Problem Solving

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)

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].

OA[spoiler]60%[/spoiler].

Many thank to Mitch, my favourite instructor besides Brent! I still remember Mitch when he started solving my problems 2 years back and he has always been there to address my questions. I regard them both as my GURU as we regard them in true Indian tradition, me being a 'SHISYA'(pupil/student). But there are others out there who are highly agile minded and won't regard me worthy of their tutelage. For them I will soon release a mental agility-test problem to enjoy.

Cheers!