2011 AMC 12B Problems/Problem 13
Problem
Brian writes down four integers whose sum is . The pairwise positive differences of these numbers are and . What is the sum of the possible values of ?
Solution
Assume that results in the greatest pairwise difference, and thus it is . This means . must be in the set . The only way for 3 numbers in the set to add up to 9 is if they are . , and then must be the remaining two numbers which are and . The ordering of must be either or .
Case 1
$(a,b,c)=(3,1,5)\\
x=w-5\\
y=w-5-1\\
x=w-5-1-3\\
w+x+y+z=4w-20=44\\
w=16\$ (Error compiling LaTeX. ! Missing $ inserted.)
Case 2
The sum of the two w's is
See also
2011 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 12 |
Followed by Problem 14 |
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All AMC 12 Problems and Solutions |
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