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# A number is to be selected at random from the set above. What is the

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Manager
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Concentration: Social Entrepreneurship, Social Entrepreneurship
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A number is to be selected at random from the set above. What is the [#permalink]

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25 Oct 2010, 07:43
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Question Stats:

66% (00:45) correct 34% (00:44) wrong based on 344 sessions

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{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}

A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation $$(x - 5)(x + 10)(2x - 5) = 0$$?

A. 1/12
B. 1/6
C. 1/4
D. 1/3
E. 1/2
[Reveal] Spoiler: OA
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Joined: 02 Sep 2009
Posts: 44322
Re: A number is to be selected at random from the set above. What is the [#permalink]

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25 Oct 2010, 07:50
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vanidhar wrote:
{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}

A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x - 5)(x + 10)(2x - 5) = 0?

A. 1/12
B. 1/6
C. 1/4
D. 1/3
E. 1/2

Solutions of the equation $$(x-5)(x+10)(2x-5)=0$$ are: $$x=5$$, $$x=-10$$ and $$x=2.5$$.

There are total of 12 numbers in the set {-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10} and it contains 2 roots: -10 and 2,5, so the probablitiy that the number selected will be a solution of the given equation is $$P=\frac{2}{12}=\frac{1}{6}$$.

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Manager
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Posts: 99
Concentration: Social Entrepreneurship, Social Entrepreneurship
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Re: A number is to be selected at random from the set above. What is the [#permalink]

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26 Oct 2010, 00:39
it contains 2 roots: -10 and 2.5 ??
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Re: A number is to be selected at random from the set above. What is the [#permalink]

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26 Oct 2010, 00:45
vanidhar wrote:
it contains 2 roots: -10 and 2.5 ??

Roots = Solution to the equation

We know the only solutions are -10,2.5,5
And of these, two are present in the set at hand
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Re: A number is to be selected at random from the set above. What is the [#permalink]

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01 May 2012, 02:30
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{-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10}

A number is to be selected at random from the set above. What is the probability that the number selected will be a solution of the equation (x-5)(x+10)(2x-5) = 0?

A. 1/12
B. 1/6
C. 1/4
D. 1/3
E. 1/2
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Last edited by Bunuel on 01 May 2012, 02:41, edited 1 time in total.
Edited the question and added the OA
Math Expert
Joined: 02 Sep 2009
Posts: 44322
Re: A number is to be selected at random from the set above. What is the [#permalink]

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01 May 2012, 02:44
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Manager
Joined: 16 Feb 2012
Posts: 212
Concentration: Finance, Economics
Re: A number is to be selected at random from the set above. What is the [#permalink]

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02 May 2012, 00:39
Aaaaaa OMG, I actually didn't notice that there isn't number 5(positive) in this bunch of numbers. I assumed it, and I got it wrong!

My advice to everyone: Don't assume anything!!!
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Re: A number is to be selected at random from the set above. What is the [#permalink]

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20 Jan 2018, 16:07
Hi All,

We're asked for the probability of choosing a number (from a given set of 12 numbers) that will "fit" a given equation. That equation is set equal to 0, which makes solving the equation rather easy. Since we're dealing with the PRODUCT of three "terms", if ANY of those terms equals 0, then the product will equal 0.

IF... we select X = -10 from the set, then we have (-15)(0)(-25) = 0, so X = -10 IS a solution.
IF... we select X = 0 from the set, then we have (-5)(10)(-5) = 250, which is NOT a solution.

The given equation has 3 solutions: +5, -10 and +5/2. However, only two of those solutions appear in the set (-10 and 2.5). Thus, the probability of selecting a number that fits the equation is 2/12 = 1/6

[Reveal] Spoiler:
B

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Re: A number is to be selected at random from the set above. What is the   [#permalink] 20 Jan 2018, 16:07
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