Orange08 wrote:

Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?

78

77 1/5

66 1/7

55 1/7

52

{

a_1,

a_2,

a_3,

a_4,

a_5}

As mean of 5 numbers is 55 then the sum of these numbers is

5*55=275;

The median of the set is equal to the mean -->

mean=median=a_3=55;

The largest number in the set is equal to 20 more than three times the smallest number -->

a_5=3a_1+20.

So our set is {

a_1,

a_2,

55,

a_4,

3a_1+20} and

a_1+a_2+55+a_4+3a_1+20=275.

The range of a set is the difference between the largest and smallest elements of a set.Range=a_5-a_1=3a_1+20-a_1=2a_1+20 --> so to maximize the range we should maximize the value of

a_1 and to maximize

a_1 we should minimize all other terms so

a_2 and

a_4.

Min possible value of

a_2 is

a_1 and min possible value of

a_4 is

median=a_3=55 --> set becomes: {

a_1,

a_1,

55,

55,

3a_1+20} -->

a_1+a_1+55+55+3a_1+20=275 -->

a_1=29 -->

Range=2a_1+20=78Answer: A.

Since the statement says that the median = mean, aren't we supposed to assume that it's an evenly spaced set? If so, wouldn't a2 and a4 be different from a1 and a3?