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## Mean

This topic has 2 expert replies and 2 member replies
GmatKiss Legendary Member
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#### Mean

Sat May 05, 2012 5:20 am
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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Scott@TargetTestPrep GMAT Instructor
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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.

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Rich.C@EMPOWERgmat.com Elite Legendary Member
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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.

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Rich

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sam2304 Legendary Member
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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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aneesh.kg Master | Next Rank: 500 Posts
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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

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GMAT Math Coach
aneesh.bangia@gmail.com

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