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GATE 2024 XH2 (English) – 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

With $n$ houses on each side, the $k$-th even number is exactly 1 more than the $k$-th odd number (302 against 301, 304 against 303, and so on). So the difference of the two sums is $n \times 1 = n$, which gives $n = 27$.