Difference between revisions of "2006 AIME A Problems/Problem 7"
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== Problem == | == Problem == | ||
| − | + | An [[angle]] is drawn on a set of equally spaced [[parallel]] [[line]]s as shown. The [[ratio]] of the [[area]] of shaded [[region]] <math> \mathcal{C} </math> to the area of shaded region <math> \mathcal{B} </math> is 11/5. Find the ratio of shaded region <math> \mathcal{D} </math> to the area of shaded region <math> \mathcal{A}. </math> | |
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| + | [[Image:2006AimeA7.PNG]] | ||
== Solution == | == Solution == | ||
Revision as of 14:30, 25 September 2007
Problem
An angle is drawn on a set of equally spaced parallel lines as shown. The ratio of the area of shaded region 
to the area of shaded region 
is 11/5. Find the ratio of shaded region 
to the area of shaded region 
Solution
There are 
numbers up to 1000 that have 0 as their units digit. All of the other excluded possibilities for 
are when or 
have a 0 in the tens digit, or if the tens digit of is 0 or 9. Excluding the hundreds, which were counted above already, there are 
numbers in every hundred numbers that have a tens digit of 0 or 9, totaling 
such numbers. However, the numbers from 1 to 9 and 991 to 999 do not have 0s, so we must subtract 
from that to get 
. Therefore, there are 
such ordered pairs.
See also
| 2006 AIME II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 6 |
Followed by Problem 8 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
| All AIME Problems and Solutions | ||
