1995 AHSME Problems/Problem 11
Problem
How many base 10 four-digit numbers, , satisfy all three of the following conditions?
(i) (ii) is a multiple of 5; (iii) .
Solution
- For condition (i), the restriction is put on ; if , and if . Therefore, .
- For condition (ii), the restriction is put on ; it must be a multiple of . Therefore, .
- For condition (iii), the restriction is put on and . The possible ordered pairs of and are , , , and and there are of them. Alternatively, we are picking from the four digits 3, 4, 5, 6, and for every combination of two, there is exactly one way to arrange them in increasing order, so we have choices for and when we consider them together.
Multiplying the possibilities for each restriction, .
See also
1995 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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