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Set S consists of five consecutive integers, and set T consi [#permalink]
19 Feb 2011, 09:43

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Difficulty:

85% (hard)

Question Stats:

46% (02:01) correct
55% (00:54) wrong based on 197 sessions

Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?

(1) The median of the numbers in Set S is 0 (2) The sum of the numbers in set S is equal to the sum of the numbers in set T

Re: Tough GMAT prep DS [#permalink]
19 Feb 2011, 10:44

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Expert's post

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Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?

Sets S and T are evenly spaced. In any evenly spaced set (aka arithmetic progression): (mean) = (median) = (the average of the first and the last terms) and (the sum of the elements) = (the mean) * (# of elements).

So the question asks whether (mean of S) = (mean of T)?

(1) The median of the numbers in Set S is 0 --> (mean of S) = 0, insufficient as we know nothing about the mean of T, which may or may not be zero.

(2) The sum of the numbers in set S is equal to the sum of the numbers in set T --> 5*(mean of S) = 7* (mean of T) --> answer to the question will be YES in case (mean of S) = (mean of T) = 0 and will be NO in all other cases (for example (mean of S) =7 and (mean of T) = 5). Not sufficient.

(1)+(2) As from (1) (mean of S) = 0 then from (2) (5*(mean of S) = 7* (mean of T)) --> (mean of T) = 0. Sufficient.

Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T? (1) The median of the numbers in Set S is 0. (2) The sum of the numbers in set S is equal to the sum of the numbers in set T.

For the above question, [C] seems logical since:

Statement 1: gives median of Set S = 0, Hence if S = {x,x+1,....x+4} median = x+2 => x+2 = 0, Hence the starting number is -2. [Not sufficient Alone] Statement 2: gives Sum of numbers in S = Sum of numbers in y i.e. Avg/Median of Set S * 5 = Avg/Median of Set T*7 => (2x+4)*5 = (2y+6)*7, where y is the starting element of Set T. => y+3 = 5*(x+2)/7, where y+3 is the median of Set T. From above, the only way the medians can be equal, is when both of the values are 0. For all other values of x and y, the medians are not equal. The choice presents a level of uncertainty, and therefore can't be sufficient.

Since x+2 = 0, from Statement 1, putting values, y+3 = 0. Hence, the median of both the sets are equal. Please verify!

Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T? (1) The median of the numbers in Set S is 0. (2) The sum of the numbers in set S is equal to the sum of the numbers in set T.

I'm happy to help with this. This is a really good question.

Statement #1 --- no info about T, obviously not sufficient by itself.

Statement #2 --- this is tricky ---- we could have two sets, say S = {5, 6, 7, 8, 9} and T = {2, 3, 4, 5, 6, 7, 8}, both of which have a sum of 35, and different medians, or we could have positives & negative centered around zero, with sums of zero and medians of zero. By itself, this statement is not sufficient.

Combined statements ---- very interesting now. If the median of S is 0, then S must be {-2, -1, 0, 1, 2}, which has a sum of zero. If the two sets have the same sum, then T must have a sum of zero, and the only way a set of an odd number of consecutive integers can have a sum of zero is if the list is centered on zero with the positives and negatives cancelling out. T must be {-3, -2, -1, 0, 1, 2, 3}, with a median of zero. The two lists have the same median. We are able to answer the prompt question, so the information is now sufficient.

ST1: Median of S = 0 No information about set T hence Insufficient.

ST2: Sum of elements in Set S = Sum of Numbers in Set T If Set s = {x-2, x-1, x, x+1, x+2} Sum = 5x If Set T = {y-3, y-2, y-1, y, y+1, y+2, y+3} Sum = 7y We are given that 5x = 7y hence CASE 1: x = y = 0 or CASE 2: X = 7, Y = 5

Case1: If S = {-2,-1,0,1,2} median = 0 and Set T = {-3,-2,-1,0,1,2,3} median = 0. the sum of elements in each set = 0 and median of S = median of T Case2: S = {5,6,7,8,9} median = 7 and Set T = {2,3,4,5,6,7,8} median = 5. the sum of elements in each set = 35 but median of S <> median of T Hence Insufficient

Together, Only Case 1 possible hence Sufficient Ans C

Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T? (1) The median of the numbers in Set S is 0. (2) The sum of the numbers in set S is equal to the sum of the numbers in set T.

Re: Set S consists of five consecutive integers, and set T consi [#permalink]
09 May 2013, 09:04

1

This post received KUDOS

Expert's post

mydreambschool wrote:

Set S consists of five consecutive integers, and set T consists of seven consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in set T?

(1) The median of the numbers in Set S is 0 (2) The sum of the numbers in set S is equal to the sum of the numbers in set T

Even though the answer to this question has been provided in detail, I would like to point out a takeaway here:

Sometimes, one statement helps you while 'analyzing the other statement alone'. It's good to forget the data of one statement while analyzing the other but don't forget the learning from the statement.

Let me explain:

S = {.........} T = {.............} Both S and T have consecutive integers. We want to know if they have the same median. If they have the same median, it means their middle number must be the same. Let's look at the statements:

(1) The median of the numbers in Set S is 0 Doesn't tell us anything about T so ignore it.

(2) The sum of the numbers in set S is equal to the sum of the numbers in set T

It's improbable that the medians will be same now, right? Can we say that certainly the median will not be the same and hence this statement alone is sufficient? To have the same median, their middle number must be the same. Say S = {2, 3, 4, 5, 6} and T = {1, 2, 3, 4, 5, 6, 7}. In this case, they will not have the same sum, right? Are we missing something? What about a case when the numbers are negative integers? Even if it doesn't occur to you by just looking at this statement, it must occur to you after reading the first statement. If 0 is the middle number, their sum could be the same while median is same. Hence you know that this statement by itself is not sufficient.

Using both statements, you can say that the sum of all members of S and sum of all members of T will be 0 and hence they DO have the same median.

Re: Set S consists of five consecutive integers, and set T consi [#permalink]
08 Sep 2013, 09:32

For those who wants to verify the insufficiency of statement 2: Infinite data sets are possible, following are few data sets for which sum of 5 consecutive numbers and 7 consecutive numbers is same. Previously I assumed that no such set is possible except a set uniform around zero. I selected B

Match found Sum -70=-70 5 consecutive no = -16,-15,-14,-13,-12 7 consecutive no = -13,-12,-11,-10,-9,-8,-7

Match found Sum -35=-35 5 consecutive no = -9,-8,-7,-6,-5 7 consecutive no = -8,-7,-6,-5,-4,-3,-2

Match found Sum 0=0 5 consecutive no = -2,-1,0,1,2 7 consecutive no = -3,-2,-1,0,1,2,3

Match found Sum 35=35 5 consecutive no = 5,6,7,8,9 7 consecutive no = 2,3,4,5,6,7,8

Match found Sum 70=70 5 consecutive no = 12,13,14,15,16 7 consecutive no = 7,8,9,10,11,12,13 _________________

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Re: Set S consists of five consecutive integers, and set T consi [#permalink]
24 Sep 2014, 06:22

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