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TAGS: Senior Manager  Joined: 22 Jun 2019
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The numbers {a,b,c} are three positive integers. [#permalink]
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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

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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

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Senior Manager  Joined: 22 Jun 2019
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Kudos [?]: 69 , given: 150

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
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Re: The numbers {a,b,c} are three positive integers. [#permalink]
Expert's post
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Re: The numbers {a,b,c} are three positive integers. [#permalink] GRE Instructor Joined: 10 Apr 2015
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Re: The numbers {a,b,c} are three positive integers. [#permalink]
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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
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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
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