Difference between revisions of "2016 AMC 10A Problems"

Revision as of 17:46, 3 February 2016

Problem 1

What is the value of $\dfrac{11!-10!}{9!}$ ?

$\textbf{(A)}\ 99\qquad\textbf{(B)}\ 100\qquad\textbf{(C)}\ 110\qquad\textbf{(D)}\ 121\qquad\textbf{(E)}\ 132$

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Five friends sat in a movie theater in a row containing 5 seats, numbered 1 to 5 from left to right. (The directions "left" and "right" are from the point of view of the people as they sit in the seats.) During the movie Ada went to the lobby to get some popcorn. When she returned, she found that Bea had moved two seats to the right, Ceci had moved one seat to the left, and Dee and Edie had switched seats, leaving an end seat for Ada. In which seat had Ada been sitting before she got up?

$\textbf{(A)}\ 1\qquad\textbf{(B)}\ 2\qquad\textbf{(C)}\ 3\qquad\textbf{(D)}\ 4\qquad\textbf{(E)}\ 5$

Problem 14

How many ways are there to write 2016 as the sum of twos and threes, ignoring order? (For example, 1008 $\cdot$ 2 + 0 $\cdot$ 3 and 402 $\cdot$ 2 + 404 $\cdot$ 3 are two such ways.)

$\textbf{(A)}\ 236\qquad\textbf{(B)}\ 336\qquad\textbf{(C)}\ 337\qquad\textbf{(D)}\ 403\qquad\textbf{(E)}\ 672$

Problem 15

Problem 16

Problem 17

Problem 18

Each vertex of a cube is to be labeled with an integer from $1$ to $8$ , with each integer being used once, in such a way that the sum of the four numbers on the vertices of a face is the same for each face. Arrangements that can be obtained from each other through rotations of the cube are considered to be the same. How many different arrangements are possible?

$(A) 1 (B) 3 (C) 6 (D) 12 (E) 24$

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 ==Problem 18==
+Each vertex of a cube is to be labeled with an integer from <math>1</math> to <math>8</math>, with each integer being used once, in such a way that the sum of the four numbers on the vertices of a face is the same for each face.  Arrangements that can be obtained from each other through rotations of the cube are considered to be the same.  How many different arrangements are possible?
+<math>(A) 1 (B) 3 (C) 6 (D) 12 (E) 24</math>
 ==Problem 19==

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