10% of all-aliens are capable of intelligent thought and have more tha

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%

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

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

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%.

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

Fact #1: "10% of all aliens are capable of intelligent thought and have more than 3 arms." 
Fact #2: "75% of aliens with 3 arms or less are capable of intelligent thought."
The first statement gives a percentage of all aliens, while the second gives a percentage of just one group. 

Solution: 
To make things simple, let's say there are 100 total aliens. We'll split them into two groups: 
More than 3 arms: x, the number we're looking for 
3 or fewer arms: 100 - x 

Fact #1 told us that 10% of all 100 aliens, or 10 aliens, are intelligent and have 3+ arms. 
Fact #2 told us that 75% of the 100 - xaliens with 3 or fewer arms are intelligent. That's 0.75(100 - x) = 75 - 0.75x. 
If we add these two together, we should have the total number of intelligent aliens, which is 40% of the 100, or 40. So, we have the equation: 
10 + 75 - 0.75x = 40 
45 = 0.75x 
180 = 3x 
x = 60 

Thus, 60/100 = 60% of aliens have more than 3 arms

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I don't understand how you got 10 have arms <3? It says 75% of all aliens with less than three arms are intelligent, not more than 3 arms.

Thought No Thought Total
> 3 arms -------10 100 - x
< 3 arms----- 0.75* X-------------------X
Total --------40 -------------------100

10 + 0.75* = 40, or 0.75* = 30. Solve for x: x = 40.

I finally got it

If it is between men and women, and required to know number of men. We have 10% of all 100% are smart. Also we have 40% of all people are smart. So we have 10 men are smart and 30 women are smart. It is known also that 75% of women are smart; so 30 woman / 75% women = 40%. The rest of all is 60 which is the required.

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