2015年AMC 10B 真题及答案

2015年AMC 10B 真题:

Problem 1

What is the value of $2-(-2)^{-2}$?

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

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?

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

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?

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

Problem 4

Four siblings ordered an extra large pizza. Alex ate $\frac15$, Beth $\frac13$, and Cyril $\frac14$ of the pizza. Dan got the leftovers. What is the sequence of the siblings in decreasing order of the part of pizza they consumed?

$\textbf{(A) } \text{Alex, Beth, Cyril, Dan}$ $\textbf{(B) } \text{Beth, Cyril, Alex, Dan}$ $\textbf{(C) } \text{Beth, Cyril, Dan, Alex}$ $\textbf{(D) } \text{Beth, Dan, Cyril, Alex}$ $\textbf{(E) } \text{Dan, Beth, Cyril, Alex}$

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 $6$th place. Who finished in $8$th place?

$\textbf{(A) } \text{David} \qquad\textbf{(B) } \text{Hikmet} \qquad\textbf{(C) } \text{Jack} \qquad\textbf{(D) } \text{Rand} \qquad\textbf{(E) } \text{Todd}$

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 she never plays tennis the day after running or swimming. Which day of the week does Marley swim?

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

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