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Set A consists of five unique prime numbers. Which of the following

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Bunuel
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Set A consists of five unique prime numbers. Which of the following [#permalink] New post   09 Apr 2018, 02:08
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Set A consists of five unique prime numbers. Which of the following values, if added as a sixth term to Set A, must increase the range of Set A?

I. 0
II. 1
III. 100

A. I only
B. II only
C. III only
D. I and II only
E. II and III only
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D
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Gladiator59
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Re: Set A consists of five unique prime numbers. Which of the following [#permalink] New post   09 Apr 2018, 02:47
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Bunuel wrote:
Set A consists of five unique prime numbers. Which of the following values, if added as a sixth term to Set A, must increase the range of Set A?

I. 0
II. 1
III. 100

A. I only
B. II only
C. III only
D. I and II only
E. II and III only


Tricky question.

Set A consists of five unique prime numbers. Lowest possible element of the set could be 2. Highest possible element could be any large prime number.

To increase the range " Difference between the largest and smallest element of the set" : we need to either lower the lowest element or increase the largest one.

Hence adding either 0 or 1 to the set will surely increase it's range by at least 2 or 1 respectively.

We cannot say the same thing about 100, as the largest prime number already existing in the set could be larger than 100.

Hence Option (D) is our answer.

+1 Kudos if you liked the explanation :-D

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SonalSinha803
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Re: Set A consists of five unique prime numbers. Which of the following [#permalink] New post   09 Apr 2018, 02:40
Since, the minimum possible prime number is 2, thus, 0 or 1 cannot be the 6 the term.

Thus, only possible number should be 100.

Thus, option C.

I am not sure, please correct me if I am wrong.

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Set A consists of five unique prime numbers. Which of the following [#permalink] New post   09 Apr 2018, 02:49
Bunuel wrote:
Set A consists of five unique prime numbers. Which of the following values, if added as a sixth term to Set A, must increase the range of Set A?

I. 0
II. 1
III. 100

A. I only
B. II only
C. III only
D. I and II only
E. II and III only




Only I (0) and II (1) will increase the range of set A. This is because minimum prime number is 2. Assume the prime numbers are 2,3,5, 97 and 109. Only I (0) and II (1) will increase the range of set A. III(100) will not increase the range. Therefore option "D" is the answer.
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Re: Set A consists of five unique prime numbers. Which of the following [#permalink] New post   09 Apr 2018, 03:03
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Only by adding 0 or 1 can we extend the range.. as unsure if the last prime number is less than 100..
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Re: Set A consists of five unique prime numbers. Which of the following [#permalink] New post   10 Apr 2018, 17:16
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Bunuel wrote:
Set A consists of five unique prime numbers. Which of the following values, if added as a sixth term to Set A, must increase the range of Set A?

I. 0
II. 1
III. 100

A. I only
B. II only
C. III only
D. I and II only
E. II and III only


Since 1 and 0 are not prime and the lowest prime number is 2, 1 and 0 will increase the range.

100 will not necessarily increase the range. If the largest of the 5 prime numbers is 101, then the range won't increase, however, if the largest of the numbers is 97, then the range will increase.

Answer: D
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Set A consists of five unique prime numbers. Which of the following [#permalink] New post   25 Sep 2018, 22:06
Quote:
Importantly for this question, the range is calculated as the greatest value minus the least value in a set.
So in order for a new term to increase the range, it would have to be either the "new" least value or the new greatest value.


Because the question doesn't specify which prime numbers are in the set, we can't tell what the greatest value of the set will be. It could be the usual suspects (2, 3, 5, 7, 11, 13, 17, 19...) or it could be a bigger number like 199. So 100 doesn't necessarily increase the range.

But we do know that the lowest the least value could possibly be is 2. 2 is the lowest prime number, so a new term less than 2 (like 0 or 1) must therefore become the new lowest value. This then means that the range must increase.

So both options I and II are correct, making D the right answer.
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Re: Set A consists of five unique prime numbers. Which of the following [#permalink] New post   03 Oct 2018, 07:58
Bunuel

Hi.....in one of your posts, you had given the formula of range as (highest - lowest) + 1 ......or something similar
i have searched but have not been able to find that formula.
can you kindly reproduce that formula please?
regards
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Re: Set A consists of five unique prime numbers. Which of the following [#permalink] New post   14 Dec 2021, 11:46
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Re: Set A consists of five unique prime numbers. Which of the following [#permalink]
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