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# The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2

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Math Expert
Joined: 02 Sep 2009
Posts: 59588
The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2  [#permalink]

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03 Jul 2017, 03:43
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69% (02:04) correct 31% (02:10) wrong based on 194 sessions

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The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2/2. What is the range of the above set of integers?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

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The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2  [#permalink]

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03 Jul 2017, 03:57
2
1
Assume that the missing value is x

We know that mean = $$\frac{x^2}{2}$$
$$\frac{24 + x}{6} = \frac{x^2}{2}$$
$$3x^2 - x - 24 = 0$$

Solving for x,
x=3 and -8/3(not possible since as x is an integer)

Range : Maximum value - Minimum value = 6-3 = 3(Option C)
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Re: The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2  [#permalink]

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04 Oct 2018, 00:35
Bunuel wrote:
The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2/2. What is the range of the above set of integers?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Mean = Sum $${4, 4, 5, 5, 6, x} / 6 = (24+x)/6 = x^2/2$$

i.e. $$24+x = 3x^2$$

i.e. $$x(3x-1) = 24$$

i.e. $$x = 3$$

I.e. range = Highest value - Lowest value = 6-3 = 3

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Re: The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2  [#permalink]

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06 Oct 2018, 13:38
Bunuel, can you please explain this one? I can't understand from the already given explanation. Thanks.
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The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2  [#permalink]

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06 Oct 2018, 14:51
1
Hi MsInvBanker

Mean formula is $$\frac{sum of elements}{number of elements}$$

from this you will get $$\frac{24+x}{6}$$ . Equate this to given mean $$\frac{x^2}{2}$$ to get below quadratic equation :

$$3x^2−x−24=0$$
Factorize this equation : $$3x^2 -9x+8x-24=0$$ ==> $$3x(x-3)+8(x-3)=0$$ ==> $$(x-3)(3x+8)=0$$==> $$x=3$$ as in question it is given x is +ve

Range is Maximum value in set- Minimum value in set ==> $$6 - 3 = 3$$

Please +1 kudos if you liked my post
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Re: The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2  [#permalink]

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07 Oct 2018, 00:25
1
Thank you very much pranjal123

I was messing up on the factorization step. I was mistakenly putting them in for $$+x$$ instead of $$-x$$. Thanks again.
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Re: The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2  [#permalink]

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07 Oct 2018, 06:29
Bunuel wrote:
The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2/2. What is the range of the above set of integers?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

$$\frac{24+x}{6} =\frac{x^2}{2}$$

$$(24+x)2 = 6x^2$$ (cross multiply)

$$48+2x=6x^2$$

$$48+2x-6x^2=0$$ (rearrange and multiply by -1)

$$6x^2-2x-48=0$$ (divide by 2)

$$3x^2 - x - 24 = 0$$ (factorize ) -24 *3 = -72 ---> -9*8 = -72

$$(3x^2 - 9x)+(8x - 24) = 0$$ factor out

$$3x(x-3)+8(x-3)=0$$

$$(3x+8)(x-3)=0$$
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Re: The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2  [#permalink]

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13 Jan 2019, 23:47
Bunuel wrote:
The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2/2. What is the range of the above set of integers?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Dear Moderator,
This same question has been duplicated in the link below, you may wish to merge the same, also let me know if I am missing anything.Thank you.

https://gmatclub.com/forum/the-mean-of- ... 43880.html
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Re: The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2  [#permalink]

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13 Jan 2019, 23:50
stne wrote:
Bunuel wrote:
The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2/2. What is the range of the above set of integers?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Dear Moderator,
This same question has been duplicated in the link below, you may wish to merge the same, also let me know if I am missing anything.Thank you.

https://gmatclub.com/forum/the-mean-of- ... 43880.html

____________________
Merged. Thank you.
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Re: The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2  [#permalink]

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14 Jan 2019, 04:01
1
Bunuel wrote:
The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2/2. What is the range of the above set of integers?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

solve for x
we get 3x^2-9x+8x-24=0
x= 3 and -8/3

range would be 6-3 = 3 IMO C
Re: The mean of the set of the positive integers {4, 4, 5, 5, 6, x} is x^2   [#permalink] 14 Jan 2019, 04:01
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