The problem should read as follows:
sapuna wrote:
If n is an odd number, and the sum of all the even numbers between 1 and n is equal to the product of 79 and 80, what is the value of n ?
1)79
2)81
3)83
4)157
5)159
For any set of evenly spaced integers:
Number of integers = (biggest - smallest)/interval + 1, where the interval is the distance between one integer and the next.
Average = (biggest + smallest)/2.
Sum = (number of integers)(average).
We can PLUG IN THE ANSWERS, which represent the value of n.
When the correct answer choice is plugged in, the sum of the even integers between 1 and n = 79*80.
Answer choice D: 157
Since n=157, we must calculate the sum of the even integers between 1 and 157:
{2, 4, 6....152, 154, 156}.
In the set above:
Smallest = 2.
Biggest = 156.
Since all of the integers are even, the INTERVAL -- the distance between one integer and the next -- is 2.
Thus:
Number of integers = (156-2)/2 + 1 = 78.
Average = (156+2)/2 = 79.
Sum = 78*79.
Too small.
For the sum increase to 79*80, the value of n must increase.
The correct answer is
E.
Answer choice E: 159
Since n=159, we must calculate the sum of the even integers between 1 and 159:
{2, 4, 6....154, 156, 158}.
In the set above:
Smallest = 2.
Biggest = 158.
Since all of the integers are even, the INTERVAL -- the distance between one integer and the next -- is 2.
Thus:
Number of integers = (158-2)/2 + 1 = 79.
Average = (158+2)/2 = 80.
Sum = 79*80.
Success!
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