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What is the probability that a number selected from (-10, -6

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by Anaira Mitch » Tue Jan 10, 2017 5:01 am
What is the probability that a number selected from (-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10) can fulfill (x-5)(x+10)(2x-5)=0?

a) 1/12
b) 1/6
c) 1/4
d) 1/3
e) 1/2

Please help with this problem.
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by DavidG@VeritasPrep » Tue Jan 10, 2017 5:06 am
Anaira Mitch wrote:What is the probability that a number selected from (-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10) can fulfill (x-5)(x+10)(2x-5)=0?

a) 1/12
b) 1/6
c) 1/4
d) 1/3
e) 1/2

Please help with this problem.
We've got a list of 12 numbers. So that's our denominator.

(x-5)(x+10)(2x-5) = 0 has three solutions

If x - 5 = 0, x = 5
If x +10 = 0, x = -10
If 2x - 5 = 0, x = 2.5

-10 and 2.5 are included in the list, so we have 2 eligible desired outcomes.

2/12 = 1/6, so the answer is B
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by DavidG@VeritasPrep » Tue Jan 10, 2017 5:09 am
(Note the trap. If we do this too quickly, it's very easy to think "well, there 3 desired outcomes and 12 total possibilities, so that's 3/12 = 1/4." The killer on the GMAT isn't the hard questions. It's the little traps we fall for if we're anxious or work a little quickly.)
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by [email protected] » Tue Jan 10, 2017 2:39 pm
Hi Anaira Mitch,

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: B

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