Question 23

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’?

Solution

It is given that sum of the first $$(x - 1)$$ numbers is equal to sum of the numbers from $$(x + 1)$$ to 49
or, sum of $$(x - 1)$$ numbers = sum of first 49 numbers - sum of first $$x$$ numbers
$$\dfrac{x(x - 1)}{2} = \dfrac{49 * 50}{2} - \dfrac{x(x + 1)}{2}$$
On solving, we get $$x$$ = 35
Hence, option C is the correct answer.

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