ds/mean

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advita: Senior | Next Rank: 100 Posts; Posts: 62; Joined: Mon Sep 13, 2010 8:06 pm; Thanked: 2 times

ds/mean

by advita » Wed Jan 19, 2011 9:04 pm

If sets S and T are united into a single set, will the mean of this set be smaller than the sum of means of sets S and T ?

1.S and T are one-element sets
2.Neither set S nor set T contains negative numbers

my query: what is mean of single element.

...i think it is the element itself. i.e for t={5} mean is 5.

just for confirmation. is it true.???

OA-..E

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Source: Beat The GMAT — Data Sufficiency | Wed Jan 19, 2011 9:04 pm

arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 am; Location: India; Thanked: 51 times; Followed by:27 members; GMAT Score:670

by arora007 » Wed Jan 19, 2011 9:45 pm

You are right...single element set would have the from t={5}

and with this this, I part ways with the OA.

the OA should be A, clearly.

t={5} now individual mean is 5
v={7} now individual mean is 7

their average is (5+7)/2 = 6

now t U v = {5,7} now the mean of this set is (5+7)/2 = 6.

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gmat1011: Master | Next Rank: 500 Posts; Posts: 160; Joined: Mon Apr 05, 2010 4:41 am; Thanked: 7 times

by gmat1011 » Wed Jan 19, 2011 9:46 pm

that is what "one element sets" should mean... the number is its own mean.

Here we can rules out B coz if set s and set t have only zeros... then stem 2 is disproved... you get Y if sets S and T have only +ve numbers and a N if sets S and T are made up of only zeros.

As regards A it gets disproved if you consider s and t to be both +ve and then both -ve... you get opposite results.

Together: again with only +ve one element sets you get a y and with only 0 in both sets you gets a N. so E.

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arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 am; Location: India; Thanked: 51 times; Followed by:27 members; GMAT Score:670

by arora007 » Wed Jan 19, 2011 10:01 pm

gmat1011 wrote: As regards A it gets disproved if you consider s and t to be both +ve and then both -ve... you get opposite results.

did not get that... how?? maybe an example...

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gmat1011: Master | Next Rank: 500 Posts; Posts: 160; Joined: Mon Apr 05, 2010 4:41 am; Thanked: 7 times

by gmat1011 » Wed Jan 19, 2011 10:14 pm

Hi, For considering stem 1:

+VE one set elements only

S= 5
T = 6

Sum of individual means = 11
Mean of combined set = 11/2 = 5.5

So sum of means > mean of combined

-VE one set elements only

S= -5
T= -6

Sum of individual means = -11
Mean of combined set = -11/2 = -5.5

So mean of combined > sum of means

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jaxis: Master | Next Rank: 500 Posts; Posts: 101; Joined: Sun Sep 26, 2010 9:33 am; Thanked: 5 times

by jaxis » Wed Jan 19, 2011 10:32 pm

arora007 wrote:
gmat1011 wrote: As regards A it gets disproved if you consider s and t to be both +ve and then both -ve... you get opposite results.
did not get that... how?? maybe an example...

Arora,

How abt this example...S = {0} , T = {0}

here, mean of individual set = mean of combined set.

This example can help u in Statement 2 also.

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arora007: Community Manager; Posts: 1048; Joined: Mon Aug 17, 2009 3:26 am; Location: India; Thanked: 51 times; Followed by:27 members; GMAT Score:670