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

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CEO
Joined: 11 Sep 2015
Posts: 3228
A bag contains blue, red and green marbles only.  [#permalink]

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29 Oct 2016, 08:39
2
Top Contributor
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Difficulty:

15% (low)

Question Stats:

75% (01:37) correct 25% (01:40) wrong based on 132 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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Joined: 28 Jun 2016
Posts: 207
Concentration: Operations, Entrepreneurship
Re: A bag contains blue, red and green marbles only.  [#permalink]

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29 Oct 2016, 09:12
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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Joined: 18 Sep 2016
Posts: 49
A bag contains blue, red and green marbles only.  [#permalink]

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29 Oct 2016, 09:19
1
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

$$15+16+12= 43$$

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

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29 Oct 2016, 10:16
1
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

Attachment:

Capture.PNG [ 2.36 KiB | Viewed 1756 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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13 Jul 2018, 06:20
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, 06:20
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