Problem:
José, Thuy, and Kareem each start with the number . José subtracts from the number , doubles his answer, and then adds . Thuy doubles the number , subtracts from her answer, and then adds . Kareem subtracts from the number , adds to his answer, and then doubles the result. Who gets the largest final answer?
Answer Choices:
A. José
B. Thuy
C. Kareem
D. José and Thuy
E. Thuy and Kareem
Solution:
Starting with :
José computes, consecutively, , then , and finally .
Thuy computes, consecutively, , then , and finally .
Kareem computes, consecutively, , then , and finally .
Thus Kareem gets the largest final answer.
Note. Any number could have been used instead of to obtain the same result.
Start:
First:
Then:
Finally:
First:
Then:
Finally:
First:
Then:
Finally:
Since , Kareem gets the largest final answer.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions