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’?
Explanation:
Sum of numbers before x = sum of numbers after x
∴ 1 + 2 + 3 + … + (x – 1) = (x + 1) + (x + 2) + … + 49
Adding (1 + 2 + 3 + 4 + … + (x – 1) + x) on both sides
∴ 2(1 + 2 + 3 + … +(x – 1)) + x = (1 + 2 + 3 + … + 49)
∴ 2×(x-1)x2 + x = 49×502
∴ x2 = 49 × 25
∴ x = 7× 5 = 35
Hence, option (c).
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