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

AAPL wrote:Manhattan Prep

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

OA B

\((x-5)(x+10)(2x-5)=0\) if either at least one of the factors \((x-5)\), \((x+10)\), and \((2x-5)\) is 0. Thus, if x = 5, –10 or 2.5, \((x-5)(x+10)(2x-5)=0\).

We see that among the 12 numbers in the set (-10, -6, -5, -4, -2.5, -1, 0, 2.5, 4, 6, 7, 10), only 5 and –10 are in it. Thus, the probability that a number selected from the set can fulfill \((x-5)(x+10)(2x-5)=0\) is 2/12 = 1/6.

The correct answer: B

Hope this helps!

-Jay
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AAPL wrote:Manhattan Prep

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

OA B

Since 5, -10, and 2.5 can fulfill the given equation, the probability of selecting a number from the 12-number set that fulfills the equation is 2/12 = 1/6.

Answer: B