All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #11 : Other Factors / Multiples
Which is the greater quantity?
(a) The sum of all of the two-digit even numbers
(b) 2,500
(a) is greater
(b) is greater
(a) and (b) are equal
It is impossible to tell from the information given
(b) is greater
The sum of the integers from to is equal to . We take advantage of the fact that the sum of the even numbers from 10 to 98 is equal to twice the sum of the integers from 5 to 49, as seen here:
Example Question #21 : Numbers And Operations
What is the prime factorization of ?
First make a factor tree for 16. Keep breaking it down until you get all prime numbers (for example: , which then yields ). Then, at the end, remember to factor the variables as well. Since the b term is squared, that means there are two of them. Therefore, the final answer is .
Example Question #22 : Numbers And Operations
Which one is greater?
number of factors of
it is not possible to tell based on the information given.
is greater
is greater
and are equal
is greater
Factors of are:
. So it has factors which is less than .
Example Question #23 : Numbers And Operations
Which one is greater?
The sum of all of the factors of
and are equal
is greater
it is not possible to tell based on the information given.
is greater
is greater
Factors of are:
. So we can write:
Example Question #21 : Numbers And Operations
Which one is greater?
The number of factors of
The number of factors of
is greater
It is not possible to tell based on the information given.
and are equal
is greater
and are equal
has only three factors of
and
also has three factors of
So the number of their factors are the same
Example Question #25 : Numbers And Operations
Which one is greater?
The number of factors of
The number of factors of
It is not possible to tell based on the information given.
is greater
is greater
and are equal
is greater
The factors of are . So has ten factors.
The factors of are . So has eight factors.
So is greater than .
Example Question #22 : Numbers And Operations
If we consider the factors of as a set of numbers, compare the mean and the median of the set.
It is not possible to tell based on the information given.
The mean is greater
The mean and the median are equal
The median is greater
The mean is greater
Factors of are . So we should compare the mean and the median of the following set of numbers:
The mean of a set of data is given by the sum of the data, divided by the total number of values in the set:
The median is the middle value of a set of data containing an odd number of values which is in this problem. So the mean is greater than the median.
Example Question #27 : Numbers And Operations
If we consider the factors of as a set of numbers, compare the mean and the range of the set.
The range is greater
The mean is greater
The mean and the range are equal
It is not possible to tell based on the information given.
The range is greater
Factors of are . So we should compare the median and the range of the following set of numbers:
The range is the difference between the lowest and the highest values. So we have:
The mean of a set of data is given by the sum of the data, divided by the total number of values in the set.
So the range is greater than the mean.
Example Question #23 : Numbers And Operations
If we consider the factors of as a set of numbers, compare the median and the range of the set.
The median is greater
It is not possible to tell based on the information given.
The range is greater
The range and the median are equal
The range is greater
Factors of are . So we should compare the median and the range of the following set of numbers:
The range is the difference between the lowest and the highest values. So we have:
The median is the average of the two middle values of a set of data with an even number of values:
So the range is greater than the median.
Example Question #29 : Numbers And Operations
Which one is greater?
The sum of the factors of
The sum of the factors of
and are equal
It is not possible to tell based on the information given.
is greater
is greater
is greater
Factors of are:
Factors of are:
So is greater than