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Bunuel
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The average (arithmetic mean) of four packages is 15 pounds. If the we 12 Jun 2019, 02:00
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75% (01:55) correct 25% (02:02) wrong based on 89 sessions

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The average (arithmetic mean) of four packages is 15 pounds. If the weight of the first package is x, and each package weighs twice as much as the previous package, which of the following CANNOT be the total weight, in pounds, of any combination of the packages?

A. 12
B. 24
C. 44
D. 46
E. 52
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D
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The average (arithmetic mean) of four packages is 15 pounds. If the we Updated on: 12 Jun 2019, 14:38
Originally posted by nick1816 on 12 Jun 2019, 02:19.
Last edited by nick1816 on 12 Jun 2019, 14:38, edited 1 time in total.
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Weight of the boxes are k, 2k, 4k and 8k

k+2k+4k+8k/4 = 15
15k =60
k=4

Weight of the boxes are 4,8,16 and 32
Weight of each box is a multiple of 4, hence the weight of any combination of these boxes will also be a multiple of 4.

Option D is not a multiple of 4.

Bunuel
The average (arithmetic mean) of four packages is 15 pounds. If the weight of the first package is x, and each package weighs twice as much as the previous package, which of the following CANNOT be the total weight, in pounds, of any combination of the packages?

A. 12
B. 24
C. 44
D. 46
E. 52
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The average (arithmetic mean) of four packages is 15 pounds. If the we 12 Jun 2019, 02:24
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Bunuel
The average (arithmetic mean) of four packages is 15 pounds. If the weight of the first package is x, and each package weighs twice as much as the previous package, which of the following CANNOT be the total weight, in pounds, of any combination of the packages?

A. 12
B. 24
C. 44
D. 46
E. 52
Show more

Sum of all packages=4*15; X+2X+4X+8X=60; 15X=60; X=4. So all combinations must be multiples of 4; 46 is not a multiple of 4 IMO D
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The average (arithmetic mean) of four packages is 15 pounds. If the we 12 Jun 2019, 03:18
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Bunuel
The average (arithmetic mean) of four packages is 15 pounds. If the weight of the first package is x, and each package weighs twice as much as the previous package, which of the following CANNOT be the total weight, in pounds, of any combination of the packages?

A. 12
B. 24
C. 44
D. 46
E. 52
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total weight = 60
and each package ; 4,8,16,32
so 46 sum is not possible
IMO D
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The average (arithmetic mean) of four packages is 15 pounds. If the we 12 Jun 2019, 03:55
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nick1816
Weight of the boxes are k, 2k, 4k and 8k

k+2k+4k+8k/4 = 15
15k =60
k=4

Weight of the boxes are 4,8,16 and 32
Weight of each box is a multiple of 4, hence the weight of any combination of these boxes will also be a multiple of 4.

Option C is not a multiple of 4.

Bunuel
The average (arithmetic mean) of four packages is 15 pounds. If the weight of the first package is x, and each package weighs twice as much as the previous package, which of the following CANNOT be the total weight, in pounds, of any combination of the packages?

A. 12
B. 24
C. 44
D. 46
E. 52
Show more

Option C can be created by combining x + 2x + 8x (e.g. 4 + 8 + 32 = 40)

The right answer choice is D as we cannot create 46 from any possible combination of our four given numbers.
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The average (arithmetic mean) of four packages is 15 pounds. If the we 17 Jun 2019, 17:40
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Bunuel
The average (arithmetic mean) of four packages is 15 pounds. If the weight of the first package is x, and each package weighs twice as much as the previous package, which of the following CANNOT be the total weight, in pounds, of any combination of the packages?

A. 12
B. 24
C. 44
D. 46
E. 52
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We can create the equation:

(x + 2x + 4x + 8x)/4 = 15

x + 2x + 4x + 8x = 60

15x = 60

x = 4

So the weights of the boxes are 4, 8, 16, and 32. We see that a combination of the packages could weigh 4 + 8 = 12, 8 + 16 = 24, 4 + 8 + 32 = 44 or 4 + 16 + 32 = 52.

Thus, we see that 46 cannot be the weight of a combination of any of the packages.

Answer: D
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The average (arithmetic mean) of four packages is 15 pounds. If the we 17 Jun 2019, 17:49
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Bunuel
The average (arithmetic mean) of four packages is 15 pounds. If the weight of the first package is x, and each package weighs twice as much as the previous package, which of the following CANNOT be the total weight, in pounds, of any combination of the packages?

A. 12
B. 24
C. 44
D. 46
E. 52
Show more

Weights: x, 2x, 4x and 8x
From average equation: 15x/4 = 15 so x=4
Weights: 4, 8, 16 and 32.

Now, the combination of weights must be a multiple of 4. D. 46 is not.
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