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# M09 #20

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Director
Joined: 25 Oct 2008
Posts: 608
Location: Kolkata,India
Followers: 13

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06 Oct 2009, 21:21
Are all elements of set $$S$$ smaller than 20?

1. The smallest element of $$S$$ is 0.
2. The range of $$S$$ is 20.

OA:
[Reveal] Spoiler:
C

Stmt 1 is insuff.
Stmt. 2:
Highest-Lowest no. in the set equal 20.
Suppose the lowest no. is 2 then for the range to be 20 the highest no. will be 22..ANswer to the main question becomes NO.
Similarly if the lowest no is 3,4,5...ans is NO.
Now,let the lowest no. be 0.So range =20.Therefore,highest no. 20.Still..the answer to the question:Are all elements of set $$S$$ smaller than 20 is NO..
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Manager
Joined: 08 Nov 2005
Posts: 182
Followers: 2

Kudos [?]: 20 [0], given: 10

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06 Oct 2009, 23:07
It should be C.

Range = highest-lowest
Lets consider 2) first. Range is 20 but this could be that
30, 31,32,33,34,......50.
Range is 20 but all elements are not less than 20. Ans: No
if S= -3,-2,-1,0,1,2,....17
Range is 20 but all elements are less than 20. Ans: Yes
Yes and No means Insufficient.
But if you know that smallest is 0 and range is 20 that means
20-0=20 then all elements fall between 0 and 20.

Senior Manager
Joined: 18 Sep 2009
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07 Oct 2009, 10:06
Re: M09 #20   [#permalink] 07 Oct 2009, 10:06
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# M09 #20

Moderator: Bunuel

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