Question

The houses on one side of a road are numbered using consecutive even numbers. The sum of the numbers of all the houses in that row is $170$. If there are at least $6$ houses in that row and a is the number of the sixth house, then.

• A. $2\le a\le 6$
• B. $8\le a\le 12$
• C. $14\le a\le 20$
• D. $22\le a\le 30$

Answer 1

Answer: (C)

$14\le a\le 20$

The factors of 170 are $1,2,5,10,17,34,85,170$

When the sum is divided by the number of houses, you get the average of those numbers.

Since the number of houses are atleast 6, the average would be 17 if there are 10 houses.

It would be 10 if there are 17 houses, but this case is not possible since the number assigned cannot be negative.

Similarly, there cannot be any more number of houses.

So, there are 10 houses, with the average number turning out to be 17.

5 houses before 17 and 5 after 17. The sixth house therefore becomes 18.