ISEE Upper Level Math : ISEE Upper Level (grades 9-12) Mathematics Achievement
Study concepts, example questions & explanations for ISEE Upper Level Math
All ISEE Upper Level Math Resources
Example Questions
Example Question #12 : Numbers And Operations
What is the sum of all of the factors of 60?
60 has twelve factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.
Their sum is 
Example Question #2 : How To Factor A Number
Give the prime factorization of 135.
3 and 5 are both primes, so this is as far as we can go. Rearranging, the prime factorization is
Example Question #3 : How To Factor A Number
Which of the following digits can go into the box to form a three-digit number divisible by 3?
Place each of these digits into the box in turn. Divide each of the numbers formed and see which quotient yields a zero remainder:
Only 627 is divisible by 3 so the correct choice is 2.
Example Question #4 : How To Factor A Number
Which of the following digits can go into the box to form a three-digit number divisible by 4?
None of the other choices is correct.
None of the other choices is correct.
For a number to be divisible by 4, the last two digits must form an integer divisible by 4. 2 (02), 22, 62, and 82 all yield remainders of 2 when divided by 4, so none of these alternatives make the number a multiple of 4.
Example Question #5 : How To Factor A Number
Which of the following is divisible by 
Numbers that are divisble by 6 are also divisble by 2 and 3. Only even numbers are divisible by 2, therefore, 72165 is excluded. The sum of the digits of numbers divisible by 3 are also divisible by 3. For example,
Because 18 is divisible by 3, 63,072 is divisible by 3.
Example Question #12 : Numbers And Operations
Let 
The elements are as follows:
This can be rewritten as
Therefore, there are 
Example Question #9 : Other Factors / Multiples
Let 
The elements are as follows:
This can be rewritten as
Therefore, there are 
Example Question #6 : How To Factor A Number
Add the factors of 19.
19 is a prime number and has 1 and 19 as its only factors. Their sum is 20.
Example Question #21 : Factors / Multiples
How many integers from 51 to 70 inclusive do not have 2, 3, or 5 as a factor?
None
We can eliminate the ten even integers right off the bat, since, by definition, all have 
We can now eliminate the multiples of 
The correct choice is 
Example Question #11 : How To Factor A Number
Add the factors of 
The factors of 
Their sum is 
Certified Tutor
All ISEE Upper Level Math Resources
