A prep DS

BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

This topic has expert replies

Post new topic Post Reply

Previous Topic Next Topic

yangliu0401: Senior | Next Rank: 100 Posts; Posts: 60; Joined: Tue Feb 10, 2009 11:36 am

A prep DS

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.

Quote

Source: Beat The GMAT — Data Sufficiency | Tue Mar 17, 2009 3:14 pm

GMAT/MBA Expert

Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 am; Location: Montreal; Thanked: 1090 times; Followed by:355 members; GMAT Score:780

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

ianstewartgmat.com

Quote

rs2010: Master | Next Rank: 500 Posts; Posts: 232; Joined: Fri Jul 04, 2008 4:14 pm; Thanked: 14 times; Followed by:1 members; GMAT Score:760

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.

Quote

cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pm; Thanked: 331 times; Followed by:11 members

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