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12 Jul 2008, 07:40
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Lists S and T consist of the same numer of positive integers. Is the median of integers in S greater than the average (arithmetic mean) of integers in T?
(1) The integers in S are consecutive even integers, and the integers in T are consecutive odd integers.
(2) the sum of the integers in S are greater than the sum of integers in T.
Please please pleeeaaase don't forget your detailed explanations. M :wink: erci
(1) The integers in S are consecutive even integers, and the integers in T are consecutive odd integers.
(2) the sum of the integers in S are greater than the sum of integers in T.
Please please pleeeaaase don't forget your detailed explanations. M :wink: erci
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12 Jul 2008, 08:15
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IMO C.
Statement 1:
S = {2,4,6}, T = {3,5,7} False
S = {4,6,8}, T = {3,5,7} True
Maybe case so question cannot be answered.
Statement 2:
S = {4,6,8}, T = {3,5,7} True
S = {2,3,10}, T = {3,4,5} False
Maybe case so question cannot be answered.
After combining
S = {4,6,8}, T = {3,5,7} True or similar cases.
Statement 1:
S = {2,4,6}, T = {3,5,7} False
S = {4,6,8}, T = {3,5,7} True
Maybe case so question cannot be answered.
Statement 2:
S = {4,6,8}, T = {3,5,7} True
S = {2,3,10}, T = {3,4,5} False
Maybe case so question cannot be answered.
After combining
S = {4,6,8}, T = {3,5,7} True or similar cases.
14 Jul 2008, 07:53
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First, take note of the type of numbers included in the set. You always want to do this. Write it down on paper (later you can do this in your head, but if it gives you real trouble,
Make sure you understand what the question is asking:
Is the median in S greater than the mean of the integers in T.
They're asking us to compare the middle number in S to the average of T...what will we need to know? For S, we need to know how many numbers there are. If there are 9 numbers, then the median is the 5th number. So we need to know what that 5th number is. The others don't matter as long as we know the 5th number (when listed in order).
As for the average....we need to know the total, or be able to sum the numbers in T to get a total and we need to know how many numbers there are. If you know they all add up to 90, but you don't know if there are 2 numbers of 45 numbers, that changes the average significantly.
And note that each set contains the SAME NUMBER of positive integers. meaning if there are 10 in S, there are 10 in T, if S contains 9 integers, T contains 9 as well.
Now to the statements:
(1) Completely insufficient. It tells you the types of numbers (one is even and the other odd) but it doesn't tell you anything regarding the information we just discussed as necessary to answer mean & median questions. INSUFFICIENT
(2) Again Insufficient. We're getting closer, we know the relationship of the sums, but this doesn't tell us anything about the average or media. We need to know how many numbers are in T to get its average and (2) doesn't say that at all.
(Together) If we know S has consecutive even integers and T has consecutive Odd integers, and the SUM of the integers in S is greater than the sum of integers in T, lets figure out what we really know. I sometimes will pick numbers.
S { 2, 4, 6, 8, 10} - median is 6 - there are 5 numbers so the 3rd is in the middle.
T { 1, 3, 5, 7, 9} - mean is \(\frac{1+3+5+7+9}{5}= 5\)
Now something else that may trip you up regarding this particular DS question is the question it asks. It asks "is the median of S greater than the average of T?" The key here is not yes or no. The key is "Can we answer with certainty that the answer is ALWAYS yes or ALWAYS no.?"
So the answer we came up with by using 5 numbers answers the question Yes, the median of S is greater than the mean of T, but is this always the case?
So the answer, in my opinion should be C.
HTH
Make sure you understand what the question is asking:
Is the median in S greater than the mean of the integers in T.
They're asking us to compare the middle number in S to the average of T...what will we need to know? For S, we need to know how many numbers there are. If there are 9 numbers, then the median is the 5th number. So we need to know what that 5th number is. The others don't matter as long as we know the 5th number (when listed in order).
As for the average....we need to know the total, or be able to sum the numbers in T to get a total and we need to know how many numbers there are. If you know they all add up to 90, but you don't know if there are 2 numbers of 45 numbers, that changes the average significantly.
And note that each set contains the SAME NUMBER of positive integers. meaning if there are 10 in S, there are 10 in T, if S contains 9 integers, T contains 9 as well.
Now to the statements:
(1) Completely insufficient. It tells you the types of numbers (one is even and the other odd) but it doesn't tell you anything regarding the information we just discussed as necessary to answer mean & median questions. INSUFFICIENT
(2) Again Insufficient. We're getting closer, we know the relationship of the sums, but this doesn't tell us anything about the average or media. We need to know how many numbers are in T to get its average and (2) doesn't say that at all.
(Together) If we know S has consecutive even integers and T has consecutive Odd integers, and the SUM of the integers in S is greater than the sum of integers in T, lets figure out what we really know. I sometimes will pick numbers.
S { 2, 4, 6, 8, 10} - median is 6 - there are 5 numbers so the 3rd is in the middle.
T { 1, 3, 5, 7, 9} - mean is \(\frac{1+3+5+7+9}{5}= 5\)
Now something else that may trip you up regarding this particular DS question is the question it asks. It asks "is the median of S greater than the average of T?" The key here is not yes or no. The key is "Can we answer with certainty that the answer is ALWAYS yes or ALWAYS no.?"
So the answer we came up with by using 5 numbers answers the question Yes, the median of S is greater than the mean of T, but is this always the case?
So the answer, in my opinion should be C.
HTH
erci
