Bunuel wrote:
The average (arithmetic mean) of four packages is 4 pounds. If the weight of the first package is x, and each package weighs two more pounds than the previous package, which of the following CANNOT be the total weight, in pounds, of any combination of the packages?
A. 9
B. 10
C. 12
D. 13
E. 14
If the average of four packages is 4 pounds, the total will be 16 pounds.
We have the weight of a package to be x. Since each package weighs 2
pounds more than the previous package, the other packages weigh x+2,
x+4,and x+6
x+x+2+x+4+x+6 = 16 => 4x+12 = 16 => x = 1
The weights of the packages are 1,3,5,and 7 pounds.
Evaluating answer options,
1+3+5(9) is possible
3+7(10) is possible
5+7(12) is possible
1+5+7(13) is possible
Only
14(Option E) is not possible as the total weight, in pounds, of any combination of the packages
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73% (01:52) correct 
