2015 AMC 10B Problems

Problem 1

What is the value of $2-(-2)^{-2}$ ?

$\textbf{(A)}\; -2 \qquad\textbf{(B)}\; \dfrac{1}{16} \qquad\textbf{(C)}\; \dfrac{7}{4} \qquad\textbf{(D)}\; \dfrac{9}{4} \qquad\textbf{(E)}\; 6$

Solution

Problem 2

Marie does three equally time-consuming tasks in a row without taking breaks. She begins the first task at 1:00 PM and finishes the second task at 2:40 PM. When does she finish the third task?

$\textbf{(A)}\; 3:10 PM \qquad\textbf{(B)}\; 3:30 PM \qquad\textbf{(C)}\; 4:00 PM \qquad\textbf{(D)}\; 4:10 PM \qquad\textbf{(E)}\; 4:30 PM$

Solution

Problem 3

Isaac has written down one integer two times and another integer three times. The sum of the five numbers is 100, and one of the numbers is 28. What is the other number?

$\textbf{(A)}\; 8 \qquad\textbf{(B)}\; 11 \qquad\textbf{(C)}\; 14 \qquad\textbf{(D)}\; 15 \qquad\textbf{(E)}\; 18$

Solution

Problem 4

Four siblings ordered an extra large pizza. Alex ate $\frac{1}{5}$ , Beth $\frac{1}{3}$ , and Cyril $\frac{1}{4}$ of the pizza. Dan got the leftovers. What is the sequence of the siblings in decreasing order of the part of the pizza they consumed?

$\textbf{(A)}\; ? \qquad\textbf{(B)}\; ? \qquad\textbf{(C)}\; ? \qquad\textbf{(D)}\; ? \qquad\textbf{(E)}\; ?$

Solution

Problem 5

David, Hikmet, Jack, Marta, Rand, and Todd were in a 12-person race with 6 other people. Rand finished 6 places ahead of Hikmet. Marta finished 1 place behind Jack. David finished 2 places behind Hikmet. Jack finished 2 places behind Todd. Todd finished 1 place behind Rand. Marta finished in 6th place. Who finished in 8th place?

$\textbf{(A)}\; ? \qquad\textbf{(B)}\; ? \qquad\textbf{(C)}\; ? \qquad\textbf{(D)}\; ? \qquad\textbf{(E)}\; ?$

Solution

Problem 6

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

$\textbf{(A)}\; ? \qquad\textbf{(B)}\; ? \qquad\textbf{(C)}\; ? \qquad\textbf{(D)}\; ? \qquad\textbf{(E)}\; ?$

Solution