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

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The numbers {a,b,c} are three positive integers. [#permalink] New post 03 Sep 2019, 03:08
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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] New post 03 Sep 2019, 08:09
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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
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Re: The numbers {a,b,c} are three positive integers. [#permalink] New post 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
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Re: The numbers {a,b,c} are three positive integers. [#permalink] New post 04 Sep 2019, 02:46
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About what ??
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Re: The numbers {a,b,c} are three positive integers. [#permalink] New post 04 Sep 2019, 04:26
Carcass wrote:
About what ??


the whole that u said.
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Re: The numbers {a,b,c} are three positive integers. [#permalink] New post 05 Sep 2019, 09:52
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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

Answer: A

Cheers,
Brent
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Re: The numbers {a,b,c} are three positive integers. [#permalink] New post 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
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The numbers {a,b,c} are three positive integers.

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