1995 AHSME Problems/Problem 11
Revision as of 13:59, 5 July 2013 by Nathan wailes (talk | contribs)
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 | |
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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.