Interpreting Graphs & Tables - SAT Math
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The incomplete table above shows the percentage breakdown of athletes at a cross-country invitational meet at which 60% of the athletes were girls and 35% of the athletes represented their schools’ varsity teams. If there were 480 athletes, and twice as many of the girls were junior varsity team members than were varsity team members, how many athletes were boys on a junior varsity team?
The incomplete table above shows the percentage breakdown of athletes at a cross-country invitational meet at which 60% of the athletes were girls and 35% of the athletes represented their schools’ varsity teams. If there were 480 athletes, and twice as many of the girls were junior varsity team members than were varsity team members, how many athletes were boys on a junior varsity team?
The key to incomplete tables is the “total” designation for the bottom row and for the right-hand column. Here two of those cells are filled in for you, and they form your “foothold” for solving the rest. You know that 35% of all athletes were members of varsity teams, meaning that the Varsity Girls cell plus the Varsity Boys cell must equal 35%. That also tells you that, since the total has to add up to 100%, the JV Total cell must be 65% so that Varsity + JV can add to 100%. Similarly, you know that the Girls Total is 60%, meaning that the sum of Varsity Girls and JV Girls must add to 60%. And you also know that 40% of the total athletes were boys so that that column can add to 100%. Filling in what you know now, you have the bottom row and the right-most column filled in:
You’re also told that there are twice as many JV girls as varsity girls, which allows you to set up a system of equations: Varsity Girls + JV Girls = 60 JV Girls = 2(Varsity Girls) Therefore, you can conclude that the JV Girls cell is 40% and the Varsity Girls cell is 20%, which leads you another step closer to filling in the whole table:
Since each column needs to sum to its total in the bottom row, you can conclude that Varsity Boys = 15% and JV Boys = 25%. And since you’re responsible for the JV Boys number, you can now take that 25% and apply it to the total number of athletes, 480. 25% of 480 is 120, so the correct answer is “120.”
The key to incomplete tables is the “total” designation for the bottom row and for the right-hand column. Here two of those cells are filled in for you, and they form your “foothold” for solving the rest. You know that 35% of all athletes were members of varsity teams, meaning that the Varsity Girls cell plus the Varsity Boys cell must equal 35%. That also tells you that, since the total has to add up to 100%, the JV Total cell must be 65% so that Varsity + JV can add to 100%. Similarly, you know that the Girls Total is 60%, meaning that the sum of Varsity Girls and JV Girls must add to 60%. And you also know that 40% of the total athletes were boys so that that column can add to 100%. Filling in what you know now, you have the bottom row and the right-most column filled in:
You’re also told that there are twice as many JV girls as varsity girls, which allows you to set up a system of equations: Varsity Girls + JV Girls = 60 JV Girls = 2(Varsity Girls) Therefore, you can conclude that the JV Girls cell is 40% and the Varsity Girls cell is 20%, which leads you another step closer to filling in the whole table:
Since each column needs to sum to its total in the bottom row, you can conclude that Varsity Boys = 15% and JV Boys = 25%. And since you’re responsible for the JV Boys number, you can now take that 25% and apply it to the total number of athletes, 480. 25% of 480 is 120, so the correct answer is “120.”
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In a certain boutique shop for infant toys, 20% of toys are pink and the rest are blue. One half of the toys are made of wood and the rest are made of plastic. If 10% of the toys are pink, wooden toys, and 80 are blue, plastic toys, how many total toys are there?
In a certain boutique shop for infant toys, 20% of toys are pink and the rest are blue. One half of the toys are made of wood and the rest are made of plastic. If 10% of the toys are pink, wooden toys, and 80 are blue, plastic toys, how many total toys are there?
When we’re able to create an incomplete table using two categories of information, in this case, “wood vs. plastic” and “pink vs. blue,” we can fill out any third cell horizontally or vertically if we know the other two, since our interior cells sum to each total row/column. In this case, if we know that 10% of the toys are wood, pink toys, and 50% of all toys are wood, we can fill in the blue, wood column with 40%. Similarly, if we know that wood, pink toys are 10% and total pink toys are 20%, we can fill in pink, plastic toys with the remaining 10%.
From here, we can also fill out our other total categories as follows:
Now, we have several ways to prove that blue, plastic toys make up the remaining 40% of the toys. So, if 40% of our total is equal to 80 toys, we can solve for the total number of toys as follows:
40%(T) = 80
10%(T) = 20
T = 200
When we’re able to create an incomplete table using two categories of information, in this case, “wood vs. plastic” and “pink vs. blue,” we can fill out any third cell horizontally or vertically if we know the other two, since our interior cells sum to each total row/column. In this case, if we know that 10% of the toys are wood, pink toys, and 50% of all toys are wood, we can fill in the blue, wood column with 40%. Similarly, if we know that wood, pink toys are 10% and total pink toys are 20%, we can fill in pink, plastic toys with the remaining 10%.
From here, we can also fill out our other total categories as follows:
Now, we have several ways to prove that blue, plastic toys make up the remaining 40% of the toys. So, if 40% of our total is equal to 80 toys, we can solve for the total number of toys as follows:
40%(T) = 80
10%(T) = 20
T = 200
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Of the high school seniors at a particular school, 
are left-handed, and the rest are right-handed. 
of the students take the bus to school, and the rest do not. If 30 students are right-handed students who take the bus, and half of the left-handed students take the bus, how many total high school seniors are at the school?
Of the high school seniors at a particular school, 
From the initial information presented to us in the stem, we can create a two way table using the categories left vs. right-handed, and take the bus vs. do not take the bus. We can fill in the table as follows: (*note - be very cautious mixing percent/fraction information with actual value information. It may be easier to leave the “30” out of the table and solve for right-handed seniors who take the bus in terms of a fraction.)
From here, if we know that half of the students who are left-handed take the bus, we can split up the 
of our total that is left-handed into 
and 
.
If 
of the students take the bus, and 
of the students are left-handed students who take the bus, the remaining 
are right-handed students who take the bus. Since we know the value of right-handed students who take the bus is 30, and 
of our total students, the total number of students must be
*Note, we did not need to complete the entire table to answer this question, but we could! The rest of the table is as follows:
From the initial information presented to us in the stem, we can create a two way table using the categories left vs. right-handed, and take the bus vs. do not take the bus. We can fill in the table as follows: (*note - be very cautious mixing percent/fraction information with actual value information. It may be easier to leave the “30” out of the table and solve for right-handed seniors who take the bus in terms of a fraction.)
From here, if we know that half of the students who are left-handed take the bus, we can split up the 
If 
*Note, we did not need to complete the entire table to answer this question, but we could! The rest of the table is as follows:
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Of the students in a particular collegiate debate organization, 
are men and the rest are women. 
of the students are also a member of the chess club, and the rest are not. If 
of the men are members of the chess club, what fraction of the women were not members of the chess club?
Of the students in a particular collegiate debate organization, 
For questions where we’re exclusively given “scalable relationships” (for instance, fractions or percents) and we’re asked for a scalable relationship, we can pick a total to make the question more concrete and easier to work with!
When we’re given fractions, we’ll want to pick a total that is divisible by all the denominators present in the question stem. So, the least common multiple of our denominators will likely be a convenient and easy-to-work-with option. In this case, we’ll want to pick a total of 60, since 60 is divisible by 4, 3, and 5. From here, we can begin to fill in the table as follows:
From here, we can fill out our remaining information from the question stem, as well as the remaining totals:
Now, we’re able to fill in our remaining cells horizontally and vertically:
So, if we’re looking for what fraction of the women are not members of the chess team, we want 
, in this case 
.
For questions where we’re exclusively given “scalable relationships” (for instance, fractions or percents) and we’re asked for a scalable relationship, we can pick a total to make the question more concrete and easier to work with!
When we’re given fractions, we’ll want to pick a total that is divisible by all the denominators present in the question stem. So, the least common multiple of our denominators will likely be a convenient and easy-to-work-with option. In this case, we’ll want to pick a total of 60, since 60 is divisible by 4, 3, and 5. From here, we can begin to fill in the table as follows:
From here, we can fill out our remaining information from the question stem, as well as the remaining totals:
Now, we’re able to fill in our remaining cells horizontally and vertically:
So, if we’re looking for what fraction of the women are not members of the chess team, we want 
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A teacher at a high school conducted a survey of freshmen 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 the honor roll. Last, they found that 
students did not have a curfew nor were on the honor roll. Given this information, how many students were not on the honor roll?
A teacher at a high school conducted a survey of freshmen and found that
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 curfew or do not have a curfew and the rows will contain the students who are on the honor roll or are not on the 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 the 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 the 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 the 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 not on the honor roll. We add up the numbers in the "no honor roll" row to get the total, but first we need to fill in a gap in our table, students who have a curfew but were not on the honor roll. We can take the total number of students that have a curfew, 
, and subtract the number of students who are on the honor roll, 
This means that 
students who have a curfew, aren't on the honor roll.
Now, we add up the numbers in the "no honor roll" row to get the total:
This means that 
students were not on the honor roll.
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 curfew or do not have a curfew and the rows will contain the students who are on the honor roll or are not on the honor roll. The first bit of information that we were given from the question was that
Our question asked how many students were not on the honor roll. We add up the numbers in the "no honor roll" row to get the total, but first we need to fill in a gap in our table, students who have a curfew but were not on the honor roll. We can take the total number of students that have a curfew,
This means that
Now, we add up the numbers in the "no honor roll" row to get the total:
This means that
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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?
A teacher at a high school conducted a survey of seniors and found that
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.
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
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
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A teacher at a high school conducted a survey of freshmen 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 the honor roll. Last, they found that 
students did not have a curfew nor were on the honor roll. Given this information, how many students do not have a curfew?
A teacher at a high school conducted a survey of freshmen and found that
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 curfew or do not have a curfew and the rows will contain the students who are on the honor roll or are not on the 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 the 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 the 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 the 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.
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 curfew or do not have a curfew and the rows will contain the students who are on the honor roll or are not on the honor roll. The first bit of information that we were given from the question was that
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
Compare your answer with the correct one above
A teacher at a high school conducted a survey of freshmen 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 the honor roll. Last, they found that 
students did not have a curfew nor were on the honor roll. Given this information, how many students were on the honor roll?
A teacher at a high school conducted a survey of freshmen and found that
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 curfew or do not have a curfew and the rows will contain the students who are on the honor roll or are not on the 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 the 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 the 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 the 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 the honor roll. We add up the numbers in the "honor roll" row to get the total:
This means that 
students were on the honor roll.
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 curfew or do not have a curfew and the rows will contain the students who are on the honor roll or are not on the honor roll. The first bit of information that we were given from the question was that
Our question asked how many students were on the honor roll. We add up the numbers in the "honor roll" row to get the total:
This means that
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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 the honor roll. Given this information, how many students drink soda?
A middle school teacher conducted a survey of the
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 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.
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 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
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
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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 were neither athletes nor drank soda. Given this information, how many students don't drink soda?
A middle school teacher conducted a survey of the
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 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 don't drink soda. We add up the numbers in the "doesn't drink soda" row to get the total, but first, we need to fill in a gap in our table, students who were 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.
Now, we add up the numbers in the "doesn't drink soda" row to get the total:
This means that 
students don't drink soda.
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 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
Our question asked how many students don't drink soda. We add up the numbers in the "doesn't drink soda" row to get the total, but first, we need to fill in a gap in our table, students who were athletes, but don't drink soda. We can take the total number of students who are athletes,
This means that
Now, we add up the numbers in the "doesn't drink soda" row to get the total:
This means that
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The below tables show the way that a certain high school converts letter grades to numerical grades, and the math grades of a particular high school’s 65-person graduating class.
Which of the following best describes the data outlined in the tables?
The below tables show the way that a certain high school converts letter grades to numerical grades, and the math grades of a particular high school’s 65-person graduating class.
Which of the following best describes the data outlined in the tables?
This question is a great example of a case where the SAT might try to trap you into doing more work than is necessary. Since the problem asks you whether that mean is exactly 3.0, it is possible to determine this without tedious work. If the average were 3.0, the values on either side of the twelve B (3.0) grades would all even out. And they ALMOST do: there are 6 As (4.0 each) and 6 Cs (2.0 each, so those grades all average out to 3.0); there are 8 A-s and 8 C+s, so those grades (3.7 and 2.3) all average out to 3.0; and there are 11 B+s and 11 B-s, so those all average out to 3. On the list from A on down to C, all those grades average out to 3.0…but then there are the 3 C− grades, and those do not get “averaged out” by anything above an A. So without fully calculating, you can tell that the mean is lower than 3.0. So, we can eliminate “The mean math grade of the 65 students was 3.0.”
Since two of our options deal with the median, we can focus there next. The middle of the 65 terms will be the 33rd term (32 terms above it and 32 terms below it). So when you go from the top down and see that there are 25 grades from A through B+ and then 12 grades of B, you should see that the 33rd term will fall in that group of Bs. This means that the median is 3.0.
This knowledge allows us to both eliminate “The median math grade of the 65 students is less than a 3.0” and select “The median math grade of the 65 students is higher than the mean math grade of the 65 students.” Since the mean is somewhat less than 3.0, and the median *is* 3.0, the mean is less than the median.
“If three new students were added to the class and each scored an A, the new class average would be greater than or equal to 3.0” can be eliminated on the logic of the first paragraph: The 62 grades from A down to C all average out to a 3.0, leaving the three C− grades of 1.7 to weigh down that average. In order to balance three 1.7s you’d need three 4.3s; three 4.0s, as this option presents, aren’t quite enough, so the average would still be below 3.0.
This question is a great example of a case where the SAT might try to trap you into doing more work than is necessary. Since the problem asks you whether that mean is exactly 3.0, it is possible to determine this without tedious work. If the average were 3.0, the values on either side of the twelve B (3.0) grades would all even out. And they ALMOST do: there are 6 As (4.0 each) and 6 Cs (2.0 each, so those grades all average out to 3.0); there are 8 A-s and 8 C+s, so those grades (3.7 and 2.3) all average out to 3.0; and there are 11 B+s and 11 B-s, so those all average out to 3. On the list from A on down to C, all those grades average out to 3.0…but then there are the 3 C− grades, and those do not get “averaged out” by anything above an A. So without fully calculating, you can tell that the mean is lower than 3.0. So, we can eliminate “The mean math grade of the 65 students was 3.0.”
Since two of our options deal with the median, we can focus there next. The middle of the 65 terms will be the 33rd term (32 terms above it and 32 terms below it). So when you go from the top down and see that there are 25 grades from A through B+ and then 12 grades of B, you should see that the 33rd term will fall in that group of Bs. This means that the median is 3.0.
This knowledge allows us to both eliminate “The median math grade of the 65 students is less than a 3.0” and select “The median math grade of the 65 students is higher than the mean math grade of the 65 students.” Since the mean is somewhat less than 3.0, and the median *is* 3.0, the mean is less than the median.
“If three new students were added to the class and each scored an A, the new class average would be greater than or equal to 3.0” can be eliminated on the logic of the first paragraph: The 62 grades from A down to C all average out to a 3.0, leaving the three C− grades of 1.7 to weigh down that average. In order to balance three 1.7s you’d need three 4.3s; three 4.0s, as this option presents, aren’t quite enough, so the average would still be below 3.0.
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The below tables show the way that a certain high school converts letter grades to numerical grades, and the math grades of a particular high school’s 65-person graduating class.
Henry, one of the students at the school, wants to achieve a 3.5-grade point average or better for the semester. If he takes five classes, and his grades for four of them are A−, A−, B+, and B, what is the lowest grade that he can receive for his fifth class and still achieve his goal?
The below tables show the way that a certain high school converts letter grades to numerical grades, and the math grades of a particular high school’s 65-person graduating class.
Henry, one of the students at the school, wants to achieve a 3.5-grade point average or better for the semester. If he takes five classes, and his grades for four of them are A−, A−, B+, and B, what is the lowest grade that he can receive for his fifth class and still achieve his goal?
This question is an excellent example of a case where the SAT might try to trap us into doing more math than needed. If Henry’s current grades are 3.7, 3.7, 3.3, and 3.0, his current average GPA is lower than needed for him to achieve his goal. (3.7 and 3.3 average to 3.5, so 3.7 and 3.0 will average to lower than 3.5, making his current GPA lower than needed to reach his goal.) So, his final grade needs to bring his average *up* and bridge the gap between his current, below 3.5, average, and his goal. Only “A” has the potential to do so. Keep in mind - A- wasn’t even in the running! So, before you go to tackle complex calculations, make sure you keep in mind that the answer choices are a part of the question, and you’ll want to take a look at what options are even possible before doing the math.
This question is an excellent example of a case where the SAT might try to trap us into doing more math than needed. If Henry’s current grades are 3.7, 3.7, 3.3, and 3.0, his current average GPA is lower than needed for him to achieve his goal. (3.7 and 3.3 average to 3.5, so 3.7 and 3.0 will average to lower than 3.5, making his current GPA lower than needed to reach his goal.) So, his final grade needs to bring his average *up* and bridge the gap between his current, below 3.5, average, and his goal. Only “A” has the potential to do so. Keep in mind - A- wasn’t even in the running! So, before you go to tackle complex calculations, make sure you keep in mind that the answer choices are a part of the question, and you’ll want to take a look at what options are even possible before doing the math.
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The table below displays the class status and declared major for the 37,500 undergraduate students at a state university.
Of the freshmen who have declared a major, approximately what percent have chosen a major in the sciences?
The table below displays the class status and declared major for the 37,500 undergraduate students at a state university.
Of the freshmen who have declared a major, approximately what percent have chosen a major in the sciences?
You only care about the freshmen who have declared a major. That means that you need to look at Freshmen-Sciences; Freshmen-Arts; and FreshmenProfessional. As you approach table problems on the SAT, it is important to focus on the question first and then on the table; often the table has much more information than you actually need.
Here, of the freshmen who have declared a major, 1875 are science majors, 1476 are arts majors, and 284 are majoring in a professional degree program. This should allow you to get by with an estimate: the number of “non-science majors” declared is going to be between 1700 and 1800 and the number of science majors is 1875. That should tell you that freshman science majors make up just a little more than half of all freshman declared majors, so 51% is the only answer choice that makes sense.
You only care about the freshmen who have declared a major. That means that you need to look at Freshmen-Sciences; Freshmen-Arts; and FreshmenProfessional. As you approach table problems on the SAT, it is important to focus on the question first and then on the table; often the table has much more information than you actually need.
Here, of the freshmen who have declared a major, 1875 are science majors, 1476 are arts majors, and 284 are majoring in a professional degree program. This should allow you to get by with an estimate: the number of “non-science majors” declared is going to be between 1700 and 1800 and the number of science majors is 1875. That should tell you that freshman science majors make up just a little more than half of all freshman declared majors, so 51% is the only answer choice that makes sense.
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The chart above shows the cumulative fundraising totals, in thousands of dollars, for each of five regions. If the charity has a total fundraising goal of one million dollars for the year, approximately what percent of its goal had the charity achieved by September 30?
The chart above shows the cumulative fundraising totals, in thousands of dollars, for each of five regions. If the charity has a total fundraising goal of one million dollars for the year, approximately what percent of its goal had the charity achieved by September 30?
As you’ve learned by now, you should look specifically at the question that you’re being asked before you get too concerned with the numbers in each cell. Since you’re asked about the amount raised by September 30, you’re really only concerned with the rightmost column. The sum of the cells in that column is just above 900 (you can use your calculator to add them up, or you can look at the answer choices and realize that you can get away with an estimate).
But what does that ∼900 figure represent? Twice in the problem – in the title of the table at the top and in the question stem below the table – the phrase “in thousands of dollars” appears. This means that the figure 900 actually represents approximately $900,000. So the percentage of the $1,000,000 that the charity has raised is just above 90% of the goal, making “91%” the only plausible option.
As you’ve learned by now, you should look specifically at the question that you’re being asked before you get too concerned with the numbers in each cell. Since you’re asked about the amount raised by September 30, you’re really only concerned with the rightmost column. The sum of the cells in that column is just above 900 (you can use your calculator to add them up, or you can look at the answer choices and realize that you can get away with an estimate).
But what does that ∼900 figure represent? Twice in the problem – in the title of the table at the top and in the question stem below the table – the phrase “in thousands of dollars” appears. This means that the figure 900 actually represents approximately $900,000. So the percentage of the $1,000,000 that the charity has raised is just above 90% of the goal, making “91%” the only plausible option.
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The table below displays the class status and declared major for the 37,500 undergraduate students at a state university.
For which class rank (freshman/sophomore/junior/senior/5th) is the ratio of arts majors to science majors the highest?
The table below displays the class status and declared major for the 37,500 undergraduate students at a state university.
For which class rank (freshman/sophomore/junior/senior/5th) is the ratio of arts majors to science majors the highest?
The two columns that matter are the arts column and the science column, and you’re looking for the highest ratio of arts to sciences. Furthermore, with five rows and only four answer choices, a quick scan should tell you that you don’t need to worry about the last “5th year” row, because it doesn’t match an answer choice. Since arts is less than science for freshmen but greater for the next three rows, you can quickly eliminate “freshman.” Additionally, since the totals are far apart (by more than a thousand) for sophomores and seniors but quite close together for juniors, you should focus your attention on the sophomores and seniors rows and can eliminate “junior” as well. Here, again, a relatively quick estimate should show you that the ratio will be bigger for sophomores than for seniors: for sophomores the difference between the two categories is higher and the number of science majors is lower, suggesting that the ratio will be much higher. Thus, our correct answer is “sophomore”.
The two columns that matter are the arts column and the science column, and you’re looking for the highest ratio of arts to sciences. Furthermore, with five rows and only four answer choices, a quick scan should tell you that you don’t need to worry about the last “5th year” row, because it doesn’t match an answer choice. Since arts is less than science for freshmen but greater for the next three rows, you can quickly eliminate “freshman.” Additionally, since the totals are far apart (by more than a thousand) for sophomores and seniors but quite close together for juniors, you should focus your attention on the sophomores and seniors rows and can eliminate “junior” as well. Here, again, a relatively quick estimate should show you that the ratio will be bigger for sophomores than for seniors: for sophomores the difference between the two categories is higher and the number of science majors is lower, suggesting that the ratio will be much higher. Thus, our correct answer is “sophomore”.
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A census bureau has modeled the population change of two cities, City A and City B, and published the graphs of the models as shown above. The graphs display population (p) over time (t), and the mathematical models use the variables p (population), B (beginning population as of the initial census in the year 1900), x (annual percent change), and y (number of years). Which of the following pairs of equations best explains the relationships demonstrated in the graphs?
A census bureau has modeled the population change of two cities, City A and City B, and published the graphs of the models as shown above. The graphs display population (p) over time (t), and the mathematical models use the variables p (population), B (beginning population as of the initial census in the year 1900), x (annual percent change), and y (number of years). Which of the following pairs of equations best explains the relationships demonstrated in the graphs?
The SAT will frequently test you on your ability to recognize concepts with word problems, graphs, and equations. Here the algebra in each answer choice – and the assignment of variables in the problem – looks messy, but the SAT is essentially testing whether you can recognize what type of change is occurring within each city. From the graphs you should see that City A is increasing in population and that City B is decreasing. So you’ll want the rate of change (x) to be added for City A and to be subtracted for City B. And here is where the algebraic terms “linear” and “exponential” really come to life in graphical form: you should see that City A’s graph forms a straight line, meaning that it’s a linear increase. City B’s graph is curved, suggesting a nonlinear, exponential decrease. A linear increase means that you add the same amount each period. That means that the same amount (x% of the starting value) is added each year. For an exponential change, as with City B, the exponent shows that the change is compounded. So you need addition for City A and subtraction for City B, with a linear (times y) function for City A and an exponential function (to the y power) for City B. The only option that satisfies these conditions is:
The SAT will frequently test you on your ability to recognize concepts with word problems, graphs, and equations. Here the algebra in each answer choice – and the assignment of variables in the problem – looks messy, but the SAT is essentially testing whether you can recognize what type of change is occurring within each city. From the graphs you should see that City A is increasing in population and that City B is decreasing. So you’ll want the rate of change (x) to be added for City A and to be subtracted for City B. And here is where the algebraic terms “linear” and “exponential” really come to life in graphical form: you should see that City A’s graph forms a straight line, meaning that it’s a linear increase. City B’s graph is curved, suggesting a nonlinear, exponential decrease. A linear increase means that you add the same amount each period. That means that the same amount (x% of the starting value) is added each year. For an exponential change, as with City B, the exponent shows that the change is compounded. So you need addition for City A and subtraction for City B, with a linear (times y) function for City A and an exponential function (to the y power) for City B. The only option that satisfies these conditions is:
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Which of the following expresses a strong positive correlation between W and T?
Which of the following expresses a strong positive correlation between W and T?
To express a positive correlation, as one component (our “x” axis) goes up, the other (our “y” axis) should also increase. In this case, both of the below options accomplish this to some extent:
However, of these options, the first clearly carries a closer positive relationship that appears more linear and consistent in the increasing nature of both components. Thus, it is our correct answer.
To express a positive correlation, as one component (our “x” axis) goes up, the other (our “y” axis) should also increase. In this case, both of the below options accomplish this to some extent:
However, of these options, the first clearly carries a closer positive relationship that appears more linear and consistent in the increasing nature of both components. Thus, it is our correct answer.
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Which of the following would be the most appropriate label for the y-axis of this graph if the total number of farmed animals in 2002 was closest to 9 billion?
Which of the following would be the most appropriate label for the y-axis of this graph if the total number of farmed animals in 2002 was closest to 9 billion?
If we use some relative math to draw conclusions, we can see that adding the totals for each month gets us to around 9,000. However, the prompt tells us that the total consumption of farmed animals was 9 billion. So, we need to multiply each of our values by one million (1,000,000) to achieve this total. Thus, the y axis gives us the number of animals in millions.
If we use some relative math to draw conclusions, we can see that adding the totals for each month gets us to around 9,000. However, the prompt tells us that the total consumption of farmed animals was 9 billion. So, we need to multiply each of our values by one million (1,000,000) to achieve this total. Thus, the y axis gives us the number of animals in millions.
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The table above gives the weight change measurements of 9 laboratory rats that were fed different diets under a variety of conditions over 30 days.
After all of the measurements were taken for the nine rats, researchers discovered that the scale used to measure the rats at the close of the experiment under weighed all of them by exactly 5 grams. Which of the following statistical values would change after 5 grams are added to each of the measurements above?
The table above gives the weight change measurements of 9 laboratory rats that were fed different diets under a variety of conditions over 30 days.
After all of the measurements were taken for the nine rats, researchers discovered that the scale used to measure the rats at the close of the experiment under weighed all of them by exactly 5 grams. Which of the following statistical values would change after 5 grams are added to each of the measurements above?
In this case, if we add 5 to each of the numbers in the table above, the dispersion of the set remains the same (all values remain the same distance from one another that they started out at, and just shift 5 up on the number line). However, if I add 5 to each value, the sum of my values will increase, and thus the average/mean (the sum of numbers/number of numbers) will also increase. Thus, “mean” is our correct answer.
In this case, if we add 5 to each of the numbers in the table above, the dispersion of the set remains the same (all values remain the same distance from one another that they started out at, and just shift 5 up on the number line). However, if I add 5 to each value, the sum of my values will increase, and thus the average/mean (the sum of numbers/number of numbers) will also increase. Thus, “mean” is our correct answer.
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The graph above displays the charge “C” in dollars of riding a taxi for “M” miles.
According to the graph, what does the C-intercept represent?
The graph above displays the charge “C” in dollars of riding a taxi for “M” miles.
According to the graph, what does the C-intercept represent?
Since the “C” intercept refers to the constant in the linear equation expressed by this graph, it doesn’t make sense for the intercept to refer to a charge “per” any other unknown, whether that unknown is miles or quarter miles. We know that the intercept cannot refer to miles driven, as that has been expressed to us as “M” in this linear relationship. The “C” intercept can, however, refer to an up-front fee assessed regardless of miles driven, as is expressed in our correct answer, “The initial fee of the taxi, regardless of miles driven.”
Since the “C” intercept refers to the constant in the linear equation expressed by this graph, it doesn’t make sense for the intercept to refer to a charge “per” any other unknown, whether that unknown is miles or quarter miles. We know that the intercept cannot refer to miles driven, as that has been expressed to us as “M” in this linear relationship. The “C” intercept can, however, refer to an up-front fee assessed regardless of miles driven, as is expressed in our correct answer, “The initial fee of the taxi, regardless of miles driven.”
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