List Q consists of {12, 17, 21, 24, 30 and x}. For how many integer va

Solution:

The mean is (12 + 17 + 21 + 24 + 30 + x)/6 = (104 + x)/6. Since there are 6 values, the median is the average of the two values in the middle. It could be one of the following:

(17 + 21)/2 = 19 (if x is the smallest value or the second smallest value)

(x + 21)/2 (if x is the third smallest value or the third largest value)

(21 + 24)/2 = 22.5 (if x is the second largest value or the largest value)

We are given that the mean is equal to the median. If the median is 19, we have:

(104 + x)/6 = 19

104 + x = 114

x = 10

We see that if x = 10, it will be indeed the smallest value in the set. So 10 could be a value of x.

If the median is (x + 21)/2, we have:

(104 + x)/6 = (x + 21)/2

6(x + 21) = 2(104 + x)

6x + 126 = 208 + 2x

4x = 82

x = 20.5

Since 20.5 is not an integer, 20.5 could not be a value of x.

If the median is 22.5, we have:

(104 + x)/6 = 22.5

104 + x = 135

x = 31

We see that if x = 31, it will be indeed the largest value in the set. So 31 could be a value of x.

Answer: C

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