Difference between revisions of "2016 AMC 10B Problems/Problem 6"
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<math>\textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 20</math> | <math>\textbf{(A)}\ 1\qquad\textbf{(B)}\ 4\qquad\textbf{(C)}\ 5\qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 20</math> | ||
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| + | ==Solution== | ||
| + | Since we know that the sum of two three digit positive integers cannot start with a one, we can get rid of option A. Since <math>4</math> is the next smallest integer, we can try to make an integer that starts with <math>4</math> and ends with <math>00</math> We can find that <math>143+257</math> fits the parameters(along with many others), in which all the digits are distinct, and indeed sum to <math>400</math>, summing the digits we reach the correct answer choice; <math>\textbf{(B)}\ 4</math>. | ||
Revision as of 12:28, 21 February 2016
Problem
Laura added two three-digit positive integers. All six digits in these numbers are different. Laura's sum is a three-digit number 
. What is the smallest possible value for the sum of the digits of ?
Solution
Since we know that the sum of two three digit positive integers cannot start with a one, we can get rid of option A. Since 
is the next smallest integer, we can try to make an integer that starts with and ends with 
We can find that 
fits the parameters(along with many others), in which all the digits are distinct, and indeed sum to 
, summing the digits we reach the correct answer choice; 
.
