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# m09#02 - DS - Set theory

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m09#02 - DS - Set theory [#permalink]

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04 Jun 2010, 07:21
Are all elements of set S smaller than 20?

1) The smallest element of S is 0.
2) The range of S is 20.

I am not convinced with the OA (C). OE is:
Statement (1) by itself is insufficient. Statement (2) by itself is insufficient. Statements (1) and (2) combined are sufficient. Using them together we can conclude that the biggest element in S is 20. Therefore, not all elements of S are smaller than 20.

My question:
If the set is {0,....20}, {1,...21}, {10......30} and so on. In all these cases there is atleast one term which is >= 20. For example, in set {0,...20}, the highest number is 20 which says that this is equal to 20. So, not all elements are less than 20.
I think I am missing something important.

Can someone explain?
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Re: m09#02 - DS - Set theory [#permalink]

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04 Jun 2010, 07:37
ykaiim wrote:
Are all elements of set S smaller than 20?

1) The smallest element of S is 0.
2) The range of S is 20.

I am not convinced with the OA (C). OE is:
Statement (1) by itself is insufficient. Statement (2) by itself is insufficient. Statements (1) and (2) combined are sufficient. Using them together we can conclude that the biggest element in S is 20. Therefore, not all elements of S are smaller than 20.

My question:
If the set is {0,....20}, {1,...21}, {10......30} and so on. In all these cases there is atleast one term which is >= 20. For example, in set {0,...20}, the highest number is 20 which says that this is equal to 20. So, not all elements are less than 20.
I think I am missing something important.

Can someone explain?

Are all elements of set S smaller than 20?

(1) The smallest element of S is 0. Clearly insufficient.
(2) The range of S is 20. Also insufficient: for instance if the set S={-5, 7,15} - answer YES, but if the st S={50, 51, 52, 70} - answer is NO.

(1)+(2) The range of a set is the difference between the largest and smallest elements of a set --> 20=largest-smallest=largest-0 --> largest=20. Sufficient to answer NO to the question "are ALL elements of set S smaller than 20" (at least one, 20, is not smaller, it equals to 20).

Hope it's clear.
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Re: m09#02 - DS - Set theory [#permalink]

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04 Jun 2010, 07:50
Thanks Bunuel.

I have another issue here. As per sets:
the set S={-5, 7,15} - answer YES, >>> we can answer the question that Yes, all elements are <20.

If the st S={50, 51, 52, 70} - answer is NO. >>>> we can still answer the question that No, all elements are not <20.

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Re: m09#02 - DS - Set theory [#permalink]

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04 Jun 2010, 07:56
ykaiim wrote:
Thanks Bunuel.

I have another issue here. As per sets:
the set S={-5, 7,15} - answer YES, >>> we can answer the question that Yes, all elements are <20.

If the st S={50, 51, 52, 70} - answer is NO. >>>> we can still answer the question that No, all elements are not <20.

If there can be two different answers for Yes/No Ds questions then the statement is not sufficient.
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Re: m09#02 - DS - Set theory   [#permalink] 04 Jun 2010, 07:56
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# m09#02 - DS - Set theory

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