Non-Empty Set

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

mmslf75: Legendary Member; Posts: 503; Joined: Sun Aug 09, 2009 9:53 pm; Thanked: 31 times; Followed by:2 members

Non-Empty Set

by mmslf75 » Wed Dec 16, 2009 7:16 am

Is the range of a non-empty set bigger than its mean?

1)All members of are negative
2)The median of set is negative

OA D

What does NON-EMPTY set mean ??

By the way is this question actually a sort of theorem /definition ??

Quote

Source: Beat The GMAT — Data Sufficiency | Wed Dec 16, 2009 7:16 am

Lattefah84: Senior | Next Rank: 100 Posts; Posts: 93; Joined: Mon Dec 14, 2009 4:15 am

by Lattefah84 » Wed Dec 16, 2009 7:23 am

mmslf75 wrote:Is the range of a non-empty set bigger than its mean?

1)All members of are negative
2)The median of set is negative

OA D

What does NON-EMPTY set mean ??

By the way is this question actually a sort of theorem /definition ??

that it's not empty ?

(sorry)

I don't know actually, it sounds weird...

Quote

satish.nagdev: Master | Next Rank: 500 Posts; Posts: 130; Joined: Sat Dec 29, 2007 5:35 am; Location: SGP; Thanked: 5 times

by satish.nagdev » Wed Dec 16, 2009 8:34 am

Lattefah84 wrote:
mmslf75 wrote:Is the range of a non-empty set bigger than its mean?

1)All members of are negative
2)The median of set is negative

OA D

What does NON-EMPTY set mean ??

By the way is this question actually a sort of theorem /definition ??
that it's not empty ?

(sorry)

I don't know actually, it sounds weird...

question is not weird, you've answered correctly in a way that it's not empty.
set theory basics - non empty set S contains elements e.g. S={1,2,4,100...}

here in question
stmt 1 > take a set of random negative numbers say S={-1,-2,-3,-4-5} for simplicity

Range = max term - min term = -5 -(-1) = -4
mean = sum of terms / number of terms = -15/5 = -3

I tried few combinations Range was lower than mean (i.e. you can answer question as no)

stmt 2 - for median, sort the set elements in ascending order of value, if number of terms = odd then middle term is median, if number of terms is even then median = avg. of middle 2 terms

and median is negative if terms of set are negative, hence it will be repeat of stmt1 hence you can answer question using individual stmts.

Wounded by GMAT but not dead

Quote

mehravikas: Legendary Member; Posts: 1161; Joined: Mon May 12, 2008 2:52 am; Location: Sydney; Thanked: 23 times; Followed by:1 members

by mehravikas » Wed Dec 16, 2009 8:33 pm

You have calculated it correctly but I think you have made a mistake the max term in the set below will be -1 not -5, -5 should be the lowest term and the range will be greater than the mean.

Same for statement 2.

satish.nagdev wrote: here in question
stmt 1 > take a set of random negative numbers say S={-1,-2,-3,-4-5} for simplicity

Range = max term - min term = -5 -(-1) = -4
mean = sum of terms / number of terms = -15/5 = -3

I tried few combinations Range was lower than mean (i.e. you can answer question as no)