ISEE Upper Level Quantitative : How to find out if a number is prime

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

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Example Questions

Example Question #91 : Factors / Multiples

, and  and  are positive integers.

 is a prime number;  is not a prime number.

Which is the greater quantity?

(a) 

(b) 

Possible Answers:

(b) is the greater quantity 

(a) is the greater quantity 

(a) and (b) are equal

It cannot be determined which of (a) and (b) is greater

Correct answer:

It cannot be determined which of (a) and (b) is greater

Explanation:

, and  and  are positive integers, so each of  and  is an integer from 1 to 11 inclusive.

 is a prime number, meaning that it can be equal to 2, 3, 5, 7, or 11. Testing each case:

, which is not prime.

 

, which is not prime.

 

, which is prime - we throw this case out.

 

, which is prime - we throw this case out.

 

, which is not prime.

In the first two cases, ; in the last case, . It cannot be determined which is the greater. 

Example Question #42 : How To Find Out If A Number Is Prime

 and  are positive integers.

 is a prime number.  is not.

Which is the greater quantity?

(a) 5

(b) 

Possible Answers:

(a) and (b) are equal

It cannot be determined which of (a) and (b) is greater

(a) is the greater quantity 

(b) is the greater quantity 

Correct answer:

(b) is the greater quantity 

Explanation:

, and  and  are positive integers.

Therefore,  must be an integer from 1 to 9, as must .

Since  is prime, it can be any of 2, 3, 5, or 7.

Therefore, one of the following must hold:

 

 

 



 

Only in the first case is  not a prime number (8 has four factors - 1, 2, 4, 8), so  and .

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