Difference between revisions of "2002 AMC 10B Problems"
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when <math>x=4</math>? | when <math>x=4</math>? |
Revision as of 13:43, 27 May 2011
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
The ratio is:
Problem 2
For the nonzero numbers and
define
Find
.
Problem 3
The arithmetic mean of the nine numbers in the set is a
-digit number
, all of whose digits are distinct. The number
does not contain the digit
Problem 4
What is the value of
when ?
Problem 5
Problem 6
For how many positive integers n is a prime number?
Problem 7
Let be a positive integer such that
is an integer. Which of the following statements is not true?
Problem 8
Suppose July of year has five Mondays. Which of the following must occurs five times in the August of year
? (Note: Both months have
days.)
Problem 9
Using the letters ,
,
,
, and
, we can form five-letter "words". If these "words" are arranged in alphabetical order, then the "word"
occupies position
Problem 10
Suppose that and
are nonzero real numbers, and that the equation
has positive solutions
and
. Then the pair
is
Problem 11
The product of three consecutive positive integers is times their sum. What is the sum of the squares?
Problem 12
For which of the following values of does the equation
have no solution for
?
Problem 13
Find the value(s) of such that
is true for all values of
.
Problem 14
The number is the square of a positive integer
. In decimal representation, the sum of the digits of
is
Problem 15
The positive integers ,
,
, and
are all prime numbers. The sum of these four primes is
Problem 16
For how many integers is
the square of an integer?
Problem 17
A regular octagon has sides of length two. Find the area of
.
Problem 18
Four distinct circles are drawn in a plane. What is the maximum number of points where at least two of the circles intersect?
Problem 19
Problem 20
Problem 21
Problem 22
Let be a right-triangle with
. Let
and
be the midpoints of the legs
and
, respectively. Given
and
, find
.
Problem 23
Problem 24
Problem 25
When 15 is appended to a list of integers, the mean is increased by 2. When 1 is appended to the enlarged list, the mean of the enlarged list is decreased by 1. How many integers were in the original list?