The sum of first hundred numbers, 1 to 100 is divisible by? : Quant Question Archive [LOCKED]
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 22 Jan 2017, 16:44

### 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
Your Progress

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 first hundred numbers, 1 to 100 is divisible by?

 post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
Senior Manager
Joined: 30 Aug 2003
Posts: 329
Location: BACARDIVILLE
Followers: 1

Kudos [?]: 18 [0], given: 0

The sum of first hundred numbers, 1 to 100 is divisible by? [#permalink]

### Show Tags

04 Jan 2004, 20:02
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

The sum of first hundred numbers, 1 to 100 is divisible by?

a) 2, 4, and 8
b) 2
c) 2 and 4
d) 6
Director
Joined: 14 Oct 2003
Posts: 587
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 49 [0], given: 0

### Show Tags

04 Jan 2004, 20:17
The sum of the first 100 number is 5000 - which is divisible only by a) 2,4,8
Senior Manager
Joined: 30 Aug 2003
Posts: 329
Location: BACARDIVILLE
Followers: 1

Kudos [?]: 18 [0], given: 0

### Show Tags

04 Jan 2004, 20:21
[quote="Titleist"]The sum of the first 100 number is 5000 - which is divisible only by a) 2,4,8[/quote]

Did u just know that factual tidbit, or did u do some quick calculation?

thanks
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4302
Followers: 40

Kudos [?]: 429 [0], given: 0

### Show Tags

04 Jan 2004, 20:22
B)
My reasoning was a bit long but still within 2 min. range
If you match the numbers in diff. pairs so as to have sums of 100 ( ie 1+99, 2+98, etc... ) You will then have 49 groups of 100. You then add to that 100 and the 50 which is the median number. The sum will be 50x100=5000
5000+50=5050. 5050, of the given numbers, is divisible by 2 only
_________________

Best Regards,

Paul

Director
Joined: 14 Oct 2003
Posts: 587
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 49 [0], given: 0

### Show Tags

04 Jan 2004, 20:23
sunniboy007 wrote:
Titleist wrote:
The sum of the first 100 number is 5000 - which is divisible only by a) 2,4,8

Did u just know that factual tidbit, or did u do some quick calculation?

thanks

calculation is easy 1-100 you have 100 numbers

average is 50 multiply by 100 number is 5000

which is divisible by 2, 4, 8

hope that helps
Senior Manager
Joined: 30 Aug 2003
Posts: 329
Location: BACARDIVILLE
Followers: 1

Kudos [?]: 18 [0], given: 0

### Show Tags

04 Jan 2004, 20:26
Paul thanks.
Official answer is (B) 2
Director
Joined: 14 Oct 2003
Posts: 587
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 49 [0], given: 0

### Show Tags

04 Jan 2004, 20:27
sunniboy007 wrote:
Paul thanks.
Official answer is (B) 2

oops yes - small detail it's 5050

Director
Joined: 13 Nov 2003
Posts: 964
Location: Florida
Followers: 1

Kudos [?]: 127 [0], given: 0

### Show Tags

04 Jan 2004, 20:48
sum of n natural number = n(n+1)/2

100 * 101 /2 = 50*101 = 2*5*5*101

ans: 2
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4302
Followers: 40

Kudos [?]: 429 [0], given: 0

### Show Tags

04 Jan 2004, 21:27
I like that formula dj, very neat
_________________

Best Regards,

Paul

Director
Joined: 14 Oct 2003
Posts: 587
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 49 [0], given: 0

### Show Tags

04 Jan 2004, 21:29
Dj is simply Da Man!
Director
Joined: 13 Nov 2003
Posts: 964
Location: Florida
Followers: 1

Kudos [?]: 127 [0], given: 0

### Show Tags

04 Jan 2004, 21:38
Titleist wrote:
Dj is simply Da Man!

consider some more. try getting the proof... I did it long back.

sum of squares of first n natural numbers:
n(n+1)(2n+1)/6

sum of cubes of first n natural numbers:
[n(n+1)/2]^2
GMAT Club Legend
Joined: 15 Dec 2003
Posts: 4302
Followers: 40

Kudos [?]: 429 [0], given: 0

### Show Tags

04 Jan 2004, 21:45
Beautiful! I'll memorize the sum on n numbers and sum of squares of those n numbers. I think that should be sufficient for the exam. Sum of cubes is a bit outstretched
_________________

Best Regards,

Paul

Director
Joined: 14 Oct 2003
Posts: 587
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 49 [0], given: 0

### Show Tags

04 Jan 2004, 21:48
Director
Joined: 13 Nov 2003
Posts: 964
Location: Florida
Followers: 1

Kudos [?]: 127 [0], given: 0

### Show Tags

04 Jan 2004, 21:56
Titleist wrote:
:pray

can somebody provide the list of formulae--basic maths? I have had trouble keeping it at one place. I just don't wanna kill time on something easy/stupid (in the real exam)

..basic algebra
..stats
..combination
..basic geometry
etc..

thanks!
Director
Joined: 14 Oct 2003
Posts: 587
Location: On Vacation at My Crawford, Texas Ranch
Followers: 1

Kudos [?]: 49 [0], given: 0

### Show Tags

04 Jan 2004, 22:15
dj wrote:
Titleist wrote:
:pray

can somebody provide the list of formulae--basic maths? I have had trouble keeping it at one place. I just don't wanna kill time on something easy/stupid (in the real exam)

..basic algebra
..stats
..combination
..basic geometry
etc..

thanks!

Here are a few:

basic algebra?
d=r*t
work (same thing w=r*t)

quadratics (you probably know very well)
inequalities (you probably know very well)

Stats
Averages (you're an ace)
Mean (ditto)
Media (ditto)
SD (ditto)

Combination and Permutations
You kidding me? - you know this stuff cold!

Geometry

These can be a pain in the arse - I can understand forgetting a few basic forumlae

Circles
arc length = x*/360*circumference
perimeter of sector = arc length + 2r
area of sector = x*/360*r^2pi

Surface Area of Cylinder
2pi*r^2+2pi*r*h
Volume = pi*r^2*h

Rhombus
diag1xdiag2/2

Trapezoid
(base1+base2)/2 x h

Triangles and special triangles - you know cold

Not much else - just a matter of strategy from here.

Am I missing anything?
04 Jan 2004, 22:15
Display posts from previous: Sort by

# The sum of first hundred numbers, 1 to 100 is divisible by?

 post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.