Difference between revisions of "1992 AHSME Problems/Problem 10"
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== Solution == | == Solution == | ||
<math>\fbox{D}</math> | <math>\fbox{D}</math> | ||
+ | |||
+ | <math>kx -12 = 3k</math> | ||
+ | |||
+ | <math>-12=3k-kx</math> | ||
+ | |||
+ | <math>-12=k(3-x)</math> | ||
+ | |||
+ | <math>\frac{-12}{k}=3-x</math> | ||
+ | |||
+ | Positive factors of <math>-12</math>: | ||
+ | <math>1,2,3,4,6,12</math> | ||
+ | |||
+ | 6 factors, each of which have an integer solution for <math>x</math> in <math>\frac{-12}{k}=3-x</math> | ||
== See also == | == See also == |
Latest revision as of 20:49, 2 March 2017
Problem
The number of positive integers for which the equation
has an integer solution for
is
Solution
Positive factors of :
6 factors, each of which have an integer solution for in
See also
1992 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
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