Difference between revisions of "2000 AMC 10 Problems/Problem 11"
5849206328x (talk | contribs) m |
5849206328x (talk | contribs) (→Problem) |
||
Line 1: | Line 1: | ||
==Problem== | ==Problem== | ||
+ | |||
+ | Two different prime numbers 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> | ||
==Solution== | ==Solution== |
Revision as of 20:40, 9 January 2009
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
Two prime numbers between and are both odd.
odd*odd=odd.
odd-odd-odd=odd.
Thus, we can discard the even choices.
.
.
Both of these factors are even, so the number +1 must be a multiple of .
is the only possiblity.
satisfy this, .
C
See Also
2000 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |