M24-09

Question

Set S consists of all prime integers less than 1000. What is the range of set S?

A. 982
B. 988
C. 992
D. 995
E. 997

Bunuel · Answer

Official Solution:

Set S consists of all prime integers less than 1000. What is the range of set S?

A. 982
B. 988
C. 992
D. 995
E. 997

The range of a set is defined as the difference between its largest and smallest elements: Range = Largest Element - Smallest Element.
 
The smallest element of the set is 2, which is even. The largest element of the set will obviously be odd. Since the range is given by Range = Largest Element - Smallest Element = odd - even, the range will be odd. Choices A, B, and C can be eliminated because they are even. Choice E, which is 997, is not viable because in this case the largest element would be 999, which isn't prime. Therefore, the correct range is 995, option D.

Answer: D

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

Akshay1298 · Answer

How to find out a larger number prime or not? Is there any technique to find them?

Bunuel · Answer

Generally, there’s no simple way to check if a very large number is prime (unless it has small factors, which are easier to check). For numbers like that, you’d need a computer to test.
 
On the GMAT, you won’t encounter a large number to factorize unless there’s a clear shortcut.

Here is a way though:

•  Verifying the primality  (checking whether the number is a prime) of a given number  n  can be done by trial division, that is to say dividing  n  by all integer numbers smaller than  \sqrt{n} , thereby checking whether  n  is a multiple of  m\leq{\sqrt{n}} .
 
Example:  Verifying the primality of  161 :  \sqrt{161}  is little less than  13 , from integers from  2  to  13 ,  161  is divisible by  7 , hence  161  is not prime.
Note that, it is only necessary to try dividing by  prime  numbers up to  \sqrt{n} , since if  n  has any divisors at all (besides 1 and  n ), then it must have a prime divisor.

M24-09

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