All ISEE Upper Level Quantitative Resources
Example Questions
Example Question #30 : Numbers And Operations
If we consider the factors of as a set of numbers, which one is greater?
The range of the set
Sum of the median and the mean of the set
and are equal
is greater
is greater
It is not possible to tell based on the information given.
is greater
Factors of are . So we have:
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.
The median is the average of the two middle values of a set of data with an even number of values:
So we have:
So is greater than
Example Question #31 : Numbers And Operations
If we consider the factors of as a set of numbers, which one is greater?
Product of the the median and the mean of the set
The range of the set
and are equal
It is not possible to tell based on the information given.
is greater
is greater
is greater
Factors of are . So we have:
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.
The median is the middle value of a set of data containing an odd number of values:
So we have:
So is greater than
Example Question #32 : Numbers And Operations
If we consider the factors of as a set of numbers, which one is greater?
The mean of the set
Ratio of the range and the median of the set
and are equal
It is not possible to tell based on the information given.
is greater
is greater
is greater
Factors of are . So we have:
The range is the difference between the lowest and the highest values. So we have:
The median is the middle value of a set of data containing an odd number of values, which is in this problem. So the ratio of the range and the median is:
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 is greater than
Example Question #33 : Numbers And Operations
Which one is greater?
The total number of factors of
is greater
and are equal
is greater
it is not possible to tell based on the information given.
is greater
Factors of are:
. So it has factors, which is less than .
Example Question #34 : Numbers And Operations
Which one is the greater quantity:
Sum of the factors of
Sum of the factors of
it is not possible to tell based on the information given.
and are equal
is greater
is greater
is greater
Factors of are:
and their summation is:
and the factors of are:
and their summation is:
So is greater than .
Example Question #35 : Numbers And Operations
If we consider the factors of as a set of numbers, compare the mean and the median of the set.
The mean and the median are equal
The mean is greater
The median is greater
It is not possible to tell based on the information given.
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 #36 : Numbers And Operations
Which one is greater?
The product of the factors of .
The median of the following set:
is greater
and are equal
It is not possible to tell based on the information given.
is greater
is greater
Factors of are: . So the product of the factors of are:
The median is the middle value of a set of data containing an odd number of values, which is in this problem. So is greater than .
Example Question #31 : Numbers And Operations
Which one is greater?
The sum of the factors of
The product of the factors of
is greater
and are equal
is greater
It is not possible to tell based on the information given.
is greater
Factors of are
Factors of are
So is greater thaan .
Example Question #29 : How To Factor A Number
and are positive integers; ; is an even number. Which of the following also must be even?
If is even, then and are either both even or both odd. The difference of two even numbers is even, and so is the difference of two odd numbers, so must be even. Let's check the other choices, however:
must be even, so must be odd.
is either the product of two even numbers, which is even, or the product of two odd numbers, which is odd. Therefore, is of indeterminate sign. Similarly, is as well.
is even for any integer , so takes the same sign as ; but this is not given to us.
is the correct choice.
Example Question #21 : Other Factors / Multiples
Which is the greater quantity?
(A)
(B) The sum of the factors of 28 except for 28 itself.
It is impossible to determine which is greater from the information given
(B) is greater
(A) and (B) are equal
(A) is greater
(A) and (B) are equal
Leaving out 28 itself, the factors of 28 are . The sum of all of these factors is , making the quantities equal.