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Bunuel
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Bunuel
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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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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Bunuel
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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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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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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The shortest prime number is 2 so anything less than 2 will definitely add to the range of this set which only contains prime number.
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