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Source: — Problem Solving |
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by papgust » Sun Mar 07, 2010 8:58 am
Sum of six consecutive integers is 18.5 * 6 = 111

a+(a+1)+(a+2)+(a+3)+(a+4)+(a+5) = 111
6a + 15 = 111
6a = 96
a = 16

Nos are 16,17,18,19,20,21

Average of first 5 integers = 18
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by kstv » Sun Mar 07, 2010 9:49 am
The average of 6 consecutive integers is 18.5, what is the average of first 5 of these integers?

The mean of cosecutive no is = median.
In consecutive no the median is = mean
The median of 6 no will be between the average of 3rd and 4th term, 18.5 is (18+19) /2
The mean of 5 consecutive no will be the 3rd term i.e. 18.

This invloves no calculation.

If this Q replicates GMAT closely then it gives credence to the fact that there are few concepts tested often. One is Mean and Median of cosecutive no is the same.
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by bpgen » Sun Mar 07, 2010 9:56 am
Another quick one:

as per integer's consecutive properties-
avg of 6 consecutive integers is: (a+(a+(6-1)))/2, i.e (first+last)/2
Therefore (2a+5)/2=18.5=>a=16

Therefore avg of 5 consecutive integers is: (a+(a+(5-1)))/2=>(2a+4)/2=>18(substituting value for a)
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by sarthak » Mon Mar 08, 2010 6:21 pm
a quick tip : while picking consequitive numbers take them as a-1,a,a+1 like that
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by bpgen » Mon Mar 08, 2010 6:45 pm
sarthak, I like your thought ..."if World were easy enough for all of us!" ...but it is not! Alas!

Therefore, stick to some formula always, you don't know if question could be asked for manipulating hundreds of number... though something that you mentioned could be simple if number of digits are very less...
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