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What is the average (arithmetic mean) of all the even

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What is the average (arithmetic mean) of all the even [#permalink] New post 24 Dec 2003, 14:09
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What is the average (arithmetic mean) of all the even integers greater than 25 and less than 325?

(A) 144
(B) 167
(C) 175
(D) 206
(E) 212

Is there a shortcut to do this ?
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 [#permalink] New post 24 Dec 2003, 14:33
MartinMag wrote:
I vote for C also: ((325-25)/2)+25=175


How will you do it if the question is What is the average (arithmetic mean) of all the even integers greater than 24 and less than 325?
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 [#permalink] New post 24 Dec 2003, 14:58
all even integers greater than 24 and less than 325 is the same as your former question... Therefore the answer is the same
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 [#permalink] New post 24 Dec 2003, 22:15
i got it till 150 .. but how wil you add even integers??
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 [#permalink] New post 24 Dec 2003, 22:17
Paul wrote:
all even integers greater than 24 and less than 325 is the same as your former question... Therefore the answer is the same


I want to know a easy way to these kind of problems without listing them.
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 [#permalink] New post 25 Dec 2003, 00:33
Hmmm, I think that a way to solve these kind of problems is to look at them this way:

If you take the average of (26 + 324)/2, you will get an average of 175
Then, you take the next pair of even integers at both extremes: (28 + 322)/2 and you will also get 175, you do this all the way until you get to the pair of integers in the center of the set: (174 + 176)/2 = 175. Hence, the answer resides in understanding that the average of all the numbers in the set is simply the spread of the extreme numbers ( ie 26 and 324) divided by 2. Hope I was clear enough.
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 [#permalink] New post 25 Dec 2003, 09:43
Paul wrote:
Hmmm, I think that a way to solve these kind of problems is to look at them this way:

If you take the average of (26 + 324)/2, you will get an average of 175
Then, you take the next pair of even integers at both extremes: (28 + 322)/2 and you will also get 175, you do this all the way until you get to the pair of integers in the center of the set: (174 + 176)/2 = 175. Hence, the answer resides in understanding that the average of all the numbers in the set is simply the spread of the extreme numbers ( ie 26 and 324) divided by 2. Hope I was clear enough.


Thank you. This helps. I was wondering whether I need to apply arithmetic progression for these problems. Now I understand this is more simpler than that.
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 [#permalink] New post 30 Dec 2003, 14:45
Yep. The rule is given in Kaplan. The average of evenly spaces numbers is the average of the smallest and the largest numbers. So all we need to do in our example is to find out the smallest possible and largest possible number in the range given to us. And then take the average of the two numbers.
  [#permalink] 30 Dec 2003, 14:45
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