Question

Emily has 300 books. if frank were to double the number of books that he now owns, he would still have fewer than Emily has

Answer 1

This statement is false. 
If he were to double the amount that Emily has to get franks, franks would have more. 
Look :)
Emily's = 300
Frank's = 300 x 2 = 600

now...
Emily's = 300
Frank's = 600

So frank has more! NOT fewer. 

Answer 2

It never stated how many books frank had