Difference between revisions of "1995 AHSME Problems/Problem 11"
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Revision as of 22:15, 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
; 
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.
; 
if 
, and 
if 
. Therefore, 
.
; it must be a multiple of 
. Therefore, 
.
and 
. The possible ordered pairs of 
, 
, 
, 
and 
and there are 
of them.Multiplying the possibilities for each restriction, 
.
