# 2015 AMC 10B Problems/Problem 6

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## Problem

Mahdi practices exactly one sport each day of the week. He runs three days a week but never on two consecutive days. On Monday he plays basketball and two days later golf. He swims and plays tennis, but he never plays tennis the day after running or swimming. Which day of the week does Mahdi swim?

$\textbf{(A) } \text{Sunday} \qquad\textbf{(B) } \text{Tuesday} \qquad\textbf{(C) } \text{Thursday} \qquad\textbf{(D) } \text{Friday} \qquad\textbf{(E) } \text{Saturday}$

## Solution

Mahdi does basketball on Monday and golf on Wednesday. Since there are four consecutive days between Wednesday and Monday exclusive, he must run on Tuesday. Thus, he must also run on Thursday and Saturday or Friday and Sunday. He can't run on Thursday and Saturday because he would have to do tennis after running, which is not allowed. Thus, he runs on Friday and Sunday, so he must do tennis on Thursday, so he swims on $\boxed{\mathbf{(E)}\ \mathrm{Saturday}}$

## Video Solution 1

~Education, the Study of Everything

## Video Solution

~savannahsolver

 2015 AMC 10B (Problems • Answer Key • Resources) Preceded byProblem 5 Followed byProblem 7 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AMC 10 Problems and Solutions