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# The average (arithmetic mean) weight of the six men in a van is 257 lb

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Math Expert
Joined: 02 Sep 2009
Posts: 53795
The average (arithmetic mean) weight of the six men in a van is 257 lb  [#permalink]

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20 Dec 2017, 06:13
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Difficulty:

25% (medium)

Question Stats:

82% (02:26) correct 18% (01:31) wrong based on 23 sessions

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The average (arithmetic mean) weight of the six men in a van is 257 lbs. If 3 men with an average weight of 263 lbs, board the van, what will be the average weight of the men in the van?

A. 263
B. 262
C. 261
D. 260
E. 259

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The average (arithmetic mean) weight of the six men in a van is 257 lb  [#permalink]

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21 Dec 2017, 09:55
Bunuel wrote:
The average (arithmetic mean) weight of the six men in a van is 257 lbs. If 3 men with an average weight of 263 lbs, board the van, what will be the average weight of the men in the van?

A. 263
B. 262
C. 261
D. 260
E. 259

Short way

Take just the total extra weight added by the three new men. Divide by 9 to get the change in the average.

Old average: 257 (per man)
Average of three new: 263 (per man)

Difference added by 1 new man:(263-257)= 6
Difference added by 3 new men: (3*6)= 18

Now there are 9 men; 18 pounds extra must be distributed among them
$$\frac{18}{9} = 2$$ pounds per man above the original average of 257.
New average is (257 + 2) = 259

The longer way, A * n = S

First group: (6 * 257) = 1,542
Second group: (3 * 263) = 789

Sum the sums, then divide by the new $$n$$
$$(1,542 + 789) = 2,331$$

$$\frac{2,331}{9} = 259$$

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The average (arithmetic mean) weight of the six men in a van is 257 lb   [#permalink] 21 Dec 2017, 09:55
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