Show your own working for this question and i am warning: Only CuriousRose will answer no one will give answer
There are less than 10 houses on one side of a street that are numbered 5, 7, 9, etc. Hana lives in one of these houses. The numbers of all the houses numbered below hers have the same sum as all those numbered above hers. What is her house number?
Share
Answer:
18
Step-by-step explanation:
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.
Verified answer
Given :
Less than 10 houses on one side of a street.
Houses are numbered like 5, 7, 9 etc.
To find :
Hana's house number
Solution :
The pattern of the houses is 5, 7, 9, 11, 13, 15, 17
It is given that numbers of all the houses numbered below hers have the same sum as all those numbered above hers.
So to we will use the trial and error method to find an answer of such question.
----------------------------------------------------------
•If she lives in the house number 7, then
Previous house number = 5
Next house number = 9
As 5 ≠ 9 (Our assumption is wrong)
----------------------------------------------------------
•If she lives in the house number 9, then
Previous house numbers sum = 5 + 7 = 12
Next house numbers sum = 11 + 13 + 15 + 17 = 56
As 12 ≠ 56 (Our assumption is wrong)
----------------------------------------------------------
•If she lives in the house number 11, then
Previous house numbers sum = 5 + 7 + 9 = 21
Next house numbers sum = 13 + 15 + 17 = 45
As 21 ≠ 45 (Our assumption is wrong)
----------------------------------------------------------
•If she live in the house number 13, then
Previous house numbers sum = 5 + 7 + 9 + 11 = 32
Next house numbers sum = 15 + 17 = 32
As 32 = 32 (Our assumption is correct)
----------------------------------------------------------
Therefore, Hana lives in the house number 13 as the numbers of all the houses numbered below hers have the same sum as all those numbered above hers.
The correct answer is 13.