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If a, b and c are all positive integers , and 2a=7b=8c , then what is

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If a, b and c are all positive integers , and 2a=7b=8c , then what is  [#permalink]

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New post 03 Aug 2017, 03:24
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A
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C
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If a, b and c are all positive integers, and 2a=7b=8c, then what is the LEAST possible value of a+b+c?

A. 26
B. 34
C. 43
D. 50
E. 86

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Re: If a, b and c are all positive integers , and 2a=7b=8c , then what is  [#permalink]

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New post 03 Aug 2017, 04:08
Since 7 and 2 are primes.
C will need to be 7 , which makes 8c =56 and B to be 8 for 7a to be equal to 8c .
In the similar fashion a will be 28. So adding all the terms you get 43.

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Re: If a, b and c are all positive integers , and 2a=7b=8c , then what is  [#permalink]

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New post 03 Aug 2017, 04:28
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Skywalker18 wrote:
If a, b and c are all positive integers, and 2a=7b=8c, then what is the LEAST possible value of a+b+c?

A. 26
B. 34
C. 43
D. 50
E. 86



When I see two "=", I automatically tend to put another one.

2a = 7b = 8c = k

a = k/2
b = k/7
c = k/8

a:b:c = k/2 : k/7 : k/8
Multiply the ratio by 56 to get
a:b:c = 28k:8k:7k

If k = 1 (since a, b, c are positive integers), a = 28, b = 8 and c = 7 (the minimum possible values)
So min sum = 28 + 8 + 7 = 43

Answer (C)
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Re: If a, b and c are all positive integers , and 2a=7b=8c , then what is  [#permalink]

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New post 03 Aug 2017, 04:31
Skywalker18 wrote:
If a, b and c are all positive integers, and 2a=7b=8c, then what is the LEAST possible value of a+b+c?

A. 26
B. 34
C. 43
D. 50
E. 86


I would go for C

2A =7b=8C

Min value (Used case method/trial method)
2(4*7)=7 (8) =8(7)

28+8+7 =43
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Re: If a, b and c are all positive integers , and 2a=7b=8c , then what is  [#permalink]

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New post 03 Aug 2017, 04:39
Yes 43, makes sense to find a factor for the three


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Re: If a, b and c are all positive integers , and 2a=7b=8c , then what is &nbs [#permalink] 03 Aug 2017, 04:39
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