### All PSAT Math Resources

## Example Questions

### Example Question #1 : Use Data To Construct And Interpret A Two Way Table: Ccss.Math.Content.8.Sp.A.4

A teacher at a high school conducted a survey of seniors and found that students owned a laptop and of those students also had a car. There were students that did not have a laptop, but owned a car. Last, they found that students did not own a laptop nor a car. Given this information, how many students had a laptop, but did not own a car?

**Possible Answers:**

**Correct answer:**

To help answer this question, we can construct a two-way table and fill in our known quantities from the question.

The columns of the table will represent the students who have a laptop or do not have a laptop and the rows will contain the students who have a car or do not have a car. The first bit of information that we were given from the question was that students had a laptop; therefore, needs to go in the "laptop" column as the row total. Next, we were told that of those students, owned a car; therefore, we need to put in the "laptop" column and in the "car" row. Then, we were told that students do not own a laptop, but own a car, so we need to put in the "no laptop" column and the "car" row. Finally, we were told that students do not have a laptop or a car, so needs to go in the "no laptop" column and "no car" row. If done correctly, you should create a table similar to the following:

Our question asked how many students have a laptop, but do not own have a car. We can take the total number of students that own a lap top, , and subtract the number of students who have a car,

This means that students who have a laptop, don't have a car.

### Example Question #2 : Use Data To Construct And Interpret A Two Way Table: Ccss.Math.Content.8.Sp.A.4

A teacher at a high school conducted a survey of seniors and found that students owned a laptop and of those students also had a car. There were students that did not have a laptop, but owned a car. Last, they found that students did not own a laptop nor a car. Given this information, how many students do not have a laptop?

**Possible Answers:**

**Correct answer:**

To help answer this question, we can construct a two-way table and fill in our known quantities from the question.

The columns of the table will represent the students who have a laptop or do not have a laptop and the rows will contain the students who have a car or do not have a car. The first bit of information that we were given from the question was that students had a laptop; therefore, needs to go in the "laptop" column as the row total. Next, we were told that of those students, owned a car; therefore, we need to put in the "laptop" column and in the "car" row. Then, we were told that students do not own a laptop, but own a car, so we need to put in the "no laptop" column and the "car" row. Finally, we were told that students do not have a laptop or a car, so needs to go in the "no laptop" column and "no car" row. If done correctly, you should create a table similar to the following:

Our question asked how many students do not have a laptop. We add up the numbers in the "no laptop" column to get the total:

This means that students do not have a laptop.

### Example Question #2 : Use Data To Construct And Interpret A Two Way Table: Ccss.Math.Content.8.Sp.A.4

A teacher at a high school conducted a survey of seniors and found that students owned a laptop and of those students also had a car. There were students that did not have a laptop, but owned a car. Last, they found that students did not own a laptop nor a car. Given this information, how many students have a car?

**Possible Answers:**

**Correct answer:**

To help answer this question, we can construct a two-way table and fill in our known quantities from the question.

The columns of the table will represent the students who have a laptop or do not have a laptop and the rows will contain the students who have a car or do not have a car. The first bit of information that we were given from the question was that students had a laptop; therefore, needs to go in the "laptop" column as the row total. Next, we were told that of those students, owned a car; therefore, we need to put in the "laptop" column and in the "car" row. Then, we were told that students do not own a laptop, but own a car, so we need to put in the "no laptop" column and the "car" row. Finally, we were told that students do not have a laptop or a car, so needs to go in the "no laptop" column and "no car" row. If done correctly, you should create a table similar to the following:

Our question asked how many students have a car. We add up the numbers in the "car" row to get the total:

This means that students have a car.

### Example Question #3 : Use Data To Construct And Interpret A Two Way Table: Ccss.Math.Content.8.Sp.A.4

A teacher at a high school conducted a survey of seniors and found that students owned a laptop and of those students also had a car. There were students that did not have a laptop, but owned a car. Last, they found that students did not own a laptop nor a car. Given this information, how many students do not have a car?

**Possible Answers:**

**Correct answer:**

Our question asked how many students do not have a car. We add up the numbers in the "no car" row to get the total, but first we need to fill in a gap in our table, students who have a laptop, but don't have a car:

We can take the total number of students that own a lap top, , and subtract the number of students who have a car,

This means that students who have a laptop, don't have a car.

Now, we add up the numbers in the "no car" row to get the total:

This means that students do not have a car.

### Example Question #3 : Use Data To Construct And Interpret A Two Way Table: Ccss.Math.Content.8.Sp.A.4

A teacher at a high school conducted a survey of freshman and found that students had a curfew and of those students were also honor roll students. There were students that did not have a curfew, but were on honor roll. Last, they found that students did not have a curfew nor were on honor roll. Given this information, how many students had a curfew, but were not on honor roll?

**Possible Answers:**

**Correct answer:**

The columns of the table will represent the students who have a curfew or do not have a curfew and the rows will contain the students who are on honor roll or are not on honor roll. The first bit of information that we were given from the question was that students had a curfew; therefore, needs to go in the "curfew" column as the row total. Next, we were told that of those students, were on honor roll; therefore, we need to put in the "curfew" column and in the "honor roll" row. Then, we were told that students do not have a curfew, but were on honor roll, so we need to put in the "no curfew" column and the "honor roll" row. Finally, we were told that students do not have a curfew or were on honor roll, so needs to go in the "no curfew" column and "no honor roll" row. If done correctly, you should create a table similar to the following:

Our question asked how many students have a curfew, but were not on honor roll. We can take the total number of students that have a curfew, , and subtract the number of students who are on honor roll,

This means that students who have a curfew, aren't on honor roll.

### Example Question #3 : Use Data To Construct And Interpret A Two Way Table: Ccss.Math.Content.8.Sp.A.4

A teacher at a high school conducted a survey of freshman and found that students had a curfew and of those students were also honor roll students. There were students that did not have a curfew, but were on honor roll. Last, they found that students did not have a curfew nor were on honor roll. Given this information, how many students do not have a curfew?

**Possible Answers:**

**Correct answer:**

The columns of the table will represent the students who have a curfew or do not have a curfew and the rows will contain the students who are on honor roll or are not on honor roll. The first bit of information that we were given from the question was that students had a curfew; therefore, needs to go in the "curfew" column as the row total. Next, we were told that of those students, were on honor roll; therefore, we need to put in the "curfew" column and in the "honor roll" row. Then, we were told that students do not have a curfew, but were on honor roll, so we need to put in the "no curfew" column and the "honor roll" row. Finally, we were told that students do not have a curfew or were on honor roll, so needs to go in the "no curfew" column and "no honor roll" row. If done correctly, you should create a table similar to the following:

Our question asked how many students did not have a curfew. We add up the numbers in the "no curfew" column to get the total:

This means that students do not have a curfew.

### Example Question #4 : Completing Incomplete Tables

A teacher at a high school conducted a survey of freshman and found that students had a curfew and of those students were also honor roll students. There were students that did not have a curfew, but were on honor roll. Last, they found that students did not have a curfew nor were on honor roll. Given this information, how many students were on honor roll?

**Possible Answers:**

**Correct answer:**

The columns of the table will represent the students who have a curfew or do not have a curfew and the rows will contain the students who are on honor roll or are not on honor roll. The first bit of information that we were given from the question was that students had a curfew; therefore, needs to go in the "curfew" column as the row total. Next, we were told that of those students, were on honor roll; therefore, we need to put in the "curfew" column and in the "honor roll" row. Then, we were told that students do not have a curfew, but were on honor roll, so we need to put in the "no curfew" column and the "honor roll" row. Finally, we were told that students do not have a curfew or were on honor roll, so needs to go in the "no curfew" column and "no honor roll" row. If done correctly, you should create a table similar to the following:

Our question asked how many students were on honor roll. We add up the numbers in the "honor roll" row to get the total:

This means that students were on honor roll.

### Example Question #6 : Use Data To Construct And Interpret A Two Way Table: Ccss.Math.Content.8.Sp.A.4

A middle school teacher conducted a survey of the grade class and found that students were athletes and of those students drink soda. There were students that were not athletes, but drank soda. Last, they found that students did not have a curfew nor were on honor roll. Given this information, how many students were athletes, but didn't drink soda?

**Possible Answers:**

**Correct answer:**

The columns of the table will represent the students who are athletes or are not athletes and the rows will contain the students who drink soda or do not drink soda. The first bit of information that we were given from the question was that students were athletes; therefore, needs to go in the "athlete" column as the row total. Next, we were told that of those students, drinks soda; therefore, we need to put in the "athlete" column and in the "drinks soda" row. Then, we were told that students were not athletes, but drink soda, so we need to put in the "not an athlete" column and the "drinks soda" row. Finally, we were told that students are not athletes or soda drinkers, so needs to go in the "not an athlete" column and "doesn't drink soda" row. If done correctly, you should create a table similar to the following:

Our question asked how many students are athletes, but don't drink soda. We can take the total number of students who are athletes, , and subtract the number of students who drink soda,

This means that students who are athletes, don't drink soda.

### Example Question #1 : Completing Incomplete Tables

A middle school teacher conducted a survey of the grade class and found that students were athletes and of those students drink soda. There were students that were not athletes, but drank soda. Last, they found that students neither drank soda nor were athletes. Given this information, how many students were not athletes?

**Possible Answers:**

**Correct answer:**

The columns of the table will represent the students who are athletes or are not athletes and the rows will contain the students who drink soda or do not drink soda. The first bit of information that we were given from the question was that students were athletes; therefore, needs to go in the "athlete" column as the row total. Next, we were told that of those students, drinks soda; therefore, we need to put in the "athlete" column and in the "drinks soda" row. Then, we were told that students were not athletes, but drink soda, so we need to put in the "not an athlete" column and the "drinks soda" row. Finally, we were told that students are not athletes or soda drinkers, so needs to go in the "not an athlete" column and "doesn't drink soda" row. If done correctly, you should create a table similar to the following:

Our question asked how many students were not athletes. We add up the numbers in the "not an athlete" column to get the total:

This means that students were not athletes.

### Example Question #2182 : Psat Mathematics

A middle school teacher conducted a survey of the grade class and found that students were athletes and of those students drink soda. There were students that were not athletes, but drank soda. Last, they found that students did not have a curfew nor were on honor roll. Given this information, how many students drink soda?

**Possible Answers:**

**Correct answer:**

The columns of the table will represent the students who are athletes or are not athletes and the rows will contain the students who drink soda or do not drink soda. The first bit of information that we were given from the question was that students were athletes; therefore, needs to go in the "athlete" column as the row total. Next, we were told that of those students, drinks soda; therefore, we need to put in the "athlete" column and in the "drinks soda" row. Then, we were told that students were not athletes, but drink soda, so we need to put in the "not an athlete" column and the "drinks soda" row. Finally, we were told that students are not athletes or soda drinkers, so needs to go in the "not an athlete" column and "doesn't drink soda" row. If done correctly, you should create a table similar to the following:

Our question asked how many students drink soda. We add up the numbers in the "drinks soda" row to get the total:

This means that students drink soda.