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Mean

by GmatKiss » Sat May 05, 2012 5:20 am

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The average (arithmetic mean) of the integers from 200 to 400, inclusive, is how much greater than the average of the integers from 50 to 100, inclusive?

A.150
B.175
C.200
D.225
E.300
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by sam2304 » Sat May 05, 2012 5:38 am
GmatKiss wrote:The average (arithmetic mean) of the integers from 200 to 400, inclusive, is how much greater than the average of the integers from 50 to 100, inclusive?

A.150
B.175
C.200
D.225
E.300
Average of consecutive nos = sum of first and last number/2

So for 200 to 400 = 200 + 400/2 = 300
and 50 to 100 = 50 + 100/2 = 75

Difference = 300 - 75 = 225

IMO D.
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by aneesh.kg » Sat May 05, 2012 10:17 am
The problem must've used the word 'consecutive'. Without it, the language is vague.

Assuming the integers to be consecutive, it's an AP as well.

Mean of an AP = Mean of the first and the last term = (first term + last term)/2
(Do you know where this formula comes from?)

Mean1 - Mean2
=
(200 + 400)/2 - (50 + 100)/2
=
300 - 75
=
225

[spoiler](D)[/spoiler] is the answer.
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by [email protected] » Sun Feb 11, 2018 9:32 pm
Hi All,

We're asked how much greater the average (arithmetic mean) of the integers from 200 to 400, inclusive, is than the average of the integers from 50 to 100, inclusive.

When dealing with a series of consecutive integers, if we have an ODD number of integers, then the average is the 'middle' value. There are exactly 201 integers from 200 to 400, inclusive - so the average is the number in the 'middle': 300. There are exactly 51 integers from 50 to 100, inclusive - so the average is the number in the 'middle': 75.

The difference in those averages is 300 - 75 = 225.

Final Answer: D

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by Scott@TargetTestPrep » Tue Feb 13, 2018 5:35 pm
GmatKiss wrote:The average (arithmetic mean) of the integers from 200 to 400, inclusive, is how much greater than the average of the integers from 50 to 100, inclusive?

A.150
B.175
C.200
D.225
E.300
Since we have an evenly spaced set of integers, the average of the integers from 200 to 400, inclusive, is (200 + 400)/2 = 300.

Similarly, the average of the integers from 50 to 100, inclusive, is (50 + 100)/2 = 75.

Thus, the difference is 300 - 75 = 225.

Answer: D

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by palgun » Tue Sep 03, 2019 11:20 pm
GmatKiss wrote:The average (arithmetic mean) of the integers from 200 to 400, inclusive, is how much greater than the average of the integers from 50 to 100, inclusive?

A.150
B.175
C.200
D.225
E.300
As the range is inclusive and the total number in each of the range is odd number, we will have our average or arithmetic mean to be the midpoint in each range. From there you get 300 and 75 and the difference gives the answer as 225
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