Data Sufficiency

The question is:

Exactly how many show dogs does Sheila have?

(1) Of Sheila's show dogs, exactly 3 have won prizes of at least $500
(2) Of Sheila's show dogs, exactly 40% have not won a prize of $500 or more.

The answer provided is (C) because according to the book 60% represents the 3 that have won prizes and hence you can calculate the no. of dogs.

However the solution assumes that all of Sheila's dogs won a prize. Is this correct? Should the answer not be (E) because we are not told that all of Sheila's dogs have won at least one prize.

Have not won a prize of $500 or more would include all the show dogs that did not win any prizes as well. If a show dog does not win a prize, then that dog has not won a prize of $500 or more.

The correct answer is C.

A---itself not sufficient since information is provided of only three dogs.

B--itself not sufficient since only the % of dogs is given. The actual number cannot be calculated.

Taking A+B

This means that 60% Total dogs =3; So the total number of dogs can be calculated.