ISEE Upper Level Quantitative : Numbers and Operations
Study concepts, example questions & explanations for ISEE Upper Level Quantitative
All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #51 : Numbers And Operations
(a) The number of factors of
(b) The number of factors of
(b) is greater
(a) is greater
(a) and (b) are equal
It is impossible to tell which is greater from the information given
It is impossible to tell which is greater from the information given
Since 
We show that 
Case 1: 
Then 
Case 2:
Then 
Therefore, we have at least one situation in which 
Example Question #41 : Other Factors / Multiples
(a) The number of factors of
(b) The number of factors of
(a) is greater
(b) is greater
(a) and (b) are equal
It is impossible to tell which is greater from the information given
(a) is greater
Since 
Since 
This makes (a) greater.
Example Question #1 : How To Find Out If A Number Is Prime
Multiply the two greatest prime numbers less than 100.
The two greatest prime numbers less than 100 are 97 and 89. Their product is:
Example Question #2 : How To Find Out If A Number Is Prime
Which of the following numbers has exactly two factors?
None of the other choices is correct.
Every number except 1 has at least two factors - 1 and itself. So we are looking for a number with no other factors - that is, a prime.
3 is a factor of both 33 and 39, and 5 is a factor of 35, so we can eliminate those choices. We cannot eliminate 37, since it is a prime, having only 1 and 37 as factors.
Example Question #3 : How To Find Out If A Number Is Prime
Multiply the two smallest prime numbers greater than 100.
The first two primes after 100 are 101 and 103; their product is
Example Question #1 : How To Find Out If A Number Is Prime
Which is the greater quantity?
(a) The number of prime numbers between 70 and 110
(b) The number of prime numbers between 80 and 120
(a) is greater
It is impossible to tell from the information given
(b) is greater
(a) and (b) are equal
(a) is greater
The primes between 80 and 110 are included in both sets, so all we need to do is to compare the number of primes between 70 and 80 and the number of primes between 110 and 120.
(a) The primes between 70 and 80 are 71, 73, and 79 - three primes
(b) The only prime between 110 and 120 is 113.
(a) is the greater quantity
Example Question #5 : How To Find Out If A Number Is Prime
Which is the greater quantity?
(a) The number of prime numbers between 1 and 20 inclusive
(b) The number of composite numbers between 21 and 30 inclusive
(a) is greater
It is impossible to tell from the information given
(b) is greater
(a) and (b) are equal
(a) and (b) are equal
(a) The prime numbers between 1 and 20 inclusive are 2, 3, 5, 7, 11, 13, 17, 19 - eight total.
(b) The prime numbers between 21 and 30 inclusive are 23 and 29 - two prime numbers out of ten integers. This leaves eight composite numbers.
(a) and (b) are therefore equal.
Example Question #1 : Prime Numbers
Which is the greater quantity?
(a) The number of prime numbers between 1 and 20 inclusive
(b) The number of composite numbers between 1 and 20 inclusive
(a) is greater
It is impossible to tell from the information given
(a) and (b) are equal
(b) is greater
(b) is greater
The prime numbers between 1 and 20 inclusive are 2, 3, 5, 7, 11, 13, 17, 19 - eight total. Since 1 is neither prime nor composite, this leaves 11 composite numbers. (b) is the greater quantity.
Example Question #2 : Prime Numbers
Which is the greater quantity?
(a) The sum of the prime numbers between 11 and 19 inclusive
(b) The sum of the composite numbers between 11 and 19 inclusive
(b) is the greater quantity
(a) and (b) are equal
(a) is the greater quantity
It is impossible to tell from the information given
(b) is the greater quantity
(a) The prime numbers in the 11-19 range are 11, 13, 17, and 19. Their sum:
(b) The composite numbers in the 11-19 range are 12, 14, 15, 16, and 18. Their sum:
(b) is greater.
Example Question #8 : How To Find Out If A Number Is Prime
Which quantity is greater?
(a) The number of composite numbers between 1 and 1,000 inclusive.
(b) The number of even integers between 1 and 1,000 inclusive.
(a) and (b) are equal
(a) is greater
It is impossible to tell from the information given
(b) is greater
(a) is greater
It is not necessary to count all of the composite numbers in the 1-1,000 range. Except for 2, every even number is composite, and there are more than one odd composite numbers (15, 25) to make up for 2. This makes (a) greater.
All ISEE Upper Level Quantitative Resources
