TRAIN FOR THE AMC 10 WITH AoPS
Thousands of top-scorers on the AMC 10 have used our Introduction series of textbooks and Art of Problem Solving Volume 1 for their training.
CHECK OUT THE BOOKS

Difference between revisions of "2019 AMC 10A Problems"

m (Problem 25)
(Problem 3)
Line 9: Line 9:
  
 
==Problem 3==
 
==Problem 3==
 +
Ana and Bonita were born on the same date in different years, <math>n</math> years apart. Last year Ana was <math>5</math> times as old as Bonita. This year Ana's age is the square of Bonita's age. What is <math>n?</math>
 +
 +
<math>\textbf{(A) } 3 \qquad\textbf{(B) } 5 \qquad\textbf{(C) } 9 \qquad\textbf{(D) } 12 \qquad\textbf{(E) } 15</math>
 +
 
==Problem 4==
 
==Problem 4==
 
==Problem 5==
 
==Problem 5==

Revision as of 15:12, 9 February 2019

Problem 1

What is the value of \[2^{\left(0^{\left(1^9\right)}\right)}+\left(\left(2^0\right)^1\right)^9?\] $\textbf{(A) } 0 \qquad\textbf{(B) } 1 \qquad\textbf{(C) } 2 \qquad\textbf{(D) } 3 \qquad\textbf{(E) } 4$

Problem 2

What is the hundreds digit of $(20!-15!)\ ?$

$\textbf{(A) }0\qquad\textbf{(B) }1\qquad\textbf{(C) }2\qquad\textbf{(D) }4\qquad\textbf{(E) }5$

Problem 3

Ana and Bonita were born on the same date in different years, $n$ years apart. Last year Ana was $5$ times as old as Bonita. This year Ana's age is the square of Bonita's age. What is $n?$

$\textbf{(A) } 3 \qquad\textbf{(B) } 5 \qquad\textbf{(C) } 9 \qquad\textbf{(D) } 12 \qquad\textbf{(E) } 15$

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

For how many integers $n$ between 1 and 50, inclusive, is

$\frac{(n^2-1)!}{(n!)^{n}}$

an integer? (Recall that $0!=1$.)

$\textbf{(A) } 31 \qquad \textbf{(B) } 32 \qquad \textbf{(C) } 33 \qquad \textbf{(D) } 34 \qquad \textbf{(E) } 35$