There are 30 people in a room, $60 \%$ of whom are men. If no men enter or leave the room, how many women must enter the room so that $40 \%$ of the total number of people in the room are men?
(A) 10
(B) 6
(C) 20
(D) 12
(E) 15
Since there are 30 people in a room and $60 \%$ of them are men, then there are $\frac{6}{10} \times 30=18$ men in the room and 12 women.

Since no men enter or leave the room, then these 18 men represent $40 \%$ of the final number in the room.

Thus, 9 men represent $20 \%$ of the the final number in the room, and so the final number of people is $5 \times 9=45$.

Since 18 of these are men and 12 of these are the women originally in the room, then $45-18-12=15$ women entered the room.

ANswer: (E)