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# If S is a set of integers and 5 is in S, is every multiple

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If S is a set of integers and 5 is in S, is every multiple [#permalink]

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17 Jan 2004, 23:04
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If S is a set of integers and 5 is in S, is every multiple of 5 in S?

1) if x is in S, then x+5 is in S
2) if x is in S, then x-5 is in S

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18 Jan 2004, 00:37
C?

1: if 5 is in S, so is 10, so is 15 and so on...20,25 because x+5
not suff because it only goes up the positive line

2: if 5 is in S, so is 0, -5, -10 and so on because x-5
not suff because it only goes down the negative line

put then to together.

5,10,15...and 5, 0, -5, -10, -15...

and you get all multiples of 5

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19 Jan 2004, 19:40

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19 Jan 2004, 19:44
i apologize, but in my previous posting i posted the answer was E,
the actual anser is C....anyone know why?

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19 Jan 2004, 19:49
I dont think C is correct , let set={5,6,10,15,19,23,25,10000000001} and let x=10 then (x+5) 15 is in Set and (x-5) 5 is in set but the set doesnt contain all the multiples of 5.

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19 Jan 2004, 20:10
What is the source of this question? It's very unclear...

If S is a set of integers and 5 is in S, is every multiple of 5 in S?

1) if x is in S, then x+5 is in S
2) if x is in S, then x-5 is in S

This question could be interpreted in a number of ways....

First, I picked E. 1) Cause let's say that x is 5, then 5 and 10 will be in the set. Not sufficient. 2) Let's say that x is 5, then 5, and 0 will be in the set. Not sufficient. 3) Again, let's use 5.. then 5, 10, 0 will be in the set. Not sufficient. Also, you can use other numbers that are not mutliples of 5.

To accurately get the answer C, then the question needs to be reworded to something like this... For every member of set S (called x), then x+5 is in S. Or something to that "ETS verbage" stuff. The question as it is, implies that x is only one member of the set, and you use the +5 or -5 rule to only one member, not all the members.

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Senior Manager
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19 Jan 2004, 20:33
gmatanh wrote:
What is the source of this question? It's very unclear...

If S is a set of integers and 5 is in S, is every multiple of 5 in S?

1) if x is in S, then x+5 is in S
2) if x is in S, then x-5 is in S

This question could be interpreted in a number of ways....

First, I picked E. 1) Cause let's say that x is 5, then 5 and 10 will be in the set. Not sufficient. 2) Let's say that x is 5, then 5, and 0 will be in the set. Not sufficient. 3) Again, let's use 5.. then 5, 10, 0 will be in the set. Not sufficient. Also, you can use other numbers that are not mutliples of 5.

To accurately get the answer C, then the question needs to be reworded to something like this... For every member of set S (called x), then x+5 is in S. Or something to that "ETS verbage" stuff. The question as it is, implies that x is only one member of the set, and you use the +5 or -5 rule to only one member, not all the members.

I am sorry but I do not agree with you. The given wording of the problem is accurate.

When the statement says that if x is in S, then x+5 is in S, then you are invited to think recursively.

We have already been given that 5 is in S, so based on the first statement 5, 10, 15, ..... infinite all are members of S. Similarly the second statment also apllies. The answer should be C.

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20 Jan 2004, 08:04
Cause the multiples of 5 are 5, 10, 15, ect. In other words, set of POSITIVE numbers only. The way of thinking stays the same.

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Senior Manager
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20 Jan 2004, 08:14
Solo wrote:
Cause the multiples of 5 are 5, 10, 15, ect. In other words, set of POSITIVE numbers only. The way of thinking stays the same.

I disagree. The multiple of any integer includes 0, -ve integers and +ve integers.

If you are interested in more sofisticated defination, here it is.

The set of all multiples of an integer a will be denoted by

{ m in Z | m = aq for some q in Z }. where Z is a set of integers {....-3, -2, -1, 0, 1, 2, 3,......}

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21 Jan 2004, 16:40
It's news to me that 0 is a multiple of 5
This was not the case where I went to school

Though this expains the answer to one of the Kaplin
maths probems in the 2004 GMAT book
Question 13 in the maths section practice test states that 0 is a multiple
of 5

I've just got to get out more
_________________

Don't die wondering

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21 Jan 2004, 16:47
Quote:
This was not the case where I went to school

Were you taught by a pack of wolves?

http://mathforum.org/library/drmath/view/60913.html

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21 Jan 2004, 16:48
That was too snarky by half. Sorry.

The stress of my looming test is getting to me.

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21 Jan 2004, 16:48
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