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

by arora007 » Sun Jul 04, 2010 7:46 am

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

[spoiler]OA is E , but how?? [/spoiler]

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Source: Beat The GMAT — Data Sufficiency | Sun Jul 04, 2010 7:46 am

kvcpk: Legendary Member; Posts: 1893; Joined: Sun May 30, 2010 11:48 pmFollowed by: 7 members; Thanked: 215 times

by kvcpk » Sun Jul 04, 2010 8:01 am

arora007 wrote: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

[spoiler]OA is E , but how?? [/spoiler]

Let S have a in the set and T have b
mean fo S is a and mean of T is b.
Mean of combined set is (a+b)/2

Now the question is is (a+b)/2 < a+b

This is true only if a an db are positive.. Take example:
let a=b=1, then, 1<2 this is true
let a=b=-1, then -1<-2 this is wrong.

Hence INSUFFICIENT

Statement B can be ruled out staright.. no mention of elements in it.

Combining:

Here comes the tricky part.. We are trapped to choose C as per our analysis above..
But what if a=b=0

Hence pick E

Hope this helps!!

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san2009: Master | Next Rank: 500 Posts; Posts: 171; Joined: Fri Apr 16, 2010 1:02 am; Thanked: 1 times

by san2009 » Mon Jul 05, 2010 2:41 am

i got E. here is how i thought about it

original question rephrased: mean of (set s, set t combined) < mean of set S + mean of set T?

statement 1:
if there is only one element in both sets, then we should look at following scenarios
I) both could have positive numbers, in which yes, the combined would have mean less than the sum of individual means
take numbers: s:[2] and t:[3]. sum of individual means = 5. mean of combined set is (2+3)/2 -- which will always be less than 5. this also makes intuitive sense
II) both could contain zero only - then the combined mean would be equal to the sum of individual means
take s:[0] and t:[0].
III) both could contain negative numbers, in which case the combined set would have mean that is greater than the sum of the individual means
take numbers: s:[-2] and t:[-3].
mean of combined set = (-2-3)/2=-2.5
sum of individual means = -2-3 = -5
note -2.5 > -5

Since we're getting yes and no for statement 1 --- it is insuff

statement 2: if both sets do not contain any negative numbers, they could still contain zeroes...as we've seen in the example for statement 1, if both sets contain only zero, then the means would be equal

statement 1 + statement 2:
rules out the possibility s and t can have negative elements. but they can still have "zero"
thus, insufficient

thus, my answer is E

let's discuss if you have concerns or better method

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