manik11 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%
OA : D
Source : Veritas Prep
L:A:E = 2:5:8
New, L:A = 2*(2:5)= 4:5
New, L:E > 2:8 i.e. L:E > 1:4 (i.e. Numerator should increase or denominator should decrease
Min value of New no. of Little dogs = 4x (where x must be Integer)
Min value of New no. of Average dogs = 5x (where x must be Integer)
Min value of New no. of Enormous dogs < 4*4x i.e. <16x (where x must be Integer)
Min total No. of Dogs = 4x+5x+(<16x) i.e. <25x which must be less than 30 and must be Integer as well for x to be Integer
i.e. Total Dogs may be 24, 23, 22, 21, 20 etc. (Given: It should be fewer than 30)
i.e. x must be 1
% of Little dogs = (4/total dogs)*100 = 400/total
% of Average dogs = (5/total dogs)*100 = 500/total
i.e. Total dogs should be factor of 400 and 500 both.
As per given information 20 fits best
Total Dogs = 20
Little = 4
Average = 5
Enourmous = 11
% of enormous = (11/20)*100 = 55%
Answer: option D
