sana.noor wrote:Of all the players in a professonal baseball league, 1/2 are foreign-born,inclding 1/3 of the pitchers. If 3/4 of the players are pitchers, what percentage of the players who are not pitchers are foreign-born?
A) 100%
B) 75%
C) 66 2/3%
D) 50%
E) 25%
OA is A
This is an EITHER/OR problem.
Every player is EITHER a pitcher OR a non-pitcher.
Every player is EITHER foreign-born OR not.
Use a GROUP GRID (also known as a matrix) to organize the data:
_______________P__________NP___________Total
F:
NF:
Total:
In the group grid, every row has to add up to the total, as does every column.
Looking at the top row, foreign-born pitchers + foreign-born non-pitchers = total foreign born.
Looking at the left-most column, foreign-born pitchers + non-foreign-born pitchers = total pitchers.
Now let's fill in the data step by step. Whenever we have 2 entries in a row or column, we can determine the remaining entry, since everything has to add up horizontally and vertically. For the total number of players, let's plug in 12 (the LCM of 2, 3 and 4, the denominators in the problem):
_______________P__________NP____________Total
F:
NF:
Total:_____________________________________12
1/2 are foreign-born, 3/4 are pitchers:
________________P__________NP____________Total
F:__________________________________________6
NF:_________________________________________6
Total:____________9__________3______________12
1/3 of the 9 pitchers are foreign-born:
_________________P__________NP___________Total
F:_______________3___________3______________6
NF:______________6___________0______________6
Total:____________9___________3_____________12
Notice that everything adds up horizontally and vertically.
Foreign-born NP/Total NP = 3/3 = 100%.
The correct answer is
A.
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