The weight of four dogs is determined to be 25 pounds, 31 pounds, 35 pounds and 41 pounds respectively. The weight of a fifth dog is determined to be y pounds. If the average (arithmetic mean) weight of the first four dogs is the same as that of all five dogs what is the value of y? A. 31 B. 33 C. 35 D. 37 E. 39

(B) The average weight of the first four dogs is: (25 + 31 + 35 + 41)/4 = 33 pounds. For the addition of a fifth dog to not change the average weight the dog must have the same weight as the average, 33 pounds. The correct answer is B.

Alternatively, the problem could be worked: (25 + 31 + 35 + 41)/4 = (25 + 31 + 35 + 41 + x)/5 where x represents the weight of the fifth dog. ---------

[color=#FF0000]The question asks for the value of y, being the weight of the fifth dog, not the weight of all five dogs together. This question is confusing.

Also, even if the arithmetic mean of the first four dogs is the same as that of all five dogs, the value of y is not the average weight of all the dogs, but the weight of one dog, the last dog.[/color]

[quote][color=#FF0000]The question asks for the value of y, being the weight of the fifth dog, not the weight of all five dogs together. This question is confusing.[/color]

The question indeed asks for the value of y (the weight of the fifth dog). It also states that adding the fifth dog does not change the average of the group. This fact implies that the weight of the fifth dog is the same as this average.

[quote][color=#FF0000]Also, even if the arithmetic mean of the first four dogs is the same as that of all five dogs, the value of y is not the average weight of all the dogs, but the weight of one dog, the last dog.[/color]We have the average of the four dogs (25 + 31 + 35 + 41)/4 = 33 pounds

The nature of the average (or consider it the property of the average) is the following: When we add a new element to an existing group it will - increase the average, if it is greater than the current average - decrease the average, if it is less than the current average - not change the average if it is the same value

So if adding the fifth element does not change the average, we know that it is the same as the average.

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