Aptitude 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.

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

\(2x^2=49\times 50\)

\(\Rightarrow x=7\times 5= 35\)