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GATE 2024 CH – Question 2

General Aptitude · Quantitative Aptitude: Algebra, Geometry and Mensuration · 1 mark · Multiple choice

In a locality, the houses are numbered in the following way: The house-numbers on one side of a road are consecutive odd integers starting from 301, while the house-numbers on the other side of the road are consecutive even numbers starting from 302. The total number of houses is the same on both sides of the road.
If the difference of the sum of the house-numbers between the two sides of the road is 27, then the number of houses on each side of the road is

  1. 27
  2. 52
  3. 54
  4. 26

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Show answer and explanation

Correct answer: (A) 27

Explanation

The $k$-th odd number is $300 + (2k - 1)$ and the $k$-th even number is $300 + 2k$, so each even number is 1 more than the odd number in the same position. With $n$ houses on each side, the difference of the sums is $n$. So $n = 27$.