Difference between revisions of "1995 AHSME Problems/Problem 11"
(→See also) |
|||
| Line 15: | Line 15: | ||
==See also== | ==See also== | ||
| − | {{ | + | {{AHSME box|year=1995|num-b=10|num-a=12}} |
[[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.
; 
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, 
.
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 | ||
