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If x is a prime number, and x-1 is the median of the set {x-1, 3x +3,

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If x is a prime number, and x-1 is the median of the set {x-1, 3x +3,  [#permalink]

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New post 15 Jan 2015, 06:40
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

82% (02:06) correct 18% (02:38) wrong based on 128 sessions

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Re: If x is a prime number, and x-1 is the median of the set {x-1, 3x +3,  [#permalink]

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New post 15 Jan 2015, 19:32
1
X is Prime. So lets put the first prime value and find out of the values of the set.

X=2 ; Set { 1,9,0 } , clearly the value x-1 is the median of the set. and the average is 10/3, which is D but hold on. lets check further to double check.

X= 3 ; Set { 2,12,2}, Here the value f x-1 can be the median ok t the average is 16/3 , no such value in the given answers. So no

X=5 and bigger prime values. the value of x-1 would be lowest in the set and therefore it cannot be the median.

Therefore D is the correct answer.



Bunuel wrote:
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?

A. 2
B. 5/3
C. 3
D. 10/3
E. 14/3
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Re: If x is a prime number, and x-1 is the median of the set {x-1, 3x +3,  [#permalink]

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New post 15 Jan 2015, 20:33
1
Answer = D. 10/3

Average \(= \frac{x-1 + 3x+3 + 2x-4}{3} = \frac{6x-2}{3}\)

Placing x = 2, mean \(= \frac{10}{3}\)

I wonder why its given that (x-1) is the median... sort of distraction?
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Re: If x is a prime number, and x-1 is the median of the set {x-1, 3x +3,  [#permalink]

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New post 15 Jan 2015, 20:45
1
Answer D - 10/3......One more answer possible 16/3....not mentioned in answer options
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Re: If x is a prime number, and x-1 is the median of the set {x-1, 3x +3,  [#permalink]

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New post 19 Jan 2015, 02:19
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Re: If x is a prime number, and x-1 is the median of the set {x-1, 3x +3,  [#permalink]

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New post 08 Jul 2016, 23:19
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?

A. 2
B. 5/3
C. 3
D. 10/3
E. 14/3


Solution:

x-1 is the median of the set, implies if we arrange the set in ascending order, the set would be [2x-4, x-1, 3x+3]. This means that:

2x-4<x-2<3x+3

solving inequality gives x>-2 and x<3. Since x is prime number and the only prime number <3 is 2, so put x=2.

Hence set becomes: [ 0, 1, 9] and avg = 10/3.

Please give kudos if this helps! :)
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Re: If x is a prime number, and x-1 is the median of the set {x-1, 3x +3,   [#permalink] 08 Jul 2016, 23:19

If x is a prime number, and x-1 is the median of the set {x-1, 3x +3,

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