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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

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

A.

1. If the difference between any two different elements of set S is 2, then there are two elements in the set S. If gthere are more than 2 elements, the the diff. betweeen any two diffeent elements would not be 2. so suff.

2. If the range of set S is 2, there could be 2 or 3 elements in the set S. For ex: If the elements are 1.5 and 3.5, the range is 2 and it has 2 elements. If the elements are 1, 2 and 3, the range is 2 and there are 3 elements. so nsf..
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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

If set \(S\) contains more than 1 element, how many elements does set \(S\) contain?

(1) The difference between any two elements of set \(S\) is 2 --> since the difference between ANY two elements is 2 then there cannot be more than 2 elements in the set, else we could select some particular two elements whose difference wouldn't be 2. Sufficient.

(2) The range of set \(S\) is 2. Clearly insufficient, consider: S={0, 2} and S={0, 0, 2}.

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

From stmt1, the elements could be 1.1, 3.1, 5.1, 7.1, 9.1,......and so on.

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

In your example, 9.1-1.1=8 (not 2). So, it doesn't work.

scthakur wrote:

From stmt2: the elements could be 0.1, 1.1, 2.1 or any such other combination. Hence, the number of elements will always be three.

set {0,2} also satisfies second condition but the number of elements is 2.

Thanks walker! I completely missed it. I agree with A.

My big problem is not completely reading the question and understanding what it is actually asking for.

I read gmat-experience-tips-760-51q-44v-6-0-awa-89590.html and now I read the question 2 times before ever looking at any of the answers. Early on I would seem to answer the wrong question a lot. Just reading the question twice and then rereading it again after I have my answer has helped me catch a lot of gotchas in my practice questions. Hope that helps.

1 => for difference between any two elements to be 2 there must be only 2 elements in the set. Hence this is sufficient. 2 => Range can be the same for a sets with different number of elements Therefore 1 is sufficient.
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If set a is {4,2} then the difference between the 2nd number and the first number is not 2 but -2. Hence its insufficient. Can someone please enlighten.

Should the question statement not say mod of the difference between any two different elements of set is 2 ?
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Quant 47-Striving for 50 Verbal 34-Striving for 40

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

It seems that i can't get any set where the difference between any two numbers is equal to 2. Statement 1 cannot be sufficient by itself.

Can someone please give me an example of a set containing TWO numbers where their difference is always equal to 2.

Thanks

Consider set \(S={0,2}\) The difference between the elements is 2.

The question says that S contains distinct integers, and A says that the difference between any two elements is 2. now consider set M for example \({0,2,4}\) This respect the question (distinct integers) but goes against A (the difference between 0 and 4 is 4, not 2)

With A we can enstablish that the set has only two elements. Is it clear? let me know
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It seems that i can't get any set where the difference between any two numbers is equal to 2. Statement 1 cannot be sufficient by itself.

Can someone please give me an example of a set containing TWO numbers where their difference is always equal to 2.

Thanks

Consider set \(S={0,2}\) The difference between the elements is 2.

The question says that S contains distinct integers, and A says that the difference between any two elements is 2. now consider set M for example \({0,2,4}\) This respect the question (distinct integers) but goes against A (the difference between 0 and 4 is 4, not 2)

With A we can enstablish that the set has only two elements. Is it clear? let me know

Hey Zarrolou

If you consider the set \(S={0,2}\) , the difference between ANY two elements you will get will not equal to 2.

For instance, 2 - 0 = 0 BUT 0-2 = -2 SO the difference between 0 and -2 is not equal to 2.

I think the stem would have been much clearer if it stated the positive difference instead

don't you think ?
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1) Different between any 2 element is 2: we need at least 2 elements, for instance a and b (a<b). Now suppose we have a third one (c): if c<a -> b-c>2 if c>a -> b-c<2 if c=a -> c-a = 0 All three scenarios above does not satisfy stat 1) -> only 2 elements -> sufficient 2) Range of set is 2: we can have {1,3} and {1,2,3} that both satisfy the requirement -> insufficient