The local baseball team employs at least 3 times as many pitchers as catchers, b
ID: 3117630 • Letter: T
Question
The local baseball team employs at least 3 times as many pitchers as catchers, but never more than 11 players total. Pitches make an average of $45,000, and catchers make an average of $30,000. Which of the following amounts are the possible averages for all the pitchers and catchers, rounded to the nearest dollar?
A.)30,000 B.)35,899 C.)40,375 D.)41,250 E.)41,956 F.)42,273 G.)43,743 H.)45,000
The answer in the gre prep book says only D is correct but I thought D, E, and F were all correct because the the question says "least." What do you think?
Explanation / Answer
You are right that since the question mention "least" there can be multiple answers. But we will have to actually check whether there is any combination which would actually produce the average as option E, F and G.
One catch here is, since average of 3 pitchers and 1 catcher is 41,250
the average in all other cases has to be more than this because in other cases no. of catchers will be more so average will be more towards 45,000
Following combinations are possible
Notice here
A.)30,000 - not possible
B.)35,899 - not possible
C.)40,375 - not possible
D.)41,250 - possible
E.)41,956 - not possible
F.)42,273 - possible
G.)43,743 - not possible
H.)45,000 - not possible
so only option D and F are correct
pitchers catchers pitcher make catchers make total average =pitcher*45000 =catcher*30000 10 1 450000 30000 480000 43636 9 1 405000 30000 435000 43500 8 1 360000 30000 390000 43333 7 1 315000 30000 345000 43125 6 1 270000 30000 300000 42857 5 1 225000 30000 255000 42500 4 1 180000 30000 210000 42000 3 1 135000 30000 165000 41250 9 2 405000 60000 465000 42273 8 2 360000 60000 420000 42000 7 2 315000 60000 375000 41667 6 2 270000 60000 330000 41250Related Questions
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