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

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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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Re: A number is to be selected at random from the set above. What is the [#permalink]

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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 \(P=\frac{2}{12}=\frac{1}{6}\).

Answer: B.
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New post 25 Oct 2010, 23:39
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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New post 25 Oct 2010, 23:45
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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{-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, 01:41, edited 1 time in total.
Edited the question and added the OA
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22. Probability



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New post 01 May 2012, 23:39
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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New post 20 Jan 2018, 15:07
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

Final Answer:
[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, 15:07
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