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, then what is the value of n?
A. 79
B. 81
C. 83
D. 157
E. 159
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Sum of numbers
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indiantiger
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sum of n numbers = n/2(2*a + (n-1)*d)
a = is the first term of the series
d= is the difference b/w consecutive numbers
so in our case sum = 79 * 80 = 6320
a = 2 (first even number)
so the equation becomes
=>n/2*(4 * (n-1)*2)
=>2n + n^2 -n = 6320
=>n^2 + n -6320 = 0
solve it for n, then you will get solutions 79,80 and we are give that n is odd so answer is 79
a = is the first term of the series
d= is the difference b/w consecutive numbers
so in our case sum = 79 * 80 = 6320
a = 2 (first even number)
so the equation becomes
=>n/2*(4 * (n-1)*2)
=>2n + n^2 -n = 6320
=>n^2 + n -6320 = 0
solve it for n, then you will get solutions 79,80 and we are give that n is odd so answer is 79
"Single Malt is better than Blended"
Basically 2+4+6+8+10+12+..............+n-1= 79*80
2(1+2+3+4+5+6+.......)=79*80
1+2+3+4+5+................= 79*40
Use Sum=n/2(2a + (n-1)d) , where a= 1st term , d= difference, n=number of terms
n/2(2*1 + (n-1)) = 79*40
Rearranging, n^2 + n - 79*80=0
From the above equation, without doing any calculations, one can see the odd answer 79.
2(1+2+3+4+5+6+.......)=79*80
1+2+3+4+5+................= 79*40
Use Sum=n/2(2a + (n-1)d) , where a= 1st term , d= difference, n=number of terms
n/2(2*1 + (n-1)) = 79*40
Rearranging, n^2 + n - 79*80=0
From the above equation, without doing any calculations, one can see the odd answer 79.
