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81) AP

by ern5231 » Wed May 12, 2010 9:40 pm
Sum of all even numbers between 1 and n is equal to 79*80. What is the value of n?

I don't have answer options. This question is picked from a high school book and i beleve we do get similar Qs in GMAT.
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by liferocks » Wed May 12, 2010 9:50 pm
the sum is 2*m/2*(m/2+1)*1/2..where m is the even number less or equal to n

now this is equal to 79*80=2*m/2*(m/2+1)*1/2
hence m/2=79..or m=158

so n can be either 158 or 159
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by ern5231 » Wed May 12, 2010 10:09 pm
Thanks liferocks. Can you break this down a little more? your answer is right.
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by rajeshsources » Wed May 12, 2010 10:57 pm
ern5231 -----

As we know, the sum of the numbers ranging from 1 to n, i.e. 1,2,3,4,......n
Sum of numbers = (n*(n+1))/2

All even numbers from 1 to n, i.e., 2,4,6,8,10,......n
Sum of these numbers (2,4,6,8,.....n) == 79 * 80. (Given)

So, we can write as,

2(1,2,3,....n/2) == 79 * 80
2 * ((n/2(n/2+1))/2) == 79 * 80 (From the above formula, substitute n = n/2)
n/2 * (n/2 + 1) == 79 * 80
From the above, we can say n/2 = 79, then n = 79*2 = 158.

So that the value of 'n' is 158.

HTH, GOOD LUCK,

Thanks,
Rajesh,
Loves GMAT....!!!!
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