Difference between revisions of "1995 AHSME Problems/Problem 11"
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Revision as of 08:11, 9 January 2008
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 a; N<4000 if a<4, and N≥6 if a≥6. Therefore, a=4,5.
For condition (ii), the condition is put on d; it must be a multiple of 5. Therefore, d=0,5.
For condition (iii), the condition is put on b and c. The possible ordered pairs of b and c are (3,4), (3,5), (3,6), (4,5), (4,6), and (5,6), and there are 6 of them.
Multiplying the possibilities for each restriction, 
See also
| 1995 AHSME (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 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
