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A certain dog kennel houses only collies, labs, and golden

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GMAT Club Legend
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Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1612 [0], given: 375

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A certain dog kennel houses only collies, labs, and golden [#permalink] New post 14 Jun 2018, 14:20
Expert's post
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Question Stats:

100% (01:30) correct 0% (00:00) wrong based on 5 sessions
A certain dog kennel houses only collies, labs, and golden retrievers. If the ratio of collies to labs is 5 : 9, there are 66 golden retrievers, and 12 more golden retrievers than labs in the kennel, what percent of the dogs in the kennel are collies?


(A) 5%
(B) 9%
(C) 12%
(D) 20%
(E) 25%
[Reveal] Spoiler: OA

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Re: A certain dog kennel houses only collies, labs, and golden [#permalink] New post 15 Jun 2018, 07:54
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sandy wrote:
A certain dog kennel houses only collies, labs, and golden retrievers. If the ratio of collies to labs is 5 : 9, there are 66 golden retrievers, and 12 more golden retrievers than labs in the kennel, what percent of the dogs in the kennel are collies?


(A) 5%
(B) 9%
(C) 12%
(D) 20%
(E) 25%


I took 3:34 secs for this question :(

collies : labs : golden retrievers => c:l:g

Given that c/l = 5x/9x --> eq 1

Given total g = 66 and now question say that golden retrievers are 12 more than labs i.e. l = 54.

From eq 1 , we can take 9x = 54, x = 6

then c = 30.

Now c/c+l+g = 30/150 => 0.2.

D.
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [0], given: 375

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Re: A certain dog kennel houses only collies, labs, and golden [#permalink] New post 05 Jul 2018, 03:02
Expert's post
Explanation

Start by assigning variables:

C = Number of collies
L = Number of labs
G = Number of golden retrievers

According to the given information:

G = 66
L = 66 – 12
L = 54

Ratios work like fractions, and you can set them up accordingly:

\(\frac{5}{9}=\frac{C}{54}\)

Cross-multiplying and simplifying, you get:

C = 30
Now take the number of collies and express it as a percent of the total number of dogs:

Total # of Dogs = 30 + 54 + 66 = 150

\(\frac{30}{150}*100=20%\)
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Re: A certain dog kennel houses only collies, labs, and golden   [#permalink] 05 Jul 2018, 03:02
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