All ISEE Upper Level Math Resources
Example Questions
Example Question #1 : How To Factor A Number
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 be the set of all integers
such that
is divisible by
and
. How many elements are in
?
The elements are as follows:
This can be rewritten as
.
Therefore, there are elements in
.
Example Question #9 : Other Factors / Multiples
Let be the set of all integers
such that
is divisible by three and
. How many elements are in
?
The elements are as follows:
This can be rewritten as
.
Therefore, there are elements in
.
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 as a factor. Of the remaining (odd) integers, we eliminate
and
, as they have
as a factor. What remains is:
We can now eliminate the multiples of . This leaves
.
The correct choice is .
Example Question #451 : Isee Upper Level (Grades 9 12) Mathematics Achievement
Add the factors of .
The factors of are:
Their sum is .
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All ISEE Upper Level Math Resources
