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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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Math Expert
Joined: 02 Sep 2009
Posts: 64068
If x is a prime number, and x-1 is the median of the set {x-1, 3x +3,  [#permalink]

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15 Jan 2015, 06:40
00:00

Difficulty:

15% (low)

Question Stats:

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

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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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Joined: 17 Sep 2011
Posts: 12
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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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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Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1709
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
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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15 Jan 2015, 20:33
1

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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Joined: 03 Oct 2014
Posts: 125
Location: India
Concentration: Operations, Technology
GMAT 1: 720 Q48 V40
WE: Engineering (Aerospace and Defense)
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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15 Jan 2015, 20:45
1
Math Expert
Joined: 02 Sep 2009
Posts: 64068
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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19 Jan 2015, 02:19
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

_________________
Manager
Joined: 27 Jan 2013
Posts: 96
Location: India
GMAT 1: 700 Q49 V35
GPA: 3.7
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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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!
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