Difference between revisions of "1995 AHSME Problems/Problem 11"
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[[Category:Introductory Combinatorics Problems]] | [[Category:Introductory Combinatorics Problems]] |
Revision as of 07:55, 17 April 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
;
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.
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 |