2014 AMC 8 Problems/Problem 22
Problem
A -digit number is such that the product of the digits plus the sum of the digits is equal to the number. What is the units digit of the number?
Video Solution
https://youtu.be/7an5wU9Q5hk?t=2226
Solution
We can think of the number as , where a and b are digits. Since the number is equal to the product of the digits () plus the sum of the digits (), we can say that . We can simplify this to , and factor to . Dividing by , we have that . Therefore, the units digit, , is
Solution 2
A two digit number is namely , where and are digits in which and . Therefore, we can make an equation with this information. We obtain . This is just Moving and to the right side, we get Cancelling out the s, we get which is our desired answer as is the second digit. Thus the answer is . ~mathboy282
See Also
2014 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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All AJHSME/AMC 8 Problems and Solutions |
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