ISEE Upper Level Quantitative : Other Factors / Multiples

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

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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

Possible Answers:

and are equal

is greater

is greater

It is not possible to tell based on the information given.

Correct answer:

is greater

Explanation:

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

Possible Answers:

and are equal

It is not possible to tell based on the information given.

is greater

is greater

Correct answer:

is greater

Explanation:

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

Possible Answers:

and are equal

It is not possible to tell based on the information given.

is greater

 is greater

Correct answer:

is greater

Explanation:

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

Possible Answers:

is greater

and are equal

is greater

it is not possible to tell based on the information given.

Correct answer:

is greater

Explanation:

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

Possible Answers:

it is not possible to tell based on the information given.

and are equal

is greater

is greater

Correct answer:

is greater

Explanation:

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.

Possible Answers:

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.

Correct answer:

The mean is greater

Explanation:

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:

Possible Answers:

 is greater

and are equal

It is not possible to tell based on the information given.

is greater

Correct answer:

is greater

Explanation:

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

Possible Answers:

is greater

and are equal

is greater

It is not possible to tell based on the information given.

Correct answer:

is greater

Explanation:

 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?

Possible Answers:

Correct answer:

Explanation:

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.

Possible Answers:

It is impossible to determine which is greater from the information given

(B) is greater

(A) and (B) are equal 

(A) is greater

Correct answer:

(A) and (B) are equal 

Explanation:

Leaving out 28 itself, the factors of 28 are .  The sum of all of these factors is , making the quantities equal.

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