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The average (arithmetic mean) of the weight of 10 vehicles

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The average (arithmetic mean) of the weight of 10 vehicles [#permalink] New post 23 Apr 2012, 04:19
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The average (arithmetic mean) of the weight of 10 vehicles is 12 tons. The average weight of the group of vehicles increased by 2.4 tons after a new heavy duty truck was added to the group? What is the weight of the heavy duty truck?

A. 35 tons
B. 38.4 tons
C. 40.2 tons
D. 41.2 tons
E. 42 tons

Could one please render a good explanation.
[Reveal] Spoiler: OA
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Re: The average (arithmetic mean) of the weight of 10 vehicles [#permalink] New post 23 Apr 2012, 04:40
Expert's post
dzodzo85 wrote:
The average (arithmetic mean) of the weight of 10 vehicles is 12 tons. The average weight of the group of vehicles increased by 2.4 tons after a new heavy duty truck was added to the group? What is the weight of the heavy duty truck?

A. 35 tons
B. 38.4 tons
C. 40.2 tons
D. 41.2 tons
E. 42 tons

Could one please render a good explanation.


The sum of the weights of 10 vehicles is 10*12=120 tons. Say the weight of 11th vehicle is x tons, then the new average, which is now 12+2.4=14.4 equal, to \(new \ average=\frac{new \ total \ weight}{new \ # \ of \ vehicles}\) --> \(14.4=\frac{120+x}{11}\) --> \(x=38.4\).

Answer: B.
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Re: The average (arithmetic mean) of the weight of 10 vehicles [#permalink] New post 26 Dec 2014, 07:35
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Re: The average (arithmetic mean) of the weight of 10 vehicles [#permalink] New post 26 Dec 2014, 09:48
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Hi All,

In these types of Weighted Average questions, you can always use the Average Formula (as Bunuel showed). There are often ways to solve the problem by doing "relationship math" - it's essentially the same math (but in a different order) and might save you some time if you're comfortable with the concepts involved.

Here, we know that the average of 10 vehicles is 12 tons. In real simple terms, we COULD say that we have 10 vehicles that weight 12 tons EACH. Adding another vehicle raises the AVERAGE WEIGHT of ALL the vehicles 2.4 tons. We're asked for the weight of this extra vehicle.

So, if we raise each of the 10 vehicles 2.4 tons, then each would weight 14.4 tons --> 10(+2.4 tons) = 24 extra tons
To keep the overall average at 14.4 tons, we have to include that weight in the extra vehicle too -->14.4 tons + the increase in the other vehicles.

This gives us 14.4 + 24 = 38.4 tons

Final Answer:
[Reveal] Spoiler:
B


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Re: The average (arithmetic mean) of the weight of 10 vehicles   [#permalink] 26 Dec 2014, 09:48
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