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# problem with Set definition?

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Manager
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21 Aug 2018, 02:25
Hi
I believe set cannot have duplicate values (also taught to us in Princeton Review classes) but I come across some questions on this platform where they are considering Duplicate values in set , Can any moderator can clearly tell me whether we can consider duplicate values in set or not?

I would Really appreciate your time .
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21 Aug 2018, 11:23
1
Hi GMATbuster92,

On the GMAT, a "set" of numbers is a 'group' of numbers. Unless the prompt gives you information that 'restricts' what could be in the set, then ANY number is possible - including duplicate numbers. The specific wording of the prompt dictates how you should think about the information provided. For example, consider...

Set X = {1, 3, 5, Z}

We're not told ANYTHING about Z, so that variable could be ANY value. It's not necessarily greater than 5 and it's not necessarily an odd number - again, because we have not been told anything about Z. By extension, Z could potentially be 1, 3 or 5.

If a question asks you to combine two sets and asks for the number of 'different' elements, then THAT would mean we should ignore the duplicates...

Set A = {1, 2, 3} and Set B = {2, 3, 4}

Combining these sets, the number of DIFFERENT elements would be 4 --> {1, 2, 3 and 4}

A similar concept can sometimes appear in Prime Factorization questions...

How many DISTINCT Prime factors are there in the number 24?

24 = (2)(2)(2)(3).... so while there are technically 4 prime numbers (three 2s and one 3), there are only 2 DISTINCT prime factors (2 and 3).

This is all meant to say that you have to pay attention to whatever 'restrictions' the prompt places on you (including the specific question that the prompts asks you to solve).

GMAT assassins aren't born, they're made,
Rich
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Manager
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Schools: CUHK '21 (II)
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Re: problem with Set definition?  [#permalink]

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21 Aug 2018, 13:04
EMPOWERgmatRichC wrote:
Hi GMATbuster92,

On the GMAT, a "set" of numbers is a 'group' of numbers. Unless the prompt gives you information that 'restricts' what could be in the set, then ANY number is possible - including duplicate numbers. The specific wording of the prompt dictates how you should think about the information provided. For example, consider...

Set X = {1, 3, 5, Z}

We're not told ANYTHING about Z, so that variable could be ANY value. It's not necessarily greater than 5 and it's not necessarily an odd number - again, because we have not been told anything about Z. By extension, Z could potentially be 1, 3 or 5.

If a question asks you to combine two sets and asks for the number of 'different' elements, then THAT would mean we should ignore the duplicates...

Set A = {1, 2, 3} and Set B = {2, 3, 4}

Combining these sets, the number of DIFFERENT elements would be 4 --> {1, 2, 3 and 4}

A similar concept can sometimes appear in Prime Factorization questions...

How many DISTINCT Prime factors are there in the number 24?

24 = (2)(2)(2)(3).... so while there are technically 4 prime numbers (three 2s and one 3), there are only 2 DISTINCT prime factors (2 and 3).

This is all meant to say that you have to pay attention to whatever 'restrictions' the prompt places on you (including the specific question that the prompts asks you to solve).

GMAT assassins aren't born, they're made,
Rich

from above I can correctly infer that , set in gmat can have duplicate values until unless there are any restrictions or specific details mentioned.Please let me know if i miss something.
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Re: problem with Set definition?  [#permalink]

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21 Aug 2018, 15:03
Hi GMATbuster92,

That's the easiest way to think of these things.

In the broader sense, you have to incorporate whatever information/restrictions you are given from the prompt into the concepts that you're thinking about - and it's important to remember that GMAT questions are specifically-worded and nothing is by 'accident' (any numbers that you're given in a Quant prompt were specifically CHOSEN by the writer and even the 4 wrong answer choices were also specifically designed). You'll find that, in certain situations, you can even use the 'design' of the prompt 'against' the prompt and take advantage of shortcuts in how the logic/math works.

GMAT assassins aren't born, they're made,
Rich
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# Rich Cohen

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Math Expert
Joined: 02 Aug 2009
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22 Aug 2018, 19:29
GMATbuster92 wrote:
Hi
I believe set cannot have duplicate values (also taught to us in Princeton Review classes) but I come across some questions on this platform where they are considering Duplicate values in set , Can any moderator can clearly tell me whether we can consider duplicate values in set or not?

I would Really appreciate your time .

As also explained above.

A set may contain 10 items and all may still be same until and unless specified.
If a question has to say otherwise, it will say set contains distinct elements or set contains consecutive integers etc.

In GMAT irrespective of the role the variables play, whether be in a set or in an equation or anywhere else, it can be same unless specified. So if set contains X and y, it could easily be the case that X=y
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Manager
Joined: 28 Jun 2018
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Schools: CUHK '21 (II)
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Re: problem with Set definition?  [#permalink]

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22 Aug 2018, 23:01
chetan2u and EMPOWERgmatRichC , Thanks a lot , really appreciate your help.
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Re: problem with Set definition?   [#permalink] 22 Aug 2018, 23:01
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# problem with Set definition?

Moderator: DisciplinedPrep