Question

In a list of 7 integers, one integer, denoted as x is unknown. The other six integers are 20, 4, 10, 4, 8, and 4. If the mean, median, and mode of these seven integers are arranged in increasing order, they form an arithmetic progression. The sum of all possible values of x is

A.
26
B.
32
C.
34
D.
38
E.
40

Accepted Answer

E. Known integers: $4, 4, 4, 8, 10, 20$. Mode = 4. Mean $= \frac{50 + x}{7}$. Case 1: $x = 6 \implies$ Median = 6, Mean = 8. AP: 4, 6, 8. Case 2: $x = 34 \implies$ Median = 8, Mean = 12. AP: 4, 8, 12. Sum of possible $x$ values $= 6 + 34 = 40$.

Statistics: AP of Mean, Median, Mode

Explanation

Practise this under exam conditions