It is currently 23 Jan 2018, 15:39

### 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

# What is the sum of the integers from 1 to 999 , inclusive?

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43380
What is the sum of the integers from 1 to 999 , inclusive? [#permalink]

### Show Tags

22 Nov 2016, 04:50
Expert's post
5
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

78% (00:40) correct 22% (00:57) wrong based on 161 sessions

### HideShow timer Statistics

What is the sum of the integers from 1 to 999, inclusive?

A. 499000
B. 499500
C. 499999
D. 500500
E. 500999
[Reveal] Spoiler: OA

_________________
Senior Manager
Joined: 06 Jun 2016
Posts: 263
Location: India
Concentration: Operations, Strategy
Schools: ISB '18 (D)
GMAT 1: 600 Q49 V23
GMAT 2: 680 Q49 V34
GPA: 3.9
Re: What is the sum of the integers from 1 to 999 , inclusive? [#permalink]

### Show Tags

22 Nov 2016, 05:47
2
This post was
BOOKMARKED
Bunuel wrote:
What is the sum of the integers from 1 to 999, inclusive?

A. 499000
B. 499500
C. 499999
D. 500500
E. 500999

B
number of integers = (999-1)+1=999
if you observe 1st term and last term gives you a sum of 1000
there are 999/2= 499.5 499 such pairs
so 499*1000+500= 499500
Intern
Joined: 06 Oct 2016
Posts: 22
Re: What is the sum of the integers from 1 to 999 , inclusive? [#permalink]

### Show Tags

22 Nov 2016, 06:37
Summation of n numbers = n*(n+1)/2

If n= 1000 summation of first 1000 numbers

So 1000*1001/2 = 500500

500500-1000 as we don't need the last term.... 499500

Sent from my A1601 using GMAT Club Forum mobile app
Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3266
Location: India
GPA: 3.5
Re: What is the sum of the integers from 1 to 999 , inclusive? [#permalink]

### Show Tags

22 Nov 2016, 06:58
Bunuel wrote:
What is the sum of the integers from 1 to 999, inclusive?

A. 499000
B. 499500
C. 499999
D. 500500
E. 500999

Sum of the integers from 1 to 999, inclusive = $$\frac{999 ( 999 + 1 )}{2} = 499500$$

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Intern
Joined: 09 Oct 2016
Posts: 19
Schools: HBS '19
Re: What is the sum of the integers from 1 to 999 , inclusive? [#permalink]

### Show Tags

03 Jun 2017, 03:05
Bunuel wrote:
What is the sum of the integers from 1 to 999, inclusive?

A. 499000
B. 499500
C. 499999
D. 500500
E. 500999

simplest way i noticed would be:

quantity of numbers: (999-1)+1 = 999 ---> (Last number - First number) + 1

Average: (999+1)/2 = 500 ----> (Last number + First number)/2

now:
Average * quantity
999* 500

for fast calc we notice that 999 i very close to 1,000, So:
500*1000 = 500,000
500,000 - 500 = 499,500

B
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10763
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: What is the sum of the integers from 1 to 999 , inclusive? [#permalink]

### Show Tags

04 Jun 2017, 15:06
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
Hi All,

These types of 'bunching' questions often come down to how you choose to 'organize' the math involved.

Here, we're asked for the sum of all of the integers from 1 to 999, inclusive. We're talking about the first 999 positive integers, but I'm going to make the math a little easier by adding one extra integer that won't affect the sum at all: the number 0.

By including 0, we now have 1,000 total integers and we can 'bunch' them into groups of 2:

0 and 999 = 999
1 and 998 = 999
2 and 997 = 999
Etc.

Since we have 1,000 total numbers, there will be 500 'pairs' that add up to 999. Thus, the sum of those terms is...

(500)(999)

While that calculation might seem a little tough, you can avoid it if you think about the math in a different way...

(500)(1000) = 500,000

999 is "one less" than 1,000 so we just have to subtract "one" of those 500s from 500,000. That gives us:

500,000 - 500 = 499,500

[Reveal] Spoiler:
B

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Intern
Joined: 19 Apr 2017
Posts: 19
Location: India
WE: Management Consulting (Consulting)
Re: What is the sum of the integers from 1 to 999 , inclusive? [#permalink]

### Show Tags

18 Aug 2017, 23:46
Sum = number of terms * mean

- # of terms = (999-1), but we need to add '1' to the resultant as this is an inclusive set, bringing us back to '999'.
- mean of the set = first term+last term divided by 2 which gives us 500 (1+999 = 1000/2 = 500)

Putting it into the original equation:
- sum = 999 (number of terms) * 500 (mean) = 499500

Hope that helps!
_________________

We are what we REPEATEDLY do. GREATNESS then is not ACT, but a HABIT.

Intern
Joined: 11 Oct 2017
Posts: 22
Re: What is the sum of the integers from 1 to 999 , inclusive? [#permalink]

### Show Tags

12 Oct 2017, 13:15
1
This post was
BOOKMARKED
Number of Integers (Inclusive) = N = (Last # - First #)+1

Sum of Integers = (First # + Last #)*N))/2

1. N= (999-1) + 1 = 999

2. (1+999)*999))/2 = 499,500 B
Re: What is the sum of the integers from 1 to 999 , inclusive?   [#permalink] 12 Oct 2017, 13:15
Display posts from previous: Sort by