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by jimmiejaz » Wed Dec 03, 2008 2:20 pm
Set S consists of distinct numbers such that the difference between any two different elements of set S is an integer. How many elements does set S contain?

1.)The difference between any two different elements of set S is 2
2.)The range of set S is 2

OA A
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by earth@work » Wed Dec 03, 2008 3:54 pm
this one has a tricky language.
"1.)The difference between any two different elements of set S is 2" this in other words means there can be only two elements in S and that is the answer we want... (i hope i m making no error here)
Eg. if we take S=(0,2,4) diff between 0&2=2, 2&4=2 but 0&4=4
So (1) is sufficient
But m also getting (2) suff. as it can have only 3 elements with difference as integer and range 2.... Eg S=(1,2,3) or S= (4.3,5.3,6.3)
my answer wud be D, but i guess it is wrong.
Last edited by earth@work on Wed Dec 03, 2008 8:42 pm, edited 1 time in total.
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by cramya » Wed Dec 03, 2008 5:09 pm
Excellent question!
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by raajan_p » Wed Dec 03, 2008 5:27 pm
it can have only 3 elements with difference as integer and range 2.... Eg S=(1,2,3) or S= (4.3,5.3,6.3)
How about these?

S = (0, 2) OR
S = (0, 0, 2)

you still have the range as 2 and the difference bet any two numbers in the set as an integer.
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by vittalgmat » Wed Dec 03, 2008 5:40 pm
raajan_p wrote:
it can have only 3 elements with difference as integer and range 2.... Eg S=(1,2,3) or S= (4.3,5.3,6.3)
How about these?

S = (0, 2) OR
S = (0, 0, 2) <--- This will violate the info in the question. "Set S consists of distinct numbers "

you still have the range as 2 and the difference bet any two numbers in the set as an integer.
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by raajan_p » Wed Dec 03, 2008 7:32 pm
vittalgmat wrote:
raajan_p wrote:
it can have only 3 elements with difference as integer and range 2.... Eg S=(1,2,3) or S= (4.3,5.3,6.3)
How about these?

S = (0, 2) OR
S = (0, 0, 2) <--- This will violate the info in the question. "Set S consists of distinct numbers "

you still have the range as 2 and the difference bet any two numbers in the set as an integer.
I agree, my bad...

but S = (1,2,3) and S = (0,2) are valid possibilities, right?
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by cramya » Wed Dec 03, 2008 7:34 pm
but S = (1,2,3)
This will violate The difference between any two different elements of set S is 2

Difference between 1 and 2 or 2 and 3 is 1 and not 2
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by logitech » Wed Dec 03, 2008 8:49 pm
Another CR question.

Differences between ANY..means there can be only two numbers ;-)

Choose A
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by jimmiejaz » Thu Dec 04, 2008 1:54 am
So, is it some kind of rule?
Everytime we see any in these type of questions, does it always mean all of them?
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by cramya » Thu Dec 04, 2008 6:11 am
Jimmie.
Good question! In this problem it means 2 since it says distinct integers which is possible with only 2 distinct integers

In other situations this may or may not be true

Lets say the set is {2,2,2,2} - Here the difference between any 2 elements is 0 and there are more than 2 (since we dint have a restriction of distinct integers)

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by raajan_p » Thu Dec 04, 2008 6:45 am
cramya wrote:
but S = (1,2,3)
This will violate The difference between any two different elements of set S is 2

Difference between 1 and 2 or 2 and 3 is 1 and not 2

LOL..Yeah, messed up..sorry abt that.
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by penumbra547 » Thu Dec 04, 2008 4:56 pm
cramya wrote:
but S = (1,2,3)
This will violate The difference between any two different elements of set S is 2

Difference between 1 and 2 or 2 and 3 is 1 and not 2
But I thought the difference between any two different elements of set S is 2 is the condition for rule #1. why is it being applied to rule #2? unless you are suggesting the answer is C?

Both S=(1,2,3) and S=(0,2) satisfies rule #2 and the stem, which is the difference of any element is an integer. Therefore, the number of elements of set S cannot be determined.

Therefore, and I could be wrong, A is the answer because rule #2 is insufficient.
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by niraj_a » Thu Dec 04, 2008 5:02 pm
so tricky
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