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The average (arithmetic mean) of four packages is 4 pounds. If the wei

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The average (arithmetic mean) of four packages is 4 pounds. If the wei [#permalink]

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New post 08 Jan 2018, 23:30
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A
B
C
D
E

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  35% (medium)

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63% (02:22) correct 38% (01:39) wrong based on 16 sessions

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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

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Re: The average (arithmetic mean) of four packages is 4 pounds. If the wei [#permalink]

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New post 09 Jan 2018, 00:02
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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Re: The average (arithmetic mean) of four packages is 4 pounds. If the wei   [#permalink] 09 Jan 2018, 00:02
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