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Starting with a positive integer M written on the board, Alice plays the following game: in each move, if x is the number on the board, she replaces it with 3 x+2 . Similarly, starting with a positive integer N written on the board, Bob plays the following game: in each move, if x is the number on the board, he replaces it with 2 x+27 . Given that Alice and Bob reach the same number after playing 4 moves each, find t

Correct answer

10

Step-by-step solution

In 4 steps Alice will write (3(3(3(3 M+2)+2)+2)+2)= and Bob will write (2(2(2(2 N+27)+27)+27)+27)= As = , we get array ll & 81 M=16 N+325 & M_ =5 and N_ =5 & (M+N)_ =10 array

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