Difference between revisions of "2018 AMC 8 Problems/Problem 14"
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== Solution == | == Solution == | ||
− | If we start off with the first digit, we know that it can't be <math>9</math> since <math>9</math> is not a factor of <math>120</math>. We go down to the digit <math>8</math>, which does work since it is a factor of <math>120</math>. Now, we have to know what digits will take up the remaining four spots. To find this result, just divide <math>\frac{120}{8}=15</math>. The next place can be <math>5</math>, as it is the largest factor, aside from <math>15</math>. Consequently, our next three values will be <math>3,1</math> and <math>1</math> if we use the same logic. Therefore, our five-digit number is <math>85311</math>, so the sum is <math>8+5+3+1+1=18\implies \boxed{\textbf{(D)}}</math>. | + | If we start off with the first digit, we know that it can't be <math>9</math> since <math>9</math> is not a factor of <math>120</math>. We go down to the digit <math>8</math>, which does work since it is a factor of <math>120</math>. Now, we have to know what digits will take up the remaining four spots. To find this result, just divide <math>\frac{120}{8}=15</math>. The next place can be <math>5</math>, as it is the largest factor, aside from <math>15</math>. Consequently, our next three values will be <math>3,1</math> and <math>1</math> if we use the same logic. Therefore, our five-digit number is <math>85311</math>, so the sum is <math>8+5+3+1+1=18\implies \boxed{\textbf{(D) 18}}</math>. |
==Video Solution== | ==Video Solution== |
Latest revision as of 14:02, 15 June 2021
Contents
Problem
Let be the greatest five-digit number whose digits have a product of . What is the sum of the digits of ?
Solution
If we start off with the first digit, we know that it can't be since is not a factor of . We go down to the digit , which does work since it is a factor of . Now, we have to know what digits will take up the remaining four spots. To find this result, just divide . The next place can be , as it is the largest factor, aside from . Consequently, our next three values will be and if we use the same logic. Therefore, our five-digit number is , so the sum is .
Video Solution
https://youtu.be/7an5wU9Q5hk?t=13
See Also
2018 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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 AJHSME/AMC 8 Problems and Solutions |
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