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# Of the 750 participants in a professional meeting, 450 are

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Of the 750 participants in a professional meeting, 450 are [#permalink]  24 Jan 2017, 02:58
Expert's post
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Question Stats:

94% (01:29) correct 5% (01:09) wrong based on 34 sessions

Of the 750 participants in a professional meeting, 450 are female and $$\frac{1}{2}$$ of the female and $$\frac{1}{4}$$ of the male participants are less than thirty years old. If one of the participants will be randomly selected to receive a prize, what is the probability that the person selected will be less than thirty years old?

A) $$\frac{1}{8}$$

B) $$\frac{1}{3}$$

C) $$\frac{3}{8}$$

D) $$\frac{2}{5}$$

E) $$\frac{3}{4}$$
[Reveal] Spoiler: OA

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Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1895 [2] , given: 397

Re: Of the 750 participants in a professional meeting, 450 are [#permalink]  28 Jan 2017, 04:27
2
KUDOS
Expert's post
Explanation

First, we determine the number of men and woman at the meeting: 750 total – 450 women 300 men

Now we determine the number of each gender under 30:

$$\frac{1}{2}$$ of the female participants are less than 30 → $$\frac{1}{2} \times 450$$ = 225 women less than thirty

$$\frac{1}{4}$$ of the male participants are less than 30 → $$\frac{1}{4} \times 300$$ = 75 men less than thirty.

The total number of people less than 30 years of age is 300 (225 + 75).

Finding the probability:

Probability = number of favorable outcomes/number of possible outcomes → $$\frac{300}{750}$$ → $$\frac{30}{75}$$ → $$\frac{2}{5}$$

Hence option D is correct.
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Sandy
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Re: Of the 750 participants in a professional meeting, 450 are   [#permalink] 28 Jan 2017, 04:27
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