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# Is the range of a combined set (S, T) bigger than the sum of

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Is the range of a combined set (S, T) bigger than the sum of  [#permalink]

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24 Feb 2009, 16:47
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Is the range of a combined set (S, T) bigger than the sum of ranges of sets S and T ?

The largest element of T is bigger than the largest element of S
The smallest element of T is bigger than the largest element of S

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Intern
Joined: 26 Dec 2008
Posts: 46
Schools: Booth (Admit R1), Sloan (Ding R1), Tuck (R1)

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24 Feb 2009, 17:43
1
Is the range of a combined set (S, T) bigger than the sum of ranges of sets S and T ?

The largest element of T is bigger than the largest element of S
The smallest element of T is bigger than the largest element of S

IMHO B, please see attached file for method
Attachments

range overlap illustration.ppt [55 KiB]

Manager
Joined: 08 Jan 2009
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24 Feb 2009, 18:04
Given
Let the Ranges of two sets be RS and RT and the combined range be RST.

Is RST > RS+RT?

stmt1:
HT > HS.
S = 10 ........20 RS = 10
T = 15.........25 RT = 10
RST = 15 here RST < RS + RT
let S remain the same and R = 21 ......25 then RST > RS+RT. Insufficient.

Stmt2:
LT > HS then definetly HT > HS then definetly RST > RS + RT.
Sufficient.

Ans:B
Director
Joined: 04 Jan 2008
Posts: 645

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25 Feb 2009, 22:58
Its B
I did it this way
say, S={s1,.........,20} ; T={21,............,t2}
where {S,T} ={s1,...........t2}
now we have to prove t2-s1>(20-s1)+(t2-21)
which is TRUE-hence B alone is SUFFICIENT

OA is B.

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Re: Is the range of a combined set (S, T) bigger than the sum of  [#permalink]

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20 Oct 2018, 22:00
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Re: Is the range of a combined set (S, T) bigger than the sum of   [#permalink] 20 Oct 2018, 22:00
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