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.
BTG Mean Problem
>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)
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)
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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...
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...
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You're right; the mean can be either 10/3 or 16/3.joytdh wrote: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...
It's not a good question.
Cheers,
Brent
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The Explanation is just one LinerIf 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
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
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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.
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.