# Moderate Algebra Solved QuestionAptitude Discussion

 Q. In a green view apartment, the houses of a row are numbered consecutively from 1 to 49. Assuming that there is a value of '$x$' such that the sum of the numbers of the houses preceding the house numbered '$x$' is equal to the sum of the numbers of the houses following it. Then, what will be the value of '$x$'?
 ✖ A. 21 ✖ B. 30 ✔ C. 35 ✖ D. 42

Solution:
Option(C) is correct

From the given information,

Sum of the first $(x-1)$ natural numbers = Sum of natural number from $(x+1)$ to 49.

$\dfrac{x(x-1)}{2}=\dfrac{49\times 50}{2}-\dfrac{x(x+1)}{2}$

$2x^2=49\times 50$

$\Rightarrow x=7\times 5= 35$