 It is currently 19 Sep 2019, 22:12 ### 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 numbers {a,b,c} are three positive integers.  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
Manager  Joined: 22 Jun 2019
Posts: 133
Followers: 0

Kudos [?]: 14 , given: 46

The numbers {a,b,c} are three positive integers. [#permalink] 00:00

Question Stats: 75% (01:03) correct 25% (01:13) wrong based on 4 sessions
The numbers {a,b,c} are three positive integers. If $$\frac{(a×b×c)}{14}$$ equals an integer and $$\frac{(b×c)}{4}$$ equals an integer, what is the smallest possible integer value of a?

A. $$1$$
B. $$2$$
C. $$4$$
D. $$7$$
E. $$14$$
[Reveal] Spoiler: OA
Founder  Joined: 18 Apr 2015
Posts: 8139
Followers: 157

Kudos [?]: 1710 , given: 7485

Re: The numbers {a,b,c} are three positive integers. [#permalink]
Expert's post
Setting the two conditions $$\frac{a \times b \times c}{14}$$ AND $$\frac{b \times c}{14}$$ we do know that $$b\times c$$ must be a multiple of 14: 14,28, so forth.

The question boils down to the value of a in the fraction above. To continue to have an integer a must be equal to 1 as minimum value to get the overall fraction an integer

Regards
_________________
Manager  Joined: 22 Jun 2019
Posts: 133
Followers: 0

Kudos [?]: 14 , given: 46

Re: The numbers {a,b,c} are three positive integers. [#permalink]
Carcass wrote:
Setting the two conditions $$\frac{a \times b \times c}{14}$$ AND $$\frac{b \times c}{14}$$ we do know that b\times c must be a multiple of 14: 14,28, so forth.

The question boils down to the value of a in the fraction above. To continue to have an integer a must be equal to 1 as minimum value to get the overall fraction an integer

Regards

still confuse
Founder  Joined: 18 Apr 2015
Posts: 8139
Followers: 157

Kudos [?]: 1710 , given: 7485

Re: The numbers {a,b,c} are three positive integers. [#permalink]
Expert's post
_________________
Manager  Joined: 22 Jun 2019
Posts: 133
Followers: 0

Kudos [?]: 14 , given: 46

Re: The numbers {a,b,c} are three positive integers. [#permalink]
Carcass wrote:

the whole that u said. GRE Instructor Joined: 10 Apr 2015
Posts: 2387
Followers: 78

Kudos [?]: 2358  , given: 33

Re: The numbers {a,b,c} are three positive integers. [#permalink]
2
KUDOS
Expert's post
huda wrote:
The numbers {a,b,c} are three positive integers. If $$\frac{(a×b×c)}{14}$$ equals an integer and $$\frac{(b×c)}{4}$$ equals an integer, what is the smallest possible integer value of a?

A. $$1$$
B. $$2$$
C. $$4$$
D. $$7$$
E. $$14$$

Notice that 28 is divisible by both 14 and 4.
So, if b equals 28, then abc/14 and bc/4 are both integers, REGARDLESS of the values of the other two variables.

For example, if a = 1, b = 28 and c = 1, then abc/14 and bc/4 both simplify to be integers.

Since variable a must be a POSITIVE INTEGER, the smallest possible value of a = 1

Cheers,
Brent
_________________

Brent Hanneson – Creator of greenlighttestprep.com Sign up for my free GRE Question of the Day emails

Intern Joined: 18 Jul 2019
Posts: 14
Followers: 0

Kudos [?]: 0 , given: 2

Re: The numbers {a,b,c} are three positive integers. [#permalink]
Ok great this is nice thank you Re: The numbers {a,b,c} are three positive integers.   [#permalink] 05 Sep 2019, 11:02
Display posts from previous: Sort by

# The numbers {a,b,c} are three positive integers.  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.