On Monday, a certain animal shelter housed 55 cats and dogs. By Friday, exactly 1/5 of the cats and 1/4 of the dogs had been adopted, no new cats or dogs were brought to the shelter during this period. What is the greatest possible number of pets that could have been adopted from the animal shelter between Monday and today?

Options

A. a.11
B. b.12
C. c.13
D. d.14

Answer

C

Explanation

According to the question
Total number of cats and dogs = 55
Out of these `1/5` cats + `1/4` dogs had been adopted.
Two possible cases for these given conditions are as follows:
(i) If cats = 15, dogs = 40
(ii) If cats = 35, dogs = 20.
[`because` In other cases, (i) will not be satisfied]
(iii) If cat = 15, dog = 40, then
`(1/5 xx 15)` cats + `(1/4 xx 40)` dogs = 3 cats + 10 dogs = 13
pets were adopted.
(ii) If cats = 35, dogs = 20, then
`(1/5 xx 35)` cats + `(1/4 xx 20) `dogs = 7 cats + 5 dogs = 12 pets were adopted.
[`because` 14 pets `gt` 12 pets]
So, the greatest possible number of adopted pets = 13.