Last visit was: 23 Jul 2024, 11:14 It is currently 23 Jul 2024, 11:14
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# The variables a, b, and c are distinct factors of 24. Which of the fol

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94592
Own Kudos [?]: 643319 [7]
Given Kudos: 86728
Manager
Joined: 11 Jun 2017
Status:In last prep stage
Posts: 114
Own Kudos [?]: 227 [3]
Given Kudos: 211
GMAT 1: 630 Q44 V33
GMAT 2: 680 Q47 V37
GPA: 3.2
Intern
Joined: 21 May 2017
Posts: 30
Own Kudos [?]: 89 [0]
Given Kudos: 8
MBA Section Director
Joined: 22 May 2017
Affiliations: GMATClub
Posts: 12761
Own Kudos [?]: 8918 [0]
Given Kudos: 3038
GRE 1: Q168 V154
GPA: 3.4
WE:Engineering (Education)
Re: The variables a, b, and c are distinct factors of 24. Which of the fol [#permalink]
The variables a, b, and c are distinct factors of 24

Distinct factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24

option A

a + b + c is even is false since 1 + 2 + 4 is odd

option B

a + b + c < 40 is false since 8 + 12 + 24 = 44 > 40

option C

$$\frac{a-b}{c}$$ is an integer is false since $$\frac{2-1}{3}$$ is not an integer

option D

abc is even since there are only two odd numbers and everything else is an even number

option E

abc is a multiple of 24 is false since 1 * 2 * 3 = 6 is not a multiple of 24

Hence option D
VP
Joined: 31 Oct 2013
Posts: 1259
Own Kudos [?]: 1195 [0]
Given Kudos: 635
Concentration: Accounting, Finance
GPA: 3.68
WE:Analyst (Accounting)
Re: The variables a, b, and c are distinct factors of 24. Which of the fol [#permalink]
Bunuel wrote:
The variables a, b, and c are distinct factors of 24. Which of the following must be true?

A. a + b + c is even.
B. a + b + c < 40
C. (a – b)/c is an integer.
D. abc is even.
E. abc is a multiple of 24

a, b, c are distinct factors of 24.

Factors of 24 : 1 , 2 , 3 , 4 , 6 , 8 , 12 , 24.

Note: Except 1 and 3 all are EVEN factors.

So, whenever we multiply abc , one of them must be EVEN. That makes the result Even.

So, abc = even.

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3710
Own Kudos [?]: 17354 [0]
Given Kudos: 165
Re: The variables a, b, and c are distinct factors of 24. Which of the fol [#permalink]

Solution

Given:
• a, b, and c are distinct factors of 24

To find:
• Among the following option which one is true.

Approach and Working:

Factors of 24= 1, 2, 3, 4, 6, 8, 12, 24
Among all the factors of 24, 2 factors are odd and the rest are even.
So, whatever be the case, abc will always be even.

Hence, the correct answer is option D.

Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3036
Own Kudos [?]: 6624 [0]
Given Kudos: 1646
Re: The variables a, b, and c are distinct factors of 24. Which of the fol [#permalink]
Bunuel wrote:
The variables a, b, and c are distinct factors of 24. Which of the following must be true?

A. a + b + c is even.
B. a + b + c < 40
C. (a – b)/c is an integer.
D. abc is even.
E. abc is a multiple of 24

Since the factors of 24 are 1, 2, 3, 4, 6, 8, 12, and 24, we see that there are only two odd factors and thus, at a minimum, one of the values of a, b, and c must be even, making the product abc even also.

Non-Human User
Joined: 09 Sep 2013
Posts: 34045
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: The variables a, b, and c are distinct factors of 24. Which of the fol [#permalink]
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: The variables a, b, and c are distinct factors of 24. Which of the fol [#permalink]
Moderator:
Math Expert
94592 posts