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# The sum of the first 50 positive even integers is 2,550.

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The sum of the first 50 positive even integers is 2,550.  [#permalink]

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22 Jun 2007, 04:36
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The sum of the first 50 positive even integers is 2,550. Wat is the sum of the even integers between 102 and 200 inclusive?

A) 5,100
B) 7,550
C) 10,100
D) 15,500
E) 20,100

Last edited by djhouse81 on 22 Jun 2007, 08:20, edited 2 times in total.
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22 Jun 2007, 04:58
OA is B.

Does anyone have a good trick for this problem and other ones like it?
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22 Jun 2007, 05:23
are you sure the question and answer choices are written correctly?

The answer would be B if the question was "what is the sum of the integers between 101 and 150"

i dont see how it could possibly be B, when the ssum of the first 50 is 2550 already.

here is the method i use:

since we know that sum of 1-50 is 2550, we can find the sum of 102 to 151 (which is 50 numbers as well), by noticing that every respective number in these two sets differs by 101. (ie 102-1 = 101, 103-2 = 101, 104-3 = 101, etc)

so if we take 101x50 = 5050, and then add this to the sum of 1-50, 2550, we get 7600 as the sum of the integers from 102 to 151. You can repeat this process to get the sum of 152-200, but we're already beyond the OA of 7550 and im thoroughly confused because the final answer i'm getting is like 17,499.

Maybe i'm doing something wrong here.
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Re: GMAT Prep CAT PS [#permalink]

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22 Jun 2007, 05:37
djhouse81 wrote:
The sum of the first 50 positive integers is 2,550. Wat is the sum of the integers between 102 and 200 inclusive?

A) 5,100
B) 7,550
C) 10,100
D) 15,500
E) 20,100

102 to 200 is an AP with first term 102, number of terms 99 and common difference 1.

therefore, sum = (99/2)*(2*102 + 98*1) = 99*(102+49)=99*151=14949 !!!

Where am I going wrong???
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22 Jun 2007, 08:10
I apologize. I copied the question from the test incorrectly, again. I fixed it in the first message, but here it is again just for clarification.

The sum of the first positive even integers is 2550. What is the sum of the even integers from 102 to 200, inclusive.

Sorry for the confusion. I know the OA is still B because I did a quick spreadsheet total, and 7550 is correct. Unfortunately, we do not have Excel at Pearson Vue, so how do I solve this during the actual test?
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22 Jun 2007, 08:35
my way of solution:

[n*(n+1)]/2 = formula to claculate the sum of consecutive numbers

we only need the even numbers hence 200/100 = 100 numbers X 2

(100*101/2)*2 = 10,100

less (50*51/2)*2 = 2,550

10,100 - 2,550= 7,550

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Re: GMAT Prep CAT PS [#permalink]

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22 Jun 2007, 08:53
sumande wrote:
djhouse81 wrote:
The sum of the first 50 positive integers is 2,550. Wat is the sum of the integers between 102 and 200 inclusive?

A) 5,100
B) 7,550
C) 10,100
D) 15,500
E) 20,100

102 to 200 is an AP with first term 102, number of terms 99 and common difference 1.

therefore, sum = (99/2)*(2*102 + 98*1) = 99*(102+49)=99*151=14949 !!!

Where am I going wrong???

Now the number of terms become 50 and common difference 2.

Sum=(50/2)*(2*102 + 49*2) = 25*(204+98)=25*302=7550.

Last edited by sumande on 22 Jun 2007, 08:57, edited 1 time in total.
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22 Jun 2007, 08:55
I figured it out =P

The question needs a little more clarification, djhouse.

I think the question is saying that the sum of the first 100 even integers is 2550. This makes the problem a lot easier than before =P

we know that there are 50 even integers from 2 to 100, and we can see that there are 50 even integers from 102 to 200. Each of the numbers in the latter set is 100 greater than the previous, so we can find the sum of the even intgers from 102 to 200 by multiplying the difference by the number of values, (100 x 50), then add on the sum of the integers from 2 to 100.

100x500 + 2550 = 5000 + 2550 = 7550.
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Re: GMAT Prep CAT PS [#permalink]

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22 Jun 2007, 09:22
djhouse81 wrote:
The sum of the first 50 positive even integers is 2,550. Wat is the sum of the even integers between 102 and 200 inclusive?

A) 5,100
B) 7,550
C) 10,100
D) 15,500
E) 20,100

Sum of integers beterrn 102 and 200 = (Its Avg) * (Number of Intergers)
Since they are consecutive, the avg will be the same as counting all integers.

Avg = (200+102) / 2 = 302/2 = 151
Number of Integers = (200 - 102) / 2 +1 = 50

151 * 50 = 7550
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Re: GMAT Prep CAT PS [#permalink]

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22 Jun 2007, 09:38
bkk145 wrote:
djhouse81 wrote:
The sum of the first 50 positive even integers is 2,550. Wat is the sum of the even integers between 102 and 200 inclusive?

A) 5,100
B) 7,550
C) 10,100
D) 15,500
E) 20,100

Sum of integers beterrn 102 and 200 = (Its Avg) * (Number of Intergers)
Since they are consecutive, the avg will be the same as counting all integers.

Avg = (200+102) / 2 = 302/2 = 151
Number of Integers = (200 - 102) / 2 +1 = 50

151 * 50 = 7550

This is exactly how I did it. This strategy is covered in the Manhattan GMAT Strat guides (How to count consecutive even/odd integers).
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22 Jun 2007, 11:35
Plaguerabbit,

I would have loved it if they clarified it for me. However, the question was written as I have written it: the sum of the first 50 even integers...

Classic case of the GMAT not necessarily testing your quantitative abilities, but more so your ability to spot the little tricks they put in there to throw you off.

However, thanks to everyone for providing the solutions. The formulas are good ones to remember.
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22 Jun 2007, 18:18
This is from other site.

without knowing the formulas.
the question gives you a clue. It says "The sum of the first 50 positive even integers is 2,550."
So
2+4+6+8....100 = 2550

you are trying to find
102+104+106+108....200

notice the terms here can be rewritten as (100+2)+(100+4)+(100+6)+(100+8)...(100+100)
which can be simplified to 100*50+(2+4+6+8...100)
22 Jun 2007, 18:18
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