ISEE Upper Level Quantitative : Numbers and Operations

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

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Example Questions

Example Question #5 : How To Find Out If A Number Is Prime

Which is the greater quantity?

(a) The number of primes between 20 and 50

(b) The number of primes between 10 and 40

Possible Answers:

(a) and (b) are equal.

It is impossible to tell from the information given.

(b) is greater.

(a) is greater.

Correct answer:

(b) is greater.

Explanation:

The primes between 20 and 40 are included in both sets, so all we need to do is to compare the number of primes between 40 and 50 with the number of primes between 10 and 20.

(a) The primes between 40 and 50 are 41, 43, and 47 - three.

(b) The primes between 10 and 20 are 11, 13, 17, and 19 - four.

Since the number of primes between 10 and 20 outnumbers those between 40 and 50, the number of primes between 10 and 40 outnumber those between 20 and 50. Therefore, (b) is the greater.

Example Question #3 : How To Find Out If A Number Is Prime

Which is the greater quantity?

(a) The product of the first five prime numbers

(b) 

Possible Answers:

(a) and (b) are equal.

(b) is greater.

(a) is greater.

It is impossible to tell from the information given.

Correct answer:

(b) is greater.

Explanation:

(a) The product of the first five prime numbers is .

(b) 

(b) is greater.

Example Question #61 : Numbers And Operations

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:

It is impossible to tell from the information given.

(a) is greater.

(a) and (b) are equal.

(b) is greater.

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 : Numbers And Operations

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) and (b) are equal

It is impossible to tell from the information given

(a) is greater

(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 : Numbers And Operations

Which is the greater quantity?

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

(b) 3,000

Possible Answers:

(a) and (b) are equal

(a) is greater

It is impossible to tell from the information given

(b) is greater

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 : Numbers And Operations

Which is the greater quantity?

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

(b) 400

Possible Answers:

(b) is greater

(a) and (b) are equal

(a) is greater

It is impossible to tell from the information given

Correct answer:

(a) is greater

Explanation:

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

Example Question #65 : Numbers And Operations

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 : Prime Numbers

Which one is greater?

 

The number of prime numbers between  and 

The number of prime numbers between  and

Possible Answers:

 is greater

and are equal.

is greater

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

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 : Prime Numbers

Which one is greater?

 

The number of prime numbers between  and 

The number of 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:

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 #16 : Prime Numbers

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.

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