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by jscpba » Mon Feb 07, 2011 6:24 pm
For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all even integers between 99 and 301?

a. 10,100
b. 20,200
c. 22,650
d. 40,200
e. 45,150

Why is it 2(150(150+1))/2 - 2(49(49+1))/2, instead of 150(150+2)/2 - 49(49+1)/2???

Why do I have to multiply by two instead of just plugging the numbers into the orginal equation?

22,200 is the correct answer and when you don't multiply by 2 you obviously come to 10,100 which is another answer choice...

Apologies if I confused anyone, I am just frustrated about this and I am sure there is an easy explanation


Thanks!
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by GMATGuruNY » Mon Feb 07, 2011 6:33 pm
jscpba wrote:For any positive integer n, the sum of the first n positive integers equals n(n+1)/2. What is the sum of all even integers between 99 and 301?

a. 10,100
b. 20,200
c. 22,650
d. 40,200
e. 45,150

Why is it 2(150(150+1))/2 - 2(49(49+1))/2, instead of 150(150+2)/2 - 49(49+1)/2???

Why do I have to multiply by two instead of just plugging the numbers into the orginal equation?

22,200 is the correct answer and when you don't multiply by 2 you obviously come to 10,100 which is another answer choice...

Apologies if I confused anyone, I am just frustrated about this and I am sure there is an easy explanation


Thanks!
We need to count the even integers from 100 to 300, inclusive.

Ignore the formula given. Instead, use the following:

Sum = (number of integers) * (average of biggest and smallest)

To count the number of evenly spaced integers in a set:

Number of integers = (Biggest - Smallest)/(distance between each successive pair) + 1

Since we're adding only the even integers, the distance between each successive pair is 2.
Thus, the number of even integers from 100 to 300 = (300-100)/2 + 1 = 101.
Average of biggest and smallest = (300+100)/2 = 200.
Sum = (number of integers) * (average of biggest and smallest) = 101*200 = 20,200.

The correct answer is B.
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by jscpba » Mon Feb 07, 2011 7:19 pm
Perfect!!

You have been of such help for me in my studies. I want to thank you for that! I sit for the exam in 18ish days, I hope I can apply all this when it counts!
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