

A>0 from this alone we cannot say anything.
1. Do not know if they are integers or fractions.
2. Do not know if B is positive or negative.

If fraction then consider and even if both positive:

A= 1/2 and B = 1/3
(A/B)^3 = ((1/2)/(1/3))^3 = (3/2)^3 = 27/8
(AB)^3 = (1/6)^3 = 1/216

Please note that since the power on both sides in ODD. Since ODD powers do not alter the sign we have

In sufficient.

Consider 2)
AB>0
1. Both are positive or both are negative.
2. Do not know if they are integers or fractions.

If fraction then consider:

A= 1/2 and B = 1/3
(A/B)^3 = ((1/2)/(1/3))^3 = (3/2)^3 = 27/8
(AB)^3 = (1/6)^3 = 1/216

In sufficient.

Consider both 1 and 2 :

1. A is positive hence B is also positive
2. Do not know if they are integers or fractions.

If integers
then the equation is true

If fraction then consider:

A= 1/2 and B = 1/3
(A/B)^3 = ((1/2)/(1/3))^3 = (3/2)^3 = 27/8
(AB)^3 = (1/6)^3 = 1/216

Hence both together are insufficient.

Regards
Raghav.V

Consider Kudos if you find my posts helpful:

Kudos [?]: 29 [0], given: 1

Manager
Joined: 16 Feb 2011
Posts: 240

Kudos [?]: 200 [0], given: 9

### Show Tags

05 Sep 2011, 08:33
Thanks Raghava..your help is much appreciated..

Is there a simpler way instead of computing random numbers as they are time consuming and i somehow donot seem to select the right set hence, get lost in the statements..

Kudos [?]: 200 [0], given: 9

Intern
Joined: 17 May 2009
Posts: 30

Kudos [?]: 105 [0], given: 0

Location: United States
GMAT 1: 770 Q51 V44
GPA: 3.62
WE: Corporate Finance (Manufacturing)

### Show Tags

05 Sep 2011, 17:36
$$\frac{a}{b} \cdot \frac{a}{b} \cdot \frac{a}{b} < ab \cdot ab \cdot ab$$?

I simplified the expression a bit before carrying on:

$$\frac{a}{b} \cdot \frac{a^2}{b^2} < a^2 \cdot b^2 \cdot ab$$?

$$\frac{a}{b} < ab^5$$?

Statement 1) if $$a > 0$$, then we need to know whether $$\frac{1}{b} < b^5$$. It can clearly be seen that this inequality is violated for $$0< b < 1$$ while it holds for $$b > 1$$.

Statement 2) if $$ab>0$$, then $$a$$ and $$b$$ have the same sign, so $$\frac{a}{b}>0$$ also. We can then simplify the question stem further and discover that we now need to know whether $$b^6 > 1$$. Again, this inequality holds for $$b > 1$$, but not for $$0 < b < 1$$

Combined) I used the same ranges for $$b$$ to demonstrate the same yes/no examples in each statement. The combined statements are insufficient.

Kudos [?]: 105 [0], given: 0

Manager
Joined: 13 Apr 2010
Posts: 164

Kudos [?]: 43 [0], given: 25

Location: singapore

### Show Tags

05 Sep 2011, 23:06
Plug in numbers (1/2 ,1 ) and check
(-1/2,-1) .You will get " E "
+1 for E
_________________

Regards,
Nagesh
My GMAT Study Plan: http://gmatclub.com/forum/my-gmat-study-plan-112833.html
Idioms List : http://gmatclub.com/forum/gmat-idioms-104283.html?hilit=idioms#p813231
--------------------------------------
Consider Kudos if you like my posts

Kudos [?]: 43 [0], given: 25

Math Forum Moderator
Joined: 20 Dec 2010
Posts: 1965

Kudos [?]: 2091 [0], given: 376

### Show Tags

06 Sep 2011, 00:08
DeeptiM wrote:
Is (A/B)^3<(AB)^3

1) A>0
2) AB>0

Let's take the back solving approach; Just try to eliminate "E" as the answer:

So,
A>0 & AB>0 are both TRUE. means; A and B are both +ves.

Now, solve the expression
$$(\frac{A}{B})^3<(AB)^3$$
$$B^6>1$$
OR
$$B>1$$

But, we won't be able to tell that using both the statements.

0<B<=1. Is (A/B)^3<(AB)^3? No.
B>1. Is (A/B)^3<(AB)^3? Yes.
Not Sufficient.

Ans: "E"
_________________

Kudos [?]: 2091 [0], given: 376

Manager
Joined: 08 Sep 2011
Posts: 68

Kudos [?]: 5 [0], given: 5

Concentration: Finance, Strategy

### Show Tags

09 Sep 2011, 08:23
E. You dont know if either a or b is a fraction which could change your result

Kudos [?]: 5 [0], given: 5

Re: Inequalities!!   [#permalink] 09 Sep 2011, 08:23
Display posts from previous: Sort by