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Difficult Math Problem #62 - Algebra

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800guy Master | Next Rank: 500 Posts Default Avatar
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Difficult Math Problem #62 - Algebra

Post Fri Nov 24, 2006 11:24 am
The sum of the even numbers between 1 and n is 79*80, where n is an odd number. n=?

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gmat_enthus Senior | Next Rank: 100 Posts Default Avatar
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Post Fri Nov 24, 2006 12:35 pm
800guy wrote:
The sum of the even numbers between 1 and n is 79*80, where n is an odd number. n=?
sum of even numbers = n1/2 ( 4 + (n1-1)2) = 79*80

n1(2+2n1)/2 = 79*80
n1(n1+1) = 79*80

=> n1=79. So 79 even numbers => nth term = 2 + 78*2 = 158

So "n" in the question should be 159

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800guy Master | Next Rank: 500 Posts Default Avatar
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Post Mon Nov 27, 2006 12:46 pm
OA:

The sum of numbers between 1 and n is = (n(n+1))/2

1+2+3+.....+n=(n(n+1))/2 {formula}

we are looking for the sum of the even numbers between 1 and n, which means:

2+4+6+.....+(n-1) n is ODD
=1*2+2*2+2*3+......+2*((n-1)/2)
=2*(1+2+3+.....+*((n-1)/2))
from the formula we obtain :
=2*(((n-1)/2)*((n-1)/2+1))/2
=((n-1)/2)*((n+1)/2) =79*80
=> (n-1)*(n+1)=158*160
=> n=159

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