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A prep DS

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by yangliu0401 » Tue Mar 17, 2009 3:14 pm
Set S consists five consecutive intengers, and set T consists 7 consecutive intengers. Is the median of the number in the set S equal to the median of the number in the set T?

1). The median of the number 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.

OA is C. While I think B. The stem.2 alone can satisfy the question.
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Source: — Data Sufficiency |

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by Ian Stewart » Tue Mar 17, 2009 4:10 pm
Using statement 2, the median of each set certainly could be zero. We only need to know if it must be zero.

In sets of consecutive integers, as in any 'evenly spaced' set, the average is always equal to the median. Since:

avg = sum/n

we have

sum = n*avg

Now, if a is the median (and thus the average) of our set of 5 consecutive integers, and b is the median (and thus the average) of our set of 7 consecutive integers, we know the sum of the first set is 5a and the sum of our second set is 7b. So we just want to know whether it's possible to find numbers a and b so that

5a = 7b

and certainly we could use a = 7, and b = 5, among many other possibilities. That is, the following two sets will have the same sum:

5, 6, 7, 8, 9

2, 3, 4, 5, 6, 7, 8

but have different medians, and Statement 2 is not sufficient alone.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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Re: A prep DS

by rs2010 » Tue Mar 17, 2009 4:12 pm
yangliu0401 wrote:Set S consists five consecutive intengers, and set T consists 7 consecutive intengers. Is the median of the number in the set S equal to the median of the number in the set T?

1). The median of the number 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.

OA is C. While I think B. The stem.2 alone can satisfy the question.
Try the following sets
S={5,6,7,8,9} T={2,3,4,5,6,7,8} median is different
S={-2,-1,0,1,2} T={-3,-2,-1,0,1,2,3} Median is same

There fore, we need C.

Since A does not tell anything about set T and B is not sufficient alone.
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by cramya » Tue Mar 17, 2009 4:21 pm
Stmt II


x x+1 x+2 x+3 x+4 x+5 -> S

a a+1 a+2 a+3 a+4 a+5 a+6 -> T

5x+10 = 7a+21

5x-7a = 11

Look when this can happen

5(12) - 7(7) = 11

12 13 14 15 16

7 8 9 10 11 12 13

Sum is the same but the median is not NO answer

-2 - 1 0 1 2

-3 -2 -1 0 1 2 3

YES answer

Hence stmt II is INSUFF

Together:

If the sum is 0 and there are odd number of consectuive terms in each set an their sume same then there has to be as many positives as negatives making 0 median

Choose C
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by yangliu0401 » Tue Mar 17, 2009 4:47 pm
Million thx to u all~~~
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