Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 25 May 2017, 10:27

### 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

# If a, b, c, and d are integers and ab2c3d4 > 0, which of the

Author Message
TAGS:

### Hide Tags

Intern
Joined: 20 Jun 2011
Posts: 46
Followers: 1

Kudos [?]: 102 [0], given: 1

If a, b, c, and d are integers and ab2c3d4 > 0, which of the [#permalink]

### Show Tags

27 Jul 2012, 09:10
9
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

71% (01:55) correct 29% (00:55) wrong based on 285 sessions

### HideShow timer Statistics

If a, b, c, and d are integers and $$ab^2c^3d^4 > 0$$, which of the following must be positive?

I. $$a^2cd$$
II. $$bc^4d$$
III. $$a^3c^3d^2$$

A) I only
B) II only
C) III only
D) I and III
E) I, II, and III
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 38869
Followers: 7731

Kudos [?]: 106111 [0], given: 11607

Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the [#permalink]

### Show Tags

27 Jul 2012, 09:29
Expert's post
1
This post was
BOOKMARKED
superpus07 wrote:
If a, b, c, and d are integers and $$ab^2c^3d^4 > 0$$, which of the following must be positive?

I. $$a^2cd$$
II. $$bc^4d$$
III. $$a^3c^3d^2$$

A) I only
B) II only
C) III only
D) I and III
E) I, II, and III

Since given that $$a*b^2*c^3*d^4 > 0$$, then we know that none of the unknowns is zero. Therefore, $$b^2>0$$ and $$d^4>0$$, which means that we can safely reduce by them to get $$a*c^3>0$$ (so, the given expression does not depend on the value of $$b$$ or $$d$$: they can be positive as well as negative).

Next, $$a*c^3>0$$ means that $$a$$ and $$c$$ must have the same sign: they are either both positive or both negative.

Evaluate each option:

I. $$a^2cd$$. Since $$d$$ can positive as well as negative then this option is not necessarily positive.

II. $$bc^4d$$. Since $$d$$ can positive as well as negative then this option is not necessarily positive.

III. $$a^3c^3d^2$$. Since $$a*c^3>0$$, then $$a^3*c^3>0$$ and as $$d^2>0$$, then their product, $$(a^3*c^3)*d^2$$ must be positive too.

_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15439
Followers: 649

Kudos [?]: 209 [0], given: 0

Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the [#permalink]

### Show Tags

31 Jul 2014, 18:32
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Manager
Joined: 11 Jun 2014
Posts: 57
Concentration: Technology, Marketing
GMAT 1: 770 Q50 V45
WE: Information Technology (Consulting)
Followers: 4

Kudos [?]: 34 [0], given: 3

Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the [#permalink]

### Show Tags

31 Jul 2014, 21:32
a*(b^2)*(c^3)*(d^4) > 0,

since b^2 and d^4 are always positive..

a*(c^3) is positive .. so 'a' and 'c' are of the same sign, eithr positive or negative. we have no information about 'b' and 'd' , so they could b negative..

so the first 2 statements ( I and II ) have 'd' in them, which could be negative.. so we can eliminate them then and there.

in statement III, 'd' is squared, so thats positive and since 'a' and 'c' are of the same sign, a^3 * c^3 must be positive.

so III only , that option C.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15439
Followers: 649

Kudos [?]: 209 [0], given: 0

Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the [#permalink]

### Show Tags

11 Nov 2015, 20:28
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15439
Followers: 649

Kudos [?]: 209 [0], given: 0

Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the [#permalink]

### Show Tags

30 Nov 2016, 01:44
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the   [#permalink] 30 Nov 2016, 01:44
Similar topics Replies Last post
Similar
Topics:
4 If a, b, and c are all integers divisible by 3 and a > b > c > 0, then 5 25 Apr 2017, 16:40
1 If b<c<d and c>0, which of the following cannot be true if b,c and d 5 06 Apr 2017, 09:57
3 On a certain number line, conditions are a<b<c<d<e and abcde>0. Which 1 14 Sep 2016, 02:39
8 If a > b and if c > d , then which of the following must be 7 03 Oct 2016, 02:34
11 If d > 0 and 0 < 1 - c/d < 1, which of the following must be true? 6 02 Sep 2014, 20:04
Display posts from previous: Sort by