2005 AMC 12A Problems/Problem 23
Problem
Two distinct numbers a and b are chosen randomly from the set . What is the probability that
is an integer?
Solution
Let , so
. Define
,
; then
, so
. Here we can just make a table and count the number of values of
per value of
. The largest possible value of
is 12, and we get
.
The total number of ways to pick two distinct numbers is , so we get a probability of
.
See also
2007 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 22 |
Followed by Problem 24 |
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All AMC 12 Problems and Solutions |