The sum of the first 50 positive even integers is 2550. What : Quant Question Archive [LOCKED]
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 15:40

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# The sum of the first 50 positive even integers is 2550. What

Author Message
Director
Joined: 10 Feb 2006
Posts: 658
Followers: 3

Kudos [?]: 459 [0], given: 0

The sum of the first 50 positive even integers is 2550. What [#permalink]

### Show Tags

12 Jun 2008, 03:54
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 102 to 200, inclusive?

5100
7550
10100
15500
20100

I know that there are 200 -102 =98 = 49 even numbers.

_________________

GMAT the final frontie!!!.

Director
Joined: 01 Jan 2008
Posts: 629
Followers: 4

Kudos [?]: 175 [0], given: 1

Re: Sum of even integers [#permalink]

### Show Tags

12 Jun 2008, 05:55
The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 102 to 200, inclusive?

5100
7550
10100
15500
20100

I know that there are 200 -102 =98 = 49 even numbers.

actually there are 50 even numbers (200-102)/2+1 /// think about counting 1, 2, 3 ... 10 (10 -1 = 9 but there are 10 numbers)
i would say the sum is equal to 2*(sum of all numbers between 51 and 100) = 2*(100+51)*50/2=151*50=7550 -> B
Senior Manager
Joined: 29 Aug 2005
Posts: 283
Followers: 2

Kudos [?]: 51 [0], given: 0

Re: Sum of even integers [#permalink]

### Show Tags

13 Jun 2008, 03:40
The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 102 to 200, inclusive?

5100
7550
10100
15500
20100

I know that there are 200 -102 =98 = 49 even numbers.

this will be an AP series question
102,104,106....200

a = 102 (the first term)
d = 2 (the common difference)
n = 50 (total even numbers for which the sum will be calculated)

now the formula for sum of an AP series is

S = N/2(2a + (n-1)d)

= 50/2 (2*102 + (50-1)2)

=25(204+98)
=25*302
=7,550

_________________

The world is continuous, but the mind is discrete

Current Student
Joined: 12 Jun 2008
Posts: 287
Schools: INSEAD Class of July '10
Followers: 7

Kudos [?]: 52 [0], given: 0

Re: Sum of even integers [#permalink]

### Show Tags

13 Jun 2008, 03:51
A more simple way to solve that without knowing any formula is to use what they say in the question :

sum of [even integers between 102 and 200 (inclusive)] = sum of [100 + even integers between 2 and 100 (inclusive)] = 50*100 + sum of the first 50 positive even integers = 5000 + 2550 = 7550
Intern
Joined: 25 Jun 2008
Posts: 13
Followers: 0

Kudos [?]: 2 [0], given: 0

Re: Sum of even integers [#permalink]

### Show Tags

02 Jul 2008, 03:22
we can use elimination.

1. upper cap 50*200 =10000 therefore option C/D/E are out. Now choose between A and E

2. There are 50 even numbers between 102-200 including 102 therefore the sume should be greater than 50*100=5000.

3. The sum has to be more than 5100 therefore only choice left is 7550
Senior Manager
Joined: 07 Jan 2008
Posts: 412
Followers: 3

Kudos [?]: 216 [0], given: 0

Re: Sum of even integers [#permalink]

### Show Tags

02 Jul 2008, 03:54
The sum of the first 50 positive even integers is 2550. What is the sum of the even integers from 102 to 200, inclusive?

5100
7550
10100
15500
20100

I know that there are 200 -102 =98 = 49 even numbers.

I do not understand why they give us "The sum of the first 50 positive even integers is 2550".

We can find "the sum of the even integers from 102 to 200" without any additional information.
200-102 = 98 ==> Their are 50 even-numbers in the set.
S=50*(102*2+49*2)/2 = 7550.
Current Student
Joined: 12 Jun 2008
Posts: 287
Schools: INSEAD Class of July '10
Followers: 7

Kudos [?]: 52 [0], given: 0

Re: Sum of even integers [#permalink]

### Show Tags

02 Jul 2008, 04:09
lexis wrote:
I do not understand why they give us "The sum of the first 50 positive even integers is 2550".

We can find "the sum of the even integers from 102 to 200" without any additional information.
200-102 = 98 ==> Their are 50 even-numbers in the set.
S=50*(102*2+49*2)/2 = 7550.

Yes we can. But even without knowing the formula you used we could have solved the question with the piece of information they give us.

As I wrote above :

$$\sum_{n=102}^{200} n_{even} = \sum_{k=51}^{100} 2k = \sum_{k=1}^{50} (100+2k) = \sum_{k=1}^{50} 100 + \sum_{k=1}^{50} 2k = 50*100 + 2550 = 7550$$

(without calculating anything )
Re: Sum of even integers   [#permalink] 02 Jul 2008, 04:09
Display posts from previous: Sort by