Difference between revisions of "2000 AMC 12 Problems/Problem 6"
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== Problem == | == Problem == | ||
| − | Two different prime | + | Two different [[prime number]]s between <math>4</math> and <math>18</math> are chosen. When their sum is subtracted from their product, which of the following numbers could be obtained? |
<math> \mathrm{(A) \ 21 } \qquad \mathrm{(B) \ 60 } \qquad \mathrm{(C) \ 119 } \qquad \mathrm{(D) \ 180 } \qquad \mathrm{(E) \ 231 } </math> | <math> \mathrm{(A) \ 21 } \qquad \mathrm{(B) \ 60 } \qquad \mathrm{(C) \ 119 } \qquad \mathrm{(D) \ 180 } \qquad \mathrm{(E) \ 231 } </math> | ||
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== See also == | == See also == | ||
* [[2000 AMC 12 Problems]] | * [[2000 AMC 12 Problems]] | ||
| − | *[[2000 AMC 12/Problem 5|Previous Problem]] | + | * [[2000 AMC 12 Problems/Problem 5|Previous Problem]] |
| − | *[[2000 AMC 12/Problem 7|Next problem]] | + | *[[2000 AMC 12 Problems/Problem 7|Next problem]] |
[[Category:Introductory Algebra Problems]] | [[Category:Introductory Algebra Problems]] | ||
Revision as of 12:09, 13 November 2006
Problem
Two different prime numbers between 
and 
are chosen. When their sum is subtracted from their product, which of the following numbers could be obtained?
Solution
Let the primes be 
and 
.
The problem asks us for possible values of 
where 
Using Simon's Favorite Factoring Trick:
Possible values of 
and 
are:
The possible values for 
(formed by multipling two distinct values for and ) are:
So the possible values of are:
The only answer choice on this list is 
