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# M14 #18

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M14 #18 [#permalink]

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02 Feb 2009, 20:55
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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

[Reveal] Spoiler: OA
A

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REVISED VERSION OF THIS QUESTION IS HERE: m14-75340.html#p1336423
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Re: GMATCLUB M14#18 [#permalink]

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02 Feb 2009, 21:11
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topmbaseeker wrote:
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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Re: GMATCLUB M14#18 [#permalink]

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03 Feb 2009, 00:41
It should be B.

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

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.
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Re: GMATCLUB M14#18 [#permalink]

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03 Feb 2009, 00:47
scthakur wrote:
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.
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Re: GMATCLUB M14#18 [#permalink]

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03 Feb 2009, 00:50
walker wrote:
scthakur wrote:
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.
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Re: M14 #18 [#permalink]

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01 Mar 2010, 05:12
topmbaseeker wrote:
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

[Reveal] Spoiler: OA
A

Source: GMAT Club Tests - hardest GMAT questions

Its A as from statement 1 it can said that there are two elements and their difference is 2.
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Re: GMATCLUB M14#18 [#permalink]

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01 Mar 2010, 07:04
scthakur wrote:
walker wrote:
scthakur wrote:
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.
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Re: M14 #18 [#permalink]

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01 Mar 2010, 12:11
Could someone please explain how they obtained A?

How does that entail how many distinct integers in a set?

Thanks
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Re: M14 #18 [#permalink]

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03 Mar 2010, 06:05
any set can have only 2 elements if the difference between any two of the elements are same

ex: s1 ={4,2} difference bewteen them is 2
s1= {4,2,4} then if we choose 4,4 then diff will be 0

so ans is A
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Re: M14 #18 [#permalink]

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13 Mar 2010, 09:24
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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Re: M14 #18 [#permalink]

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05 Mar 2011, 00:23
Answer is A because range will not tell how many different elements are there in domain.
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Re: M14 #18 [#permalink]

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30 Mar 2011, 22:29
1. The difference between any two different elements of set S is 2

If a-b=2 then b-a=-2, so S is an empty set.
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Re: M14 #18 [#permalink]

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24 Jun 2011, 23:12
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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Re: M14 #18 [#permalink]

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07 Mar 2012, 06:50
I had seen a very similar question before. This allowed me to get to answer A relatively quickly. Good question!
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Re: M14 #18 [#permalink]

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26 Apr 2012, 03:44
topmbaseeker wrote:
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

[Reveal] Spoiler: OA
A

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1: how to get any two diffferent elements is 2... we cant get 2 as difference between any two different elements if we have more than 2 elements...

take any example , u cant come with a 3 element set where there difference between any two element is 2.. can we? i am doubtful on it...

so 1 is SUFFICIENT

2: range is 2, does not mean only 2 elements.. this is known by all... hence Not sufficient

hence A is my answer.. can somebody tell me if this is fine?
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Re: M14 #18 [#permalink]

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15 May 2013, 12:38
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
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Re: M14 #18 [#permalink]

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15 May 2013, 13:09
Rock750 wrote:
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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Re: M14 #18 [#permalink]

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15 May 2013, 16:00
Zarrolou wrote:
Rock750 wrote:
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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Re: M14 #18 [#permalink]

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25 Feb 2014, 06:07
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topmbaseeker wrote:
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

[Reveal] Spoiler: OA
A

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m14 q18

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}.

Answer: A.
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Re: M14 #18 [#permalink]

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27 Apr 2014, 00:30
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

Choose A
Re: M14 #18   [#permalink] 27 Apr 2014, 00:30
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