ISEE Upper Level Quantitative : Prime Numbers

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

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Example Questions

Example Question #61 : Factors / Multiples

Which is the greater quantity?

(a) The sum of the prime numbers between  and  inclusive

(b) The sum of the prime numbers between  and  inclusive

Possible Answers:

(b) is greater.

(a) is greater.

(a) and (b) are equal.

It is impossible to tell from the information given.

Correct answer:

(a) is greater.

Explanation:

(a) The prime numbers in the to   range are , and . Their sum is

.

(b) The prime numbers in the  to  range are  and ; their sum is 

.

(a) is greater.

Example Question #62 : Factors / Multiples

Which is the greater quantity?

(a) The product of the two greatest primes less than or equal to 100

(b) 9,000

Possible Answers:

(a) is greater

(a) and (b) are equal

It is impossible to tell from the information given

(b) is greater

Correct answer:

(b) is greater

Explanation:

The two greatest primes less than or equal to 100 are 97 and 89; their product is , making (b) greater.

Example Question #63 : Factors / Multiples

Which is the greater quantity?

(a) The product of the two least primes greater than or equal to 50

(b) 3,000

Possible Answers:

(b) is greater

It is impossible to tell from the information given

(a) is greater

(a) and (b) are equal

Correct answer:

(a) is greater

Explanation:

The two least primes greater than or equal to 50 are 53 and 59; their product is .

Example Question #64 : Factors / Multiples

Which is the greater quantity?

(a) The sum of the five greatest primes less than or equal to 100

(b) 400

Possible Answers:

(a) is greater

It is impossible to tell from the information given

(b) is greater

(a) and (b) are equal

Correct answer:

(a) is greater

Explanation:

The five greatest primes less than or equal to 100 are . Their sum is 

Example Question #65 : Factors / Multiples

Which of the following is not a prime number between  and ?

Possible Answers:

Correct answer:

Explanation:

A prime number is a number that is only divisible by itself and .

 is the only number that is not prime.

Example Question #16 : How To Find Out If A Number Is Prime

Which one is greater?

 

The number of prime numbers between  and 

The number of prime numbers between  and

Possible Answers:

and are equal.

is greater

it is not possible to tell based on the information given.

 is greater

Correct answer:

and are equal.

Explanation:

A prime number is a natural number greater than  that can be divided only by  and itself.

 

The prime numbers between  and  are:

 

 

The prime numbers between and are:

 

 

So and are equal.

Example Question #17 : How To Find Out If A Number Is Prime

Which one is greater?

 

The number of prime numbers between  and 

The number of prime numbers between  and 

Possible Answers:

and are equal

it is not possible to tell based on the information given.

is greater

is greater

Correct answer:

and are equal

Explanation:

A prime number is a natural number greater than  that can be divided only by  and itself.

 

The prime numbers between  and  are:

 

 

The prime numbers between  and  are:

 

 

So there are five prime numbers between and  and there are five prime numbers between and  too. Therefore and are equal.

Example Question #18 : How To Find Out If A Number Is Prime

Which of the following numbers is not a prime number between    and ?

 

Possible Answers:

Correct answer:

Explanation:

A prime number is a natural number greater than  that can be divided only by  and itself. In this problem is the only number which is not prime.

Example Question #19 : How To Find Out If A Number Is Prime

Which one is greater?

 

The smallest prime number greater than  multiplied by the smallest prime number greater than .

 

Possible Answers:

is greater

and are equal

it is not possible to tell based on the information given.

is greater

Correct answer:

is greater

Explanation:

A prime number is a natural number greater than  that can be divided only by  and itself. The smallest prime number greater than is and the smallest prime number greater than is . So we can write:

 

 

So is greater than .

Example Question #20 : How To Find Out If A Number Is Prime

Which one is greater?

 

The number of prime numbers between and .

 

Possible Answers:

and are equal.

it is not possible to tell based on the information given.

is greater

 is greater

Correct answer:

and are equal.

Explanation:

A prime number is a natural number greater than  that can be divided only by  and itself.The prime numbers between and are:

 

 

That means there are four prime numbers between and . So and are equal.

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