Difference between revisions of "2002 AMC 10A Problems"
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== Problem 4 == | == Problem 4 == | ||
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+ | For how many positive integers m is there at least 1 positive integer n such that <math>mn \le m + n</math>? | ||
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+ | <math>\text{(A)}\ 4 \qquad \text{(B)}\ 6 \qquad \text{(C)}\ 9 \qquad \text{(D)}\ 12 \qquad \text{(E)}</math> Infinite | ||
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[[2002 AMC 10A Problems/Problem 4|Solution]] | [[2002 AMC 10A Problems/Problem 4|Solution]] |
Revision as of 01:16, 26 December 2008
Contents
[hide]- 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
Problem 2
Problem 3
Problem 4
For how many positive integers m is there at least 1 positive integer n such that ?
Infinite
Problem 5
Problem 6
Problem 7
A arc of circle A is equal in length to a arc of circle B. What is the ratio of circle A's area and circle B's area?
Problem 8
Problem 9
Problem 10
What is the sum of all of the roots of ?
Problem 11
Problem 12
Problem 13
Give a triangle with side lengths 15, 20, and 25, find the triangle's smallest height.
Problem 14
The 2 roots of the quadratic are both prime. How many values of k are there?
$\text{(A)}\ 0 \qquad \text{(B)}\ 1 \qquad \text{(C)}\ 2 \qquad \text{(D)}\ 4 \qquad \text{(E)}&$ (Error compiling LaTeX. Unknown error_msg)More than 4
Problem 15
Using the digits 1, 2, 3, 4, 5, 6, 7, and 9, form 4 two-digit prime numbers, using each digit only once. What is the sum of the 4 prime numbers?
Problem 16
Let . What is ?
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
A set of tiles numbered 1 through 100 is modified repeatedly by the following operation: remove all tiles numbered with a perfect square, and renumber the remaining tiles consecutively starting with 1. How many times must the operation be performed to reduce the number of tiles in the set to one?
Problem 23
Problem 24
Tina randomly selects two distinct numbers from the set {1, 2, 3, 4, 5}, and Sergio randomly selects a number from the set {1, 2, ..., 10}. What is the probability that Sergio's number is larger than the sum of the two numbers chosen by Tina?
Problem 25
In trapezoid with bases and , we have , , , and . The area of is