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 #21 : Prime Numbers

Which one is greater?

 

The product of the first four prime numbers

Possible Answers:

is greater

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

is greater

and are equal

Correct answer:

is greater

Explanation:

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

 

So their product is:

 

, which is greater than .

Example Question #71 : Factors / Multiples

Which one is greater?

 

The product of the two greatest prime numbers less than

Possible Answers:

is greater

is greater

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

and are equal

Correct answer:

is greater

Explanation:

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

 

So their product is:

 

, which is greater than . So is greater than .

Example Question #21 : Prime Numbers

Which one is greater?

 

The sum of the prime numbers between and

The sum of the prime numbers between and

Possible Answers:

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

and are equal

is greater

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 prime numbers between  and  are , so we have:

 

 

The prime numbers between and are , so we have:

 

 

So is greater than .

Example Question #71 : Factors / Multiples

Which is the greater quantity?

(A) The sum of the even integers from 21 to 30 inclusive

(B) Three times the sum of the prime integers from 21 to 30 inclusive

Possible Answers:

It is impossible to determine which is greater from the information given

(A) and (B) are equal

(A) is greater

(B) is greater

Correct answer:

(B) is greater

Explanation:

The even integers from 21 to 30 inclusive are 22, 24, 26, 28, and 30; their sum is 

The prime integers from 21 to 30 inclusive are 23 and 29. their sum is 

and three times this sum is 

This makes (B) greater

Example Question #72 : Factors / Multiples

What is the sum of the prime integers between 75 and 100?

Possible Answers:

Correct answer:

Explanation:

The prime integers between 75 and 100 are 

Their sum is 

Example Question #21 : Prime Numbers

Which is the greater quantity?

(A) The number of composite integers between 41 and 50 inclusive.

(B) The number of prime integers between 41 and 50 inclusive.

Possible Answers:

(A) is greater

(A) and (B) are equal

(B) is greater

It is impossible to determine which is greater from the information given

Correct answer:

(A) is greater

Explanation:

The only prime numbers among the ten in the range 41 through 50 are 41, 43, and 47; this makes three prime numbers and seven composite numbers, so (A) is greater.

Example Question #74 : Factors / Multiples

Multiply the least and greatest primes between 80 and 100.

Possible Answers:

Correct answer:

Explanation:

The least and greatest primes between 80 and 100 are 83 and 97; their product is 

Example Question #75 : Factors / Multiples

Which of the following is the greater quantity?

(A) The sum of the prime numbers between 80 and 90

(B) The sum of the prime numbers between 90 and 100

Possible Answers:

(B) is greater

(A) and (B) are equal

(A) is greater

It is impossible to determine which is greater from the information given

Correct answer:

(A) is greater

Explanation:

The prime numbers between 80 and 90 are 83 and 89, whose sum is ; the only prime number between 90 and 100 is 97. (A) is the greater quantity.

Example Question #81 : Factors / Multiples

Which is the greater quantity?

(A) Twice the number of prime numbers between 41 and 50 inclusive

(B) The number of composite numbers between 41 and 50 inclusive

Possible Answers:

It is impossible to determine which is greater from the information given

(B) is greater

(A) is greater

(A) and (B) are equal

Correct answer:

(B) is greater

Explanation:

Out of the ten integers from 41 to 50, the prime numbers are 41, 43, and 47 - therefore, there are three prime numbers and seven composite numbers. Since

,

(B) is greater.

Example Question #82 : Factors / Multiples

Which of the following is the greater quantity?

(A) The sum of the prime numbers between 50 and 60

(B) The sum of the odd composite numbers between 50 and 60

Possible Answers:

(A) is greater

(A) and (B) are equal

(B) is greater

It is impossible to determine which is greater from the information given

Correct answer:

(B) is greater

Explanation:

The prime numbers between 50 and 60 are 53 and 59; their sum is . The odd composite numbers between 50 and 60 are 51, 55, and 57; their sum is . Therefore, (B) is greater.

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