In a certain state legislature, a proposed bill was defeated with 6 fewer votes for the bill than against it. After the bill was amended, 9 members who had previously voted against the bill were now for it. This resulted in 60% of the legislature now being in favor of the bill. If all those who previously voted for the bill remained in favor of it, how many members are in this state legislature, assuming every member voted each time?
Kevin and Devin each make one hat per day for charity, but they started on different days. Today, Kevin made his 520th hat, and Devin made his 50th. A celebration is planned for the next day that Kevin’s hat count is evenly divisible by Devin’s hat count. In how many days from today will they celebrate?
Donald has nine one-day passes to Dizzyworld. He can go alone and use one, or he can take a friend and use two. If he visits every day until he uses all the passes, in how many different ways can he use them? Using two a day for four days and then going alone at the end (2, 2, 2, 2, 1) is different from reversing the order (1, 2, 2, 2, 2).
Abe chooses a number from Group A, Bob chooses a number from Group B and Charlie chooses a number from Group C.
Group A: 741 345 624 813
Group B: 519 825 717 456
Group C: 134 260 503 152
Then Abe chooses a digit X from his number, Bob chooses a digit Y from his number and Charlie chooses a digit Z from his number. The digits are arranged to form the three-digit number XYZ. Abe, Bob and Charlie, in that order, then choose different digits from their selected numbers to form a second three-digit number. Finally, in the same order, they use the remaining digits to form a third three-digit number. What is the sum of the three numbers that are formed?