Difference between revisions of "2001 AMC 12 Problems/Problem 6"
Brut3Forc3 (talk | contribs) (New page: == Problem == A telephone number has the form <math>\text{ABC-DEF-GHIJ}</math>, where each letter represents a different digit. The digits in each part of the number are in decreasing orde...) |
Pidigits125 (talk | contribs) (→See Also) |
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== See Also == | == See Also == | ||
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{{AMC12 box|year=2001|num-b=5|num-a=7}} | {{AMC12 box|year=2001|num-b=5|num-a=7}} | ||
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Revision as of 15:32, 16 March 2011
Problem
A telephone number has the form , where each letter represents a different digit. The digits in each part of the number are in decreasing order; that is, , , and . Furthermore, , , and are consecutive even digits; , , , and are consecutive odd digits; and . Find .
Solution
The last four digits are either or , and the other odd digit ( or ) must be , , or . Since , that digit must be . Thus the sum of the two even digits in is . must be , , or , which respectively leave the pairs and , and , or and , as the two even digits in . Only and has sum , so is , and the required first digit is 8, so the answer is .
See Also
2001 AMC 12 (Problems • Answer Key • Resources) | |
Preceded by Problem 5 |
Followed by Problem 7 |
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 | |
All AMC 12 Problems and Solutions |
2001 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 12 |
Followed by Problem 14 | |
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 | ||
All AMC 10 Problems and Solutions |