10% of all-aliens are capable of intelligent thought and : GMAT Problem Solving (PS)
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# 10% of all-aliens are capable of intelligent thought and

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

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14 Feb 2010, 05:31
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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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14 Feb 2010, 08:32
Let x be the number of aliens with more than 3 arms
Then 100-x with 3 or less than 3 arms

according to the question

$$75% of (100-x) = 40-10$$

solving will give x = 60
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14 Feb 2010, 08:37
I assume 100 aliens:

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)

50 + 10 = 60
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17 Feb 2010, 18:28
The above explanations were better than mine but you can do it this way too :

3arms<x 3arms>x
intell 30% 10% 40%
not in 10% 50% 60%
40% 60%
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24 Oct 2012, 00:49
can someone plz. explain the solution of this question by the method of venn diagram....
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Re: 10% of all-aliens are capable of intelligent thought and [#permalink]

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24 Oct 2012, 01:48
Drawing a grid would help solve this question very quick

>3 3 or less Total

Intelligent 10 50 60

Dumb 30 10 40

Total 40 60 100
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24 Oct 2012, 01:51
sheikhaamir wrote:
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.

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Aliens-Venn.jpg [ 17.82 KiB | Viewed 2862 times ]

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

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23 Nov 2014, 09:03
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Re: 10% of all-aliens are capable of intelligent thought and [#permalink]

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06 Nov 2016, 02:45
Hello from the GMAT Club BumpBot!

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

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13 Jan 2017, 22:01
Can anyone explain it?...
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Re: 10% of all-aliens are capable of intelligent thought and [#permalink]

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14 Jan 2017, 01:43
rikson wrote:
Can anyone explain it?...

Please refer to the solutions above and be more specific when asking a question. Thank you.
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Re: 10% of all-aliens are capable of intelligent thought and [#permalink]

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17 Jan 2017, 22:32
Is it possible to do this math with any of following formulas ?

Formula 1: Total = Group 1 + Group 2 + Group 3 - ( Two of the three) - 2( All three)

Formula 2: Group 1 + Group 2 - Both + Neither
Re: 10% of all-aliens are capable of intelligent thought and   [#permalink] 17 Jan 2017, 22:32
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