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m13#26

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m13#26 [#permalink] New post 26 Feb 2010, 08:51
Is the range of a combined set (S,T) bigger than the sum of ranges of sets S and T ?

1.The largest element of T is bigger than the largest element of S .
2.The smallest element of T is bigger than the largest element of S .

OA and OE:
[Reveal] Spoiler:
Statement (1) by itself is insufficient. Consider S=(0,1) , T=(1,2) (the answer is "no") and S=(0,1) , T=(2,3) (the answer is "yes").

Statement (2) by itself is sufficient. The range of the combined set equals the range(S) plus the range(T) plus the difference between the smallest element in T and the largest element in S . Thus, the range of the combined set will always be bigger than the sum of ranges of sets S and T .

The correct answer is B.


My question is: can set S and set T have only 1 element each [strike]and can these elements be equal[/strike](already answered below)?

Last edited by Igor010 on 26 Feb 2010, 09:37, edited 1 time in total.
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Re: m13#26 [#permalink] New post 01 Mar 2010, 16:39
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Lets take stmt 1:

1.The largest element of T is bigger than the largest element of S .
Say S = {2,3,4} T = {3,4,5,6}
R(S) = 2 , R(T) = 3 and R(S,T) = 4
is 4>2+3 No

Say S = {2,3,4} T = {5,6,7,8}
R(S) = 2 , R(T) = 3 and R(S,T) = 6
is 6>2+3 Yes

Yes and No answer hence proceed to stmt 2.

2.The smallest element of T is bigger than the largest element of S .
Say S = {2,3,4} T = {5,6,7,8}
R(S) = 2 , R(T) = 3 and R(S,T) = 6
is 6>2+3 Yes

Say S = {5,10} T = {11,20}
R(S) = 5 , R(T) = 9 and R(S,T) = 15
is 15>14 Yes

Hence Stmt 2 is suff.

B - Answer
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Re: m13#26 [#permalink] New post 26 Feb 2010, 09:28
can set S and set T have only 1 element each and can these elements be equal?
>> No. If this is the case then both the statements will become false.
As the statements explicitly say that one is bigger than other, means those are not equal even if the set has one element.
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Re: m13#26 [#permalink] New post 26 Feb 2010, 09:34
Yes, you are right! They should be different. But can these sets have only one different elment?
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Re: m13#26 [#permalink] New post 01 Mar 2010, 21:26
Nice explanation above.
Thank you sang.
Re: m13#26   [#permalink] 01 Mar 2010, 21:26
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