It is currently 18 Jan 2020, 08:42

### 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

# The numbers {a,b,c} are three positive integers.

Author Message
TAGS:
Senior Manager
Joined: 22 Jun 2019
Posts: 425
Followers: 0

Kudos [?]: 69 [1] , given: 150

The numbers {a,b,c} are three positive integers. [#permalink]  03 Sep 2019, 03:08
1
KUDOS
00:00

Question Stats:

50% (00:57) correct 50% (01:22) wrong based on 10 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

_________________

New to the GRE CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL

Questions' Banks and Collection:
ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides (Old plus New) |
3rd Party Resource's: All Quant Questions Collection (From All Other Resources) | All Verbal Questions Collection (From all Other Resources) | Manhattan 5lb All Questions Collection
BOOKS: All GRE Best Books
SCORES: Average GRE Score Required By Universities in the USA
TESTS: All Free & Paid Practice Tests

Founder
Joined: 18 Apr 2015
Posts: 9336
Followers: 193

Kudos [?]: 2268 [0], given: 8822

Re: The numbers {a,b,c} are three positive integers. [#permalink]  03 Sep 2019, 08:09
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
_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Senior Manager
Joined: 22 Jun 2019
Posts: 425
Followers: 0

Kudos [?]: 69 [0], given: 150

Re: The numbers {a,b,c} are three positive integers. [#permalink]  03 Sep 2019, 21:00
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
_________________

New to the GRE CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL

Questions' Banks and Collection:
ETS: ETS Free PowerPrep 1 & 2 All 320 Questions Explanation. | ETS All Official Guides (Old plus New) |
3rd Party Resource's: All Quant Questions Collection (From All Other Resources) | All Verbal Questions Collection (From all Other Resources) | Manhattan 5lb All Questions Collection
BOOKS: All GRE Best Books
SCORES: Average GRE Score Required By Universities in the USA
TESTS: All Free & Paid Practice Tests

Founder
Joined: 18 Apr 2015
Posts: 9336
Followers: 193

Kudos [?]: 2268 [0], given: 8822

Re: The numbers {a,b,c} are three positive integers. [#permalink]  04 Sep 2019, 02:46
Expert's post
_________________

Need Practice? 20 Free GRE Quant Tests available for free with 20 Kudos
GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Senior Manager
Joined: 22 Jun 2019
Posts: 425
Followers: 0

Kudos [?]: 69 [0], given: 150

Re: The numbers {a,b,c} are three positive integers. [#permalink]  04 Sep 2019, 04:26
GRE Instructor
Joined: 10 Apr 2015
Posts: 2672
Followers: 101

Kudos [?]: 2954 [2] , given: 45

Re: The numbers {a,b,c} are three positive integers. [#permalink]  05 Sep 2019, 09:52
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

Intern
Joined: 18 Jul 2019
Posts: 32
Followers: 0

Kudos [?]: 2 [0], given: 2

Re: The numbers {a,b,c} are three positive integers. [#permalink]  05 Sep 2019, 11:02
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