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

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The sum of first hundred numbers, 1 to 100 is divisible by? [#permalink]  04 Jan 2004, 20:02
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
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The sum of the first 100 number is 5000 - which is divisible only by a) 2,4,8
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[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
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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
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Paul

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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
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Paul thanks.
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sunniboy007 wrote:
Paul thanks.

oops yes - small detail it's 5050

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sum of n natural number = n(n+1)/2

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

ans: 2
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I like that formula dj, very neat
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Dj is simply Da Man!
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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
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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
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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!
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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?
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