# 2015 AMC 10A Problems

## Contents

- 1 Problem 1
- 2 Problem 2
- 3 Problem 3
- 4 Problem 4
- 5 Problem 5
- 6 Problem 6
- 7 Problem 7
- 8 Problem 8
- 9 Problem 9
- 10 Problem 10
- 11 Problem 11
- 12 Problem 12
- 13 Problem 13
- 14 Problem 14
- 15 Problem 15
- 16 Problem 16
- 17 Problem 17
- 18 Problem 18
- 19 Problem 19
- 20 Problem 20
- 21 Problem 21
- 22 Problem 22
- 23 Problem 23
- 24 Problem 24
- 25 Problem 25
- 26 See also

## Problem 1

What is the value of

$\textbf{(A)}\ -125\qquad\textbf{(B)}\ -120\qquad\textbf{(C)}\ \frac{1}{5}\qquad\textbf{(D)}}\ \frac{5}{24}\qquad\textbf{(E)}\ 25$ (Error compiling LaTeX. ! Extra }, or forgotten $.)

## Problem 2

A box contains a collection of triangular and square tiles. There are tiles in the box, containing edges total. How many square tiles are there in the box?

$\textbf{(A)}\ 3\qquad\textbf{(B)}\ 5\qquad\textbf{(C)}\ 7\qquad\textbf{(D)}}\ 9\qquad\textbf{(E)}\ 11$ (Error compiling LaTeX. ! Extra }, or forgotten $.)

## Problem 3

Ann made a 3-step staircase using 18 toothpicks. How many toothpicks does she need to add to complete a 5-step staircase?

(A) 9 (B) 18 (C) 20 (D) 22 (E) 24

## Problem 4

Pablo, Sofia, and Mia got some candy eggs at a party. Pablo had three times as many eggs as Sofia, and Sofia had twice as many eggs as Mia. Pablo decides to give some of his eggs to Sofia and Mia so that all three will have the same number of eggs. What fraction of his eggs should Pablo give to Sofia?

$\textbf{(A)}\ \frac{1}{12}\qquad\textbf{(B)}\ \frac{1}{6}\qquad\textbf{(C)}\ \frac{1}{4}\qquad\textbf{(D)}}\ \frac{1}{3}\qquad\textbf{(E)}\ \frac{1}{2}$ (Error compiling LaTeX. ! Extra }, or forgotten $.)

## Problem 5

Mr. Patrick teaches math to students. He was grading tests and found that when he graded everyone's test except Payton's, the average grade for the class was . After he graded Payton's test, the test average became . What was Payton's score on the test?

$\textbf{(A)}\ 81\qquad\textbf{(B)}\ 85\qquad\textbf{(C)}\ 91\qquad\textbf{(D)}}\ 94\qquad\textbf{(E)}\ 95$ (Error compiling LaTeX. ! Extra }, or forgotten $.)

## Problem 6

The sum of two positive numbers is times their difference. What is the ratio of the larger number to the smaller number?

$\textbf{(A)}\ \frac{5}{4}\qquad\textbf{(B)}\ \frac{3}{2}\qquad\textbf{(C)}\ \frac{9}{5}\qquad\textbf{(D)}}\ 2 \qquad\textbf{(E)}\ \frac{5}{2}$ (Error compiling LaTeX. ! Extra }, or forgotten $.)

## Problem 7

How many terms are there in the arithmetic sequence , , , . . ., , ?

$\textbf{(A)}\ 20\qquad\textbf{(B)}\ 21\qquad\textbf{(C)}\ 24\qquad\textbf{(D)}}\ 60\qquad\textbf{(E)}\ 61$ (Error compiling LaTeX. ! Extra }, or forgotten $.)

## Problem 8

Two years ago Pete was three times as old as his cousin Claire. Two years before that, Pete was four times as old as Claire. In how many years will the ratio of their ages be : ?

$\textbf{(A)}\ 2\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}}\ 6\qquad\textbf{(E)}\ 8$ (Error compiling LaTeX. ! Extra }, or forgotten $.)

## Problem 9

## Problem 10

How many rearrangements of are there in which no two adjacent letters are also adjacent letters in the alphabet? For example, no such rearrangements could include either or .

$\textbf{(A)}\ 0\qquad\textbf{(B)}\ 1\qquad\textbf{(C)}\ 2\qquad\textbf{(D)}}\ 3\qquad\textbf{(E)}\ 4$ (Error compiling LaTeX. ! Extra }, or forgotten $.)

## Problem 11

## Problem 12

## Problem 13

## Problem 14

## Problem 15

## Problem 16

## Problem 17

## Problem 18

## Problem 19

## Problem 20

A rectangle has area and perimeter , where and are positive integers. Which of the following numbers cannot equal ?

## Problem 21

## Problem 22

## Problem 23

The zeros of the function are integers. What is the sum of the possible values of ?

## Problem 24

## Problem 25

## See also

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.