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Question

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

earth@work · Answer

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.

cramya · Answer

Excellent question!

raajan_p · Answer

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.

vittalgmat · Answer

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.

raajan_p · Answer

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?

cramya · Answer

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

logitech · Answer

Another CR question. Differences between ANY..means there can be only two numbers Choose A

jimmiejaz · Answer

So, is it some kind of rule? Everytime we see any in these type of questions, does it always mean all of them?

cramya · Answer

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)

Regards,
CR

raajan_p · Answer

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.

penumbra547 · Answer

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.

niraj_a · Answer

so tricky

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