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Manager  Status: GMAT Preperation
Joined: 04 Feb 2010
Posts: 87
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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4 00:00

Difficulty:   35% (medium)

Question Stats: 67% (01:11) correct 33% (01:20) wrong based on 420 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
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Manager  Joined: 16 Feb 2012
Posts: 162
Concentration: Finance, Economics
Re: A number is to be selected at random from the set above. What is the  [#permalink]

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2
3
{-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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Originally posted by Stiv on 01 May 2012, 02:30.
Last edited by Bunuel on 01 May 2012, 02:41, edited 1 time in total.
Edited the question and added the OA
##### General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 57192
Re: A number is to be selected at random from the set above. What is the  [#permalink]

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1
3
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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Manager  Status: GMAT Preperation
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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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it contains 2 roots: -10 and 2.5 ??
Retired Moderator Joined: 02 Sep 2010
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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:
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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Math Expert V
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Posts: 57192
Re: A number is to be selected at random from the set above. What is the  [#permalink]

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Manager  Joined: 16 Feb 2012
Posts: 162
Concentration: Finance, Economics
Re: A number is to be selected at random from the set above. What is the  [#permalink]

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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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Failing to plan is planning to fail.
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A number is to be selected at random from the set above. What is the  [#permalink]

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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

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VP  D
Joined: 09 Mar 2016
Posts: 1258
A number is to be selected at random from the set above. What is the  [#permalink]

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Bunuel wrote:
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.

Hi pushpitkc

can you please explain what i did wrong

i did this $$x^2+10-5x-50(2x-5)$$ now left with it

$$x^2+10x-5x-100x+250 = 0$$

$$x^2+10x-5x-100x+250 = 0$$

$$x^2 -95x+250 = 0$$ now what thank you Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3355
Location: India
GPA: 3.12
Re: A number is to be selected at random from the set above. What is the  [#permalink]

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1
dave13 wrote:
Bunuel wrote:
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.

Hi pushpitkc

can you please explain what i did wrong

i did this $$x^2+10-5x-50(2x-5)$$ now left with it

$$x^2+10x-5x-100x+250 = 0$$

$$x^2+10x-5x-100x+250 = 0$$

$$x^2 -95x+250 = 0$$ now what thank you Hi dave13

You have 3 values of x possible and we need to check how many of these values are part
of the set. I don't seem to understand why are you trying to form a quadratic equation Btw, as for your question, the highlighted portion is wrong

$$(x-5)(x+10)(2x-5) = 0$$ -> $$(x^2 - 5x +10x - 50)(2x - 5) = 0$$ -> $$(x^2 + 5x - 50)(2x - 5) = 0$$
The entire equation will need to be multiplied and we will have a cubic equation

Hope this clears your confusion!
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VP  D
Joined: 09 Mar 2016
Posts: 1258
Re: A number is to be selected at random from the set above. What is the  [#permalink]

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pushpitkc thanks can you please show how do we find 2 roots: -10 and 2,5, i am kind of confused what to do with highlighted part $$(x^2 + 5x - 50)(2x - 5) = 0$$
Manager  S
Joined: 07 Feb 2017
Posts: 180
Re: A number is to be selected at random from the set above. What is the  [#permalink]

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Count there are 12 items
x = 5 or x = -10 or x = 2.5
Two are in the set
B.
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3355
Location: India
GPA: 3.12
Re: A number is to be selected at random from the set above. What is the  [#permalink]

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1
dave13 wrote:
pushpitkc thanks can you please show how do we find 2 roots: -10 and 2,5, i am kind of confused what to do with highlighted part $$(x^2 + 5x - 50)(2x - 5) = 0$$

Hey dave13

If 2x - 5 = 0 -> 2x = 5 -> x = 5/2 = 2.5
If x - 5 = 0 -> x = 5
If x + 10 = 0 -> x = -10

Therefore, the roots of the quadratic equation are -10, 5, 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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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

According to the given equation, x can equal the following:

x - 5 = 0

x = 5

or

x + 10 = 0

x = -10

or

2x - 5 = 0

2x = 5

x = 2.5

Since -10 and 2.5 are in the set, the probability of selecting one of those solutions is 2/12 = 1/6.

Answer: B
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Joined: 13 Mar 2019
Posts: 27
Re: A number is to be selected at random from the set above. What is the  [#permalink]

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1
Clearly,
There are two solutions = -10,2.5.
So P(X) = 2/12 = 1/6 Re: A number is to be selected at random from the set above. What is the   [#permalink] 08 Aug 2019, 08:34
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