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

 It is currently 14 Dec 2019, 18:57

### 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

# 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: 43
If a, b, c, and d are integers and ab2c3d4 > 0, which of the  [#permalink]

### Show Tags

27 Jul 2012, 09:10
1
13
00:00

Difficulty:

15% (low)

Question Stats:

75% (01:26) correct 25% (01:39) wrong based on 446 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
Math Expert
Joined: 02 Sep 2009
Posts: 59725
Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the  [#permalink]

### Show Tags

27 Jul 2012, 09:29
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.

_________________
##### General Discussion
Manager
Joined: 11 Jun 2014
Posts: 52
Concentration: Technology, Marketing
GMAT 1: 770 Q50 V45
WE: Information Technology (Consulting)
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.
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the  [#permalink]

### Show Tags

08 Feb 2018, 16:40
1
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

We are given that a(b^2)(c^3)(d^4) > 0.

Since b^2 and d^4 are positive, we see that the product of a and c^3 must be positive, so a and c are either both positive or both negative.

Let’s analyze each Roman numeral.

I. a^2cd

While a^2 is positive, we don’t know the sign of either c or d, so we can’t determine whether a^2cd is positive.

II. bc^4d

While c^4 is positive, we don’t know the sign of either b or d, so we can’t determine whether bc^4d is positive.

III. a^3c^3d^2

Since a and c are either both positive or both negative, a^3 and c^3 will be also either both positive or both negative. Therefore, the product a^3c^3 will be positive. Furthermore, d^2 is positive, and so a^3b^3d^2 will be positive.

_________________

# Jeffrey Miller

Jeff@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Joined: 05 Aug 2017
Posts: 3
GMAT 1: 380 Q27 V16
GMAT 2: 460 Q31 V22
Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the  [#permalink]

### Show Tags

29 Aug 2018, 17:27
I think we can realize real quick that this question is about identifying what variable might be negative and what has to be positive. We know that the given variables with their exponents will result in a positive. i.e. larger than 0. we know "a" has to be positive since we don't know if "b" might be negative or not. C is positive because the exponent is an odd exponent, and we don't know if "d" is a positive or negative. With this information, lets go down the answer choice.

Hmm, there is an issue with option 1. Because we don't know if "d" is a positive or negative, c*d could be a negative. so thats out.

Same principle with option 2. We don't know if "d" is negative or positive, so thats out too.

Which leaves us with only option 3, but lets take a quick look. We know "a" and "c" is positive, so the odd exponent is no issue, and since "d" has an even exponent, we know for sure that it must be positive.
Re: If a, b, c, and d are integers and ab2c3d4 > 0, which of the   [#permalink] 29 Aug 2018, 17:27
Display posts from previous: Sort by