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Set S consists of 5 consecutive integers, and set T consists [#permalink]
04 Nov 2006, 03:25

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Difficulty:

85% (hard)

Question Stats:

36% (02:11) correct
64% (01:14) wrong based on 114 sessions

Set S consists of 5 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 5 consecutive integers, and set T consists [#permalink]
28 May 2013, 11:40

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

Here is how I see it...

1) S could be (-2, -1, 0, 1, 2)....but set T could be anything. INSUFFICIENT

2) Set S could be (5, 6, 7, 8, 9) with sum of 35 and median of 7
but....
Set T could be (2, 3, 4, 5, 6, 7, 8) with sum of 35 and median of 5 INSUFFICIENT

Combine: S must be (-2, -1, 0, 1, 2) with a sum of 0 and a median of 0
T must then have sum of 0, so T is (-3, -2, -1, 0, 1, 2, 3) sum 0 and median 0. SUFFICIENT

Set S consists of 5 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 O
2) The sum of the numbers in set S is equal to the sum of the numbers in set T

set s( s-2,s-1,s,s+1,s+2) set t (b-3,b-2,b-1,b,b+1,b+2,b+3)

from one

insuff if s = 0 b could be anything

from two

5s = 7b , if s = 7 then t = 5 or s, b = zero....insuff

Set S consists of 5 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 O 2) The sum of the numbers in set S is equal to the sum of the numbers in set T

Here is how I see it...

1) S could be (-2, -1, 0, 1, 2)....but set T could be anything. INSUFFICIENT

2) Set S could be (5, 6, 7, 8, 9) with sum of 35 and median of 7 but.... Set T could be (2, 3, 4, 5, 6, 7, 8) with sum of 35 and median of 5 INSUFFICIENT

Combine: S must be (-2, -1, 0, 1, 2) with a sum of 0 and a median of 0 T must then have sum of 0, so T is (-3, -2, -1, 0, 1, 2, 3) sum 0 and median 0. SUFFICIENT

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