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10% of all-aliens are capable of intelligent thought and [#permalink]

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14 Feb 2010, 06:31

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10% of all-aliens are capable of intelligent thought and have more than 3 arms, and 75% of aliens with 3 arms or less are capable of intelligent thought. If 40% of all aliens are capable of intelligent thought, what percent of aliens have more than 3 arms?

Ans: 60% Explanation: Ques: % of aliens having more than 3 Arms.

Lets the total no of aliens be 100 Form 3 categories: Less than equal to 3 Arms;More than 3 Arms;Intelligent Thoughts From the ques: More than 3 Arms & intelligent thoughts = 10% of total Aliens = 10 Let the other aliens which have more than 3 Arms but dont have intelligent thoughts be x

This gives total no of aliens with Less than or equal to 3 Arms (Intelligent or not) = 100 - x - 10 = 90 - x

From the ques: Aliens having less than or equal to 3 Arms & Intelligent Thoughts = 75% of total no of aliens with Less than or equal to 3 Arms = 0.75 (90 - x)

It's given total no of intelligent Aliens = 40% of all the aliens = 40

Therefore 40 = 10 + 0.75(90-x) Solve for x... , x = 50

Therefore % of aliens having more than 3 Arms = x + 10 = 60%

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40 are intelligent: :30 have arms < 3 :10 have arms >= 3

60 are dumb: :10 have arms < 3 given the fact that 75% of all aliens with more than three arms are intelligent. :The remaining aliens have arms >=3 (50)

can someone plz. explain the solution of this question by the method of venn diagram....

See the attached diagram: I denotes intelligent aliens, and m3 denotes those with more than 3 arms. Among those who don't have more than 3 arms, the ratio between those who are intelligent and those who aren't is 75:25, therefore 3x and x in the diagram. Knowing that 3x + 10 = 40, it follows that x =10, and from the diagram, those who have more than 3 arms is 100 - 30 - 10 = 60.

Answer: 60%.

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Aliens-Venn.jpg [ 17.82 KiB | Viewed 2383 times ]

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Re: 10% of all-aliens are capable of intelligent thought and [#permalink]

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