Data Analysis and Probability - ISEE Lower Level Quantitative Reasoning
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Use the following table to determine the cost of purchasing two books.
Use the following table to determine the cost of purchasing two books.
The relationship between the values is 
,
where 
represents the cost of purchased books and 
represents the number of books purchased.
Once we realize this, we can determine how much purchasing two books 
would cost:
The relationship between the values is
where
Once we realize this, we can determine how much purchasing two books
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Use the table to determine how much one cupcake would cost.
Use the table to determine how much one cupcake would cost.
We can determine the relationship between the values by creating a ratio of number of cupcakes to cost:
Where 
represents the cost of 1 cupcake.
We can now solve for 
:
The cost of one cupcake is then $0.85
We can determine the relationship between the values by creating a ratio of number of cupcakes to cost:
Where
We can now solve for
The cost of one cupcake is then $0.85
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The following table consists of the test grades from 
students. Use the table to determine how many students received a 
on the test.
The following table consists of the test grades from
We were told the grades are from 
students. The most direct way to solve this problem is to add the numbers of students listed so far:
We know there is a total of 
students so we can set up the equation:
which leaves us with 
.
So the missing value is eight.
We were told the grades are from
We know there is a total of
So the missing value is eight.
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Use the table to determine how much one cupcake would cost.
Use the table to determine how much one cupcake would cost.
We can determine the relationship between the values by creating a ratio of number of cupcakes to cost:
Where represents the cost of 1 cupcake.
We can now solve for :
The cost of one cupcake is then 
We can determine the relationship between the values by creating a ratio of number of cupcakes to cost:
Where
We can now solve for
The cost of one cupcake is then
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Students were asked if they prefer TV or radio. The following Venn Diagram depicts the number of students who said TV, radio, or both. How many students like both TV and radio?
Students were asked if they prefer TV or radio. The following Venn Diagram depicts the number of students who said TV, radio, or both. How many students like both TV and radio?
The blue circle of the Venn diagram depicts the number of students who prefer TV, the orange circle depicts the number of students who prefer radio, and the region of overlap indicates the number of students who like both. Therefore, 7 students like both TV and radio.
The blue circle of the Venn diagram depicts the number of students who prefer TV, the orange circle depicts the number of students who prefer radio, and the region of overlap indicates the number of students who like both. Therefore, 7 students like both TV and radio.
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Aracely posted a survey question using one of her social network accounts. She grouped the results into three categories. The response results are represented by the Venn diagram shown above.
Group 
represents the respondents that answered "yes" to the survey question. Group 
represents the respondents that answered "no" to the survey question. And, the overlapping part of the diagram represents the respondents that answered "maybe" to the survey question.
What percentage of the respondents answered "maybe" to Aracely's survey question?
Aracely posted a survey question using one of her social network accounts. She grouped the results into three categories. The response results are represented by the Venn diagram shown above.
Group
What percentage of the respondents answered "maybe" to Aracely's survey question?
The overlapping portion of the Venn diagram represents the percentage of respondents that answered "maybe" to Aracely's survey question.
Since the diagram shows that exactly 
percent of the respondents answered "yes" or "no" to the question
.
The solution is the total percent population take away the percent that answered "yes" or "no":
The overlapping portion of the Venn diagram represents the percentage of respondents that answered "maybe" to Aracely's survey question.
Since the diagram shows that exactly
The solution is the total percent population take away the percent that answered "yes" or "no":
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The Venn diagram shown above has three categories that represent information about the Wildcats varsity baseball team.
Category 
represents the number of players on the team that are left-handed.
Category 
represents the numebr of players on the team that are pitchers.
And, the overlapping portion of the Venn diagram represents the number of players that are left-handed pitchers.
Given that 
and that there are 
players in the overlapping region of the diagram.
What fraction of the players are left-handed pitchers?
The Venn diagram shown above has three categories that represent information about the Wildcats varsity baseball team.
Category
Category
And, the overlapping portion of the Venn diagram represents the number of players that are left-handed pitchers.
Given that
What fraction of the players are left-handed pitchers?
Since there are 
left-handed pitchers and 
total players that are either left-handed, pitchers or both the solution is:
Since there are
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The Venn diagram above represents the results from a recent survey given to middle school students. Category 
represents the amount of students that only like pizza. Category 
represents the amount of students that only chicken nuggets.
What percentage of students like both chicken nuggets and pizza?
The Venn diagram above represents the results from a recent survey given to middle school students. Category
What percentage of students like both chicken nuggets and pizza?
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
.
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
.
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
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The Venn diagram above represents the results from a recent survey given to middle school students. Category represents the amount of students that only like pizza. Category represents the amount of students that only chicken nuggets.
What percentage of students like both chicken nuggets and pizza?
The Venn diagram above represents the results from a recent survey given to middle school students. Category
What percentage of students like both chicken nuggets and pizza?
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
.
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
.
Since we are asked to find the percent of students that like both chicken nuggets and pizza we need to first add the percentages together.
Thus we get,
The amount of students that like both pizza and chicken nuggets is going to be all of the students minus those that like only chicken nuggets and only pizza.
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What is the next number in the series?
What is the next number in the series?
First, determine what the pattern is in the series. The pattern here is to multiply the previous number by 2 and then add 1. Therefore, multiply 47 by 2 (which is 94), and then add 1. The result is 95.
First, determine what the pattern is in the series. The pattern here is to multiply the previous number by 2 and then add 1. Therefore, multiply 47 by 2 (which is 94), and then add 1. The result is 95.
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What is the missing value of w in this sequence?
What is the missing value of w in this sequence?
In this sequence, every subsequent number is 7 less than the preceding number. Given that the number that precedes w is 71, the value of w is 
. Therefore, 64 is the correct answer.
In this sequence, every subsequent number is 7 less than the preceding number. Given that the number that precedes w is 71, the value of w is
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What is the value of n in the sequence below?
What is the value of n in the sequence below?
The numbers increase by 5. Given that the number before n is 20, the value of n is 
.
The numbers increase by 5. Given that the number before n is 20, the value of n is
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What is the next term in the following sequence?
What is the next term in the following sequence?
What is the next term in the following sequence?
This is an arithmetic sequence with a common difference of 
. To find the next term in an arithmetic sequence, add the common difference to the previously listed term:
What is the next term in the following sequence?
This is an arithmetic sequence with a common difference of
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Find the missing number in the sequence:
Find the missing number in the sequence:
In this sequence, the difference between each number is double the difference between the number that came prior to it in the sequence. For example, 
and 
. Thus, the missing number must be greater than 
by a difference of 
and therefore 
In this sequence, the difference between each number is double the difference between the number that came prior to it in the sequence. For example,
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Find the missing number:
Find the missing number:
In this sequence of numbers, there is an important pattern to recognize. Each number is greater than the number prior to it by a margin of 
. Thus, the correct answer is 
, because 
In this sequence of numbers, there is an important pattern to recognize. Each number is greater than the number prior to it by a margin of
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Find the missing number in the list below:
Find the missing number in the list below:
In this sequence of numbers, there is an important pattern to recognize. Each number is greater than the number prior to it by a margin of 9. Thus, the correct answer is 
because 
.
In this sequence of numbers, there is an important pattern to recognize. Each number is greater than the number prior to it by a margin of 9. Thus, the correct answer is
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What is the missing number in the following sequence:
What is the missing number in the following sequence:
In this sequence of numbers, there is an important pattern to recognize. Each number is greater than the number prior to it by a margin of 
. In other words, each number in this list is a multiple of 
. 
, 
, thus the next number in this sequence is the product of 
which equals 
.
In this sequence of numbers, there is an important pattern to recognize. Each number is greater than the number prior to it by a margin of
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What is the missing number in the following list:
What is the missing number in the following list:
In this sequence of numbers, there is an important pattern to recognize. In this sequence each number is a prime number, however the sequence skips every other prime number. Thus, the sequence begins with the prime number 
and then skips the prime number 
(which is the only even prime number) and goes to 
. From 
the next prime number is 
, however since the pattern in this sequence skips every other prime number--the missing number is 
.
In this sequence of numbers, there is an important pattern to recognize. In this sequence each number is a prime number, however the sequence skips every other prime number. Thus, the sequence begins with the prime number
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Find the missing number in this set:
Find the missing number in this set:
In this sequence of numbers, there is an important pattern to recognize. Each number in this sequence is a composite number--however, the sequence skips every other composite number. Thus, the next composite number after 
is 
--which is skipped because of the pattern, making the correct answer 
.
In this sequence of numbers, there is an important pattern to recognize. Each number in this sequence is a composite number--however, the sequence skips every other composite number. Thus, the next composite number after
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Find the next number in the list:
Find the next number in the list:
In this sequence of numbers, there is an important pattern to recognize. Each number is greater than the number prior to it by a margin of 
. In other words, each number in this list is a multiple of 
. Thus, 
In this sequence of numbers, there is an important pattern to recognize. Each number is greater than the number prior to it by a margin of
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