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The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive inte

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The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive inte  [#permalink]

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New post 29 Jun 2016, 19:23
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The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of them is 18, what is the value of a?
A. 3
B. 6
C. 9
D. 12
E. 15

*An answer will be posted in 2 days.

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Re: The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive inte  [#permalink]

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New post 29 Jun 2016, 20:34
(2+3+4)x =18*3
x=6
=>a=2x=2*6=12

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Re: The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive inte  [#permalink]

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New post 03 Jul 2016, 04:42
a=2k, b=3k, c=4k, a+b+c=2k+3k+4k=(18)(3), 9k=18(3), k=6. Therefore, a=2k=2(6)=12, and the correct answer is D.
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Re: The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive inte  [#permalink]

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New post 03 Jul 2016, 05:02
D. 12
simply 3x will be the AM

X=6
a=2x=12


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Re: The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive inte  [#permalink]

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New post 03 Jul 2016, 05:52
MathRevolution wrote:
The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive integers. If the average (arithmetic mean) of them is 18, what is the value of a?
A. 3
B. 6
C. 9
D. 12
E. 15

*An answer will be posted in 2 days.

Plugging in Answer Choice worked for me

Here given a:b:c=2:3:4 ,So a:b:c=1:\(\frac{3}{2}\):2

Now by putting value of a=12 on the ratio we can find that only answer choice D matched with a:b:c=12:18:24 ,arithmetic mean of them is \(\frac{12+18+24}{3}\)=18

Correct Answer D
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Re: The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive inte  [#permalink]

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New post 03 Jul 2016, 06:33
If a list of numbers is 'evenly spaced out,' then the average equals the median. (e.g. in the list {7, 14, 21, 28, 25}, 21 is immediately apparent as the average because each term is separated from the preceding term by the same number)

In this question, a, b and c are evenly spaced out, so we know that b is the average. Therefore b's real value is 18. this means our multiplier is 6. So a is 2*6=12.
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Re: The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive inte   [#permalink] 03 Jul 2016, 06:33

The ratio of a to b to c is 2 to 3 to 4, and a, b, c are positive inte

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