Approached the problem using, the calculating the mean and then plugging in the answer choices.

The median value is (x-1). The other two are not symmetric about this value. So mean for these 3 values is (sum of 3 values)/3.

The mean comes as 2x-(2/3).

I then equated this with the answer choices, the one which gives x=prime number is the correct answer.

Only D satisfies this equation with the answer as x=2.

Hence went for D. On the flip side, took me 2:20 mins.

>now 2x-4<x-1=>x<3 ; prime number less than 3 is 2 so x=2

I think, there should be "less than or equal to" instead of "less than"

2x-4<=x-1 => x<=3
2x-4+x-1+3x+3/3 = 6x-2/3 = 10/3 (putting x=2)
OR = 16/3 (putting x=3)
So the right answer is (D) 10/3 (because there is no option 16/3)

(D) 10/3

My take on the problem,
Since x-1 is the median,we can arrange them in ascending order
2x-4, x-1 and 3x+3

2x-4<= x-1
x<=3 and x is a prime number...so started with x=2 and got 0,1,9
The mean then is 10/3.... even 3 as x can be applied but in that case the mean =16/3 which is not one of the options...

GOOD Q
IMO:D

If x is a prime number, and x-1 is the median of the set {x-1, 3x +3, 2x-4}, then what is the average (arithmetic mean) of the set?

1. 2
2. 5/3
3. 3
4. 10/3
5. 14/3

The Explanation is just one Liner

Mean of {x-1, 3x +3, 2x-4} = (6x - 2)/3

x can be 2, 3, 5, 7, 11 etc...

@x=2, (6x - 2)/3 = (6*2-2)/3 = 10/3

Answer: Option D

simple way to solve this question to find the mean & assign the value from answers & see if x is coming as prime or not.

mean = (x -1 + 2x -4 + 3x+3 )/3 = (6x-2)/3

if 6x-2/3 = 10/3
solving it gives x =2 which is prime number.

Answer D.