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01 Aug 2006, 07:53
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N
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A Business School has $88,000 for scholarships for students over the age of 45. It wants to award scholarships of $500, $2500, $12,500 and $62,500. What is the median size of the scholarships that it will award?
(1) At least one scholarship of each possible amount will be awarded.
(2) The mean amount of the scholarships awarded will be $11,000.
(1) At least one scholarship of each possible amount will be awarded.
(2) The mean amount of the scholarships awarded will be $11,000.
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01 Aug 2006, 08:41
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C
St1: Multiple possibilities.
Sum of all four = 78000
Remaining 10000 could be 4 of 2500 - Median = 2500
OR
20 of 500 - Median = 500: INSUFF
St2: Total of 8 scholarship awarded.
Could be (500,........7 of 12500) - Median = 12500
Could be (500, 5 of 2500.......,12500,62500)- Median = 2500: INSUFF
Combined:
Sum of all four = 78000
So remaining 10000 should be distributed to only 4 people.
Only possible set is (500,5 of 2500.......,12500, 62500) - Median = 2500: SUFF
St1: Multiple possibilities.
Sum of all four = 78000
Remaining 10000 could be 4 of 2500 - Median = 2500
OR
20 of 500 - Median = 500: INSUFF
St2: Total of 8 scholarship awarded.
Could be (500,........7 of 12500) - Median = 12500
Could be (500, 5 of 2500.......,12500,62500)- Median = 2500: INSUFF
Combined:
Sum of all four = 78000
So remaining 10000 should be distributed to only 4 people.
Only possible set is (500,5 of 2500.......,12500, 62500) - Median = 2500: SUFF
01 Aug 2006, 08:42
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kevincan
(1) If there's one scholarship for each amount, the sum = $78,000 --> still $10,000 left --> this can be for 20 of $500 scholarship or 4 of $2500 scholarship --> There're at least two ways of distribution ---> the medians of the two ways are different. --> insuff
(2) Firstly we observe that the amount has the form: 500, 500*5, 500*25,500*125
from this statement ---> there're 8 scholarships in all.
we have: 88,000= 500*176
176= 125+ 25+5+5+5+5+5+1 --> there're 1 of 64,500 , 1 of 12,500 , 5 of 2500 and 1 of 500 ---> one way of distribution
176= 25+25+25+25+25+25 +25 +1 --> there're 7 of 12,500 and 1 of 500 --> another way of distribution
---> they very probably have different median
--->insuff
(1) and (2) --> the only way of distribution is one for 500, 12500, 62500 and 5 for 2,500 ---> the median can be determined ---> suff
Uhm, C ....but i think there's much shorter way
