The houses on one side of a road are numbered using consecutive even numbers .The sum of the numbers of all the houses in that row is 170. If there are at least 6 houses in that row and a is the number of the sixth house then

Options

A. `2leale6`
B. `8leale12`
C. `14leale20`
D. `22leale30`

Answer

C

Explanation

Let maximum house is 'n', sum of first 'n' evenb natural numbers `=n^(2)+n`
Let first 'm' even natural numbers are left in numbering the houses.
`(n^(2)+n)=(m^(2)+m)=170`
`rArr (n^(2)-m^(2)+n-m=170`
`rArr(n-m)(n+b+1)=170`
`n-m=10rArrn-m=10` ltbr. `n+m+1=17rArrn+m=16`
`1n=13,m=3`
`nle13`
If first terms is a - 10 then sixth = a
`n/2[2(a-10)+2(n-1)]=170`
`rArrn[a+n-11]=170`
`rArra=170/n+11-n`
`:.n=10`(only will make'a' integer)
`rArr `a=17+11-10=18`