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A bag contains blue, red and green marbles only.

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A bag contains blue, red and green marbles only.  [#permalink]

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New post 29 Oct 2016, 09:39
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E

Difficulty:

  25% (medium)

Question Stats:

70% (01:24) correct 30% (01:09) wrong based on 124 sessions

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A bag contains blue, red and green marbles only. If the ratio of blue marbles to red marbles is 4 to 5, and the ratio of green marbles to blue marbles is 4 to 3, what is the minimum number of marbles in the bag?

A) 12
B) 16
C) 28
D) 41
E) 43

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Re: A bag contains blue, red and green marbles only.  [#permalink]

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New post 29 Oct 2016, 10:12
1
b:r = 4:5

b:g= 3:4

b:r:g = 12:15:16

Minimum total = 12+15+16 = 43

E


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A bag contains blue, red and green marbles only.  [#permalink]

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New post 29 Oct 2016, 10:19
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GMATPrepNow wrote:
A bag contains blue, red and green marbles only. If the ratio of blue marbles to red marbles is 4 to 5, and the ratio of green marbles to blue marbles is 4 to 3, what is the minimum number of marbles in the bag?

A) 12
B) 16
C) 28
D) 41
E) 43

* Kudos for all correct solutions



let's call the number of marbles r, b and g
from the question we can easily get that \(b=\frac{4}{5}*r\) and \(b=\frac{3}{4}*g\)

combining the two equation we have that \(\frac{4}{5}*r=\frac{3}{4}*g\) and therefore, \(r=\frac{15}{16}*g\)

as both r and g must be integers r must be 15 and g must be 16.
from one of the first two equations we can find by sobstitution that b=12

\(15+16+12= 43\)

answer E
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A bag contains blue, red and green marbles only.  [#permalink]

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New post 29 Oct 2016, 11:16
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GMATPrepNow wrote:
A bag contains blue, red and green marbles only. If the ratio of blue marbles to red marbles is 4 to 5, and the ratio of green marbles to blue marbles is 4 to 3, what is the minimum number of marbles in the bag?

A) 12
B) 16
C) 28
D) 41
E) 43

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Capture.PNG [ 2.36 KiB | Viewed 1620 times ]

Minimum Number of marbles is 15 + 16 + 12 = 43

Hence answer will be (E) 43

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Re: A bag contains blue, red and green marbles only.  [#permalink]

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New post 13 Jul 2018, 07:20
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: A bag contains blue, red and green marbles only. &nbs [#permalink] 13 Jul 2018, 07:20
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