Difference between revisions of "2019 AMC 10A Problems"
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==Problem 24== | ==Problem 24== | ||
==Problem 25== | ==Problem 25== | ||
− | For how many integers <math>n</math> between 1 and 50, inclusive, is | + | For how many integers <math>n</math> between <math>1</math> and <math>50</math>, inclusive, is <cmath>\frac{(n^2-1)!}{(n!)^{n}}</cmath> an integer? (Recall that <math>0!=1</math>.) |
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− | an integer? (Recall that <math>0!=1</math>.) | ||
<math>\textbf{(A) } 31 \qquad \textbf{(B) } 32 \qquad \textbf{(C) } 33 \qquad \textbf{(D) } 34 \qquad \textbf{(E) } 35</math> | <math>\textbf{(A) } 31 \qquad \textbf{(B) } 32 \qquad \textbf{(C) } 33 \qquad \textbf{(D) } 34 \qquad \textbf{(E) } 35</math> |
Revision as of 16:14, 9 February 2019
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
Problem 1
What is the value of
Problem 2
What is the hundreds digit of
Problem 3
Ana and Bonita were born on the same date in different years, years apart. Last year Ana was
times as old as Bonita. This year Ana's age is the square of Bonita's age. What is
Problem 4
A box contains red balls,
green balls,
yellow balls,
blue balls,
white balls, and
black balls. What is the minimum number of balls that must be drawn from the box without replacement to guarantee that at least
balls of a single color will be drawn
Problem 5
What is the greatest number of consecutive integers whose sum is
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Let be an isosceles triangle with
and
. Contruct the circle with diameter
, and let
and
be the other intersection points of the circle with the sides
and
, respectively. Let
be the intersection of the diagonals of the quadrilateral
. What is the degree measure of
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 between
and
, inclusive, is
an integer? (Recall that
.)