Problem Solving

Set B has three positive integers with a
median of 9. If the largest possible range of the
three numbers is 19, given a certain mean, what is
that mean?

1. 9
2. 9.6
3. 10
4. 22
5. 21

Rajani wrote:Set B has three positive integers with a
median of 9. If the largest possible range of the
three numbers is 19, given a certain mean, what is
that mean?

1. 9
2. 9.6
3. 10
4. 22
5. 21

as the three nos. are positive integers least no. may be 1 but less than 9 (since median is 9) so the greatest no. lies between (1+19) and (8+19)

i.e. between 20 and 27

so the mean can lie between (1+9+20)/3 and (8+9+27)/3 (including this limiting means) i.e. 10 and 14.66

now choice C satisfies the condition.

so the mean can lie between (1+9+20)/3 and (8+9+27)/3 (including this limiting means) i.e. 10 and 14.66

I agree with your statement..

can you tell me how can we proceed if we have 2 options which are in btn 10 and 14.66???

if u have to find the largest range, the smallest number here has to be 1 and so the third number must be 20. avg=1+9+20/3=10