Aman verma wrote:Q:10% of all aliens cuckoos are capable of intelligent thought and have more than 3 arms, and 75% of aliens cuckoos with three arms or less are capable of intelligent thought.If 40% of all alien cuckoos are capable of intelligent thought , what percent of alien cuckoos have more than 3 arms ?
Source: Manhattan (MGMAT); not from some cuckoo-prep or some cuckoo instructor.
This is an EITHER/OR group question.
Every alien is EITHER intelligent OR not.
Every alien EITHER has more then 3 arms Christmas OR 3 arms or less.
For an EITHER/OR group problem, use a GROUP GRID to organize the data.
Let I = intelligent, NI = not intelligent, >3 = more than 3 arms, ≤3 = 3 arms or less.
Here's the grid, with 100 plugged in for the total:
Now let's use the information in the problem to complete the grid step by step.
As soon as we know 2 entries in a row or a column, we can calculate the remaining entry in that row or column.
40% of all alien cuckoos are capable of intelligent thought.
10% of all alien cuckoos BOTH are capable of intelligent thought AND have more than 3 arms.
The following grid is yielded:
75% of alien cuckoos with three arms or less are capable of intelligent thought.
According to the grid, 30 aliens with 3 arms or less are also intelligent.
These 30 aliens constitute 75% of the total number of aliens with 3 arms or less.
Since 30 is 75% of 40, the total number of aliens with 3 arms or less = 40.
The following grid is yielded:
Now we can answer the question:
Percentage with more than 3 arms = [spoiler]60%[/spoiler].
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