GATE CE 2024 Set 1 — Question 2
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General Aptitude → Analytical Aptitude → Numerical Relations & Reasoning
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Question
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
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
Correct answer
(A) 27
Solution
Let be the number of houses on each side of the road.Side 1 (Odd numbers):
The house numbers are .Side 2 (Even numbers):
The house numbers are .Let be the sum of house numbers on Side 1 and be the sum on Side 2.
We are given that the difference of the sums is 27. Since each even number is exactly 1 greater than its corresponding odd number on the other side:
( times)
Given , we have .Thus, the number of houses on each side is 27.
The house numbers are .Side 2 (Even numbers):
The house numbers are .Let be the sum of house numbers on Side 1 and be the sum on Side 2.
We are given that the difference of the sums is 27. Since each even number is exactly 1 greater than its corresponding odd number on the other side:
( times)
Given , we have .Thus, the number of houses on each side is 27.
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