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Math Expert V
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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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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Senior SC Moderator V
Joined: 22 May 2016
Posts: 2570
The average (arithmetic mean) weight of the six men in a van is 257 lb  [#permalink]

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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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SC Butler (two Sentence Correction questions per day from Nov 7 to Mar 1) is here. 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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# The average (arithmetic mean) weight of the six men in a van is 257 lb

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