emmak wrote:
At a local beach, the ratio of little dogs to average dogs to enormous dogs is 2:5:8. Late in the afternoon, the ratio of little dogs to average dogs doubles and the ratio of little dogs to enormous dogs increases. If the new percentage of little dogs and the new percentage of average dogs are both integers and there are fewer than 30 total dogs at the beach, which of the following represents a possible new percentage of enormous dogs?
A. 25%
B. 40%
C. 50%
D. 55%
E. 70%
I like to go straight forward and with the question stem. This is how I solved analyzing the question sentence by sentence.
1) Initially the ratio of Local : Average : Enormous is 2:5:8.
2) After afternoon ratios become :- 4:5:x (since we do not know in what ratio are enormous dogs in)
3) Initially Local : Enormous ratio is 1:4. Now, Ques stem says that this ratio increases. Therefore new ratio i.e. 4:x > 1:4 ; this gives us x < 16.
4) Now, percentage of Local dogs in afternoon is \(\frac{(4*100)}{(9+x)}\) and average dogs is \(\frac{(5*100)}{(9+x)}\)
5) These ratios will be integers only when the denominators of these terms are common factors of 400 and 500 and the multiplication of those factors such as 2,5,10,20,50 etc. Since x is less than 16, x can only be 1 and 11 so that the denominators are 10 and 20 respectively.
6) Therefore the possible percentages of Enormous dogs can be 10% (i.e. (1/(9+1))*100 considering x = 1) and 55% (i.e. (11/(9+11))*100 considering x = 11)
Only 55% is in the options hence D
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40% (02:34) correct 
