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 #11 : Other Factors / Multiples

Which is the greater quantity?

(a) The sum of all of the two-digit even numbers 

(b) 2,500

Possible Answers:

(a) is greater

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

Correct answer:

(b) is greater

Explanation:

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 ?

Possible Answers:

Correct answer:

Explanation:

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 

Possible Answers:

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

is greater

 

is greater

and are equal

Correct answer:

is greater

Explanation:

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

 

Possible Answers:

and are equal

is greater

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

is greater

Correct answer:

is greater

Explanation:

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

Possible Answers:

is greater

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

and are equal

is greater

Correct answer:

and are equal

Explanation:

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 

Possible Answers:

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

is greater

is greater

and are equal

Correct answer:

is greater

Explanation:

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.

Possible Answers:

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

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 #27 : Numbers And Operations

If we consider the factors of  as a set of numbers, compare the mean and the range of the set.

Possible Answers:

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.

Correct answer:

The range is greater

Explanation:

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.

Possible Answers:

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

Correct answer:

The range is greater

Explanation:

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

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:

 

Factors of  are:

 

So  is greater than

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