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What is the difference between the sum of the numbers from 1

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What is the difference between the sum of the numbers from 1 [#permalink] New post 12 Oct 2006, 12:36
What is the difference between the sum of the numbers from 1 to 600 and the sum of the even numbers from 460 to 600, inclusive?

a) 180300
b) 142670
c) 371000
d) 124760
e) 359540
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 [#permalink] New post 12 Oct 2006, 13:20
Cicerone, can you show how you derive your answers, please?
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 [#permalink] New post 12 Oct 2006, 13:30
Sum of the first n natural numbers is n(n+1)/2.

So sum of the first 600 numbers is 600x601/2 = 300x601=180300

Next even numbers from 460 to 600

i.e. 460,462,464,...........................596.598,600

Totally there will be 141 numbers from 460 to 600
Out of these 141 numbers, 71 will even and 70 will be odd.

I mean to say that from 460 to 600 there will be 71 even numbers.

So the sum of the above series (which is in ARITHMETIC PROGRESSION) will be N/2(FIRST TERM + LAST TERM), where N = number of terms in the series.

So 71/2(460+600) = 71x530 = 37630.

Hence the answer will be 180300-37630=142,670
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 [#permalink] New post 12 Oct 2006, 18:19
B

Sum of all numbers from 1-600 = 600/2(1+600) = 180300

Number of all even numbers from 460 - 600 = 600-460/2 = 70.5 = 71 (Since starting and ending numbers are even, there will be one more even number than odd numbers).

Sum of all even numbers from 460-600 = 71/2(460+600) = 37630

Difference = 142670
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 [#permalink] New post 13 Oct 2006, 12:41
B

sum of 1-600 = 601/2 * 600 = 180300

sum of evens = 1060/2 * 71 = 530 * 71 = 37630

= 142760
  [#permalink] 13 Oct 2006, 12:41
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