It is currently 20 May 2019, 22:35

### 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

# a^3b^4c^7>0

Author Message
TAGS:
Founder
Joined: 18 Apr 2015
Posts: 6562
Followers: 107

Kudos [?]: 1253 [0], given: 5955

a^3b^4c^7>0 [#permalink]  18 Jul 2018, 17:00
Expert's post
00:00

Question Stats:

37% (00:40) correct 62% (00:47) wrong based on 58 sessions
$$a^3b^4c^7>0$$

Which of the following statements must be true?

Indicate all such statements.

A. $$ab$$ is negative

B. $$abc$$ is positive

C. $$ac$$ is positive
[Reveal] Spoiler: OA

_________________
Director
Joined: 20 Apr 2016
Posts: 864
WE: Engineering (Energy and Utilities)
Followers: 11

Kudos [?]: 645 [2] , given: 141

Re: a^3b^4c^7>0 [#permalink]  18 Jul 2018, 19:53
2
KUDOS
Carcass wrote:
$$a^3b^4c^7>0$$

Which of the following statements must be true?

Indicate all such statements.

A. $$ab$$ is negative

B. $$abc$$ is positive

C. $$ac$$ is positive

the above statement will be true if any of the following statement are true,

1. a , b , c are all positive numbers

2. if a is +ve, b is -ve and c is +ve

3. if a is -ve, b is +ve and c is -ve

Therefore only option C is always true
_________________

If you found this post useful, please let me know by pressing the Kudos Button

Rules for Posting https://greprepclub.com/forum/rules-for ... -1083.html

GRE Instructor
Joined: 10 Apr 2015
Posts: 1746
Followers: 58

Kudos [?]: 1660 [1] , given: 8

Re: a^3b^4c^7>0 [#permalink]  29 Aug 2018, 07:38
1
KUDOS
Expert's post
Carcass wrote:
$$a^3b^4c^7>0$$

Which of the following statements must be true?

Indicate all such statements.

A. $$ab$$ is negative

B. $$abc$$ is positive

C. $$ac$$ is positive

Key Concept: (any number)^(EVEN INTEGER) ≥ 0

First, since $$a^3b^4c^7>0$$, we know that a ≠ 0, b ≠ 0, and c ≠ 0

Next, since $$b^4$$ must be POSITIVE, we can safely divide both sides of the inequality by $$b^4$$ to get: $$a^3c^7>0$$
Also, since $$c^6$$ must be POSITIVE, we can safely divide both sides of the inequality by $$c^6$$ to get: $$a^3c>0$$
Finally, since $$a^2$$ must be POSITIVE, we can safely divide both sides of the inequality by $$a^2$$ to get: $$ac>0$$

So, the ONLY relevant conclusion we can make is that $$ac>0$$

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com

Manager
Joined: 22 Feb 2018
Posts: 163
Followers: 2

Kudos [?]: 108 [1] , given: 22

Re: a^3b^4c^7>0 [#permalink]  16 Nov 2018, 18:20
1
KUDOS
A: if ab <0 then:
a<0 and b>0 : then c should be negative to have a^3*b^4*c^7 >0
a>0 and b<0 : then it’s ok because b’s power is even.
So A is possible but not obligatory.

B: it’s possible, But it’s not obligatory.

C: ac is positive: True
Because power of a and c are odd, they both should have same sign, both negative or positibve to have the whole expression positive.
_________________

Re: a^3b^4c^7>0   [#permalink] 16 Nov 2018, 18:20
Display posts from previous: Sort by