Data Analysis and Probability - ISEE Upper Level Quantitative Reasoning
Card 0 of 592
The following Venn diagram depicts the number of students who play hockey, football, and baseball. How many students play football and baseball?
The following Venn diagram depicts the number of students who play hockey, football, and baseball. How many students play football and baseball?
The number of students who play football or baseball can by finding the summer of the number of students who play football alone, baseball alone, baseball and football, and all three sports.
The number of students who play football or baseball can by finding the summer of the number of students who play football alone, baseball alone, baseball and football, and all three sports.
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A class of 
students was asked whether they have cats, dogs, or both.The results are depicted in the following Venn diagram. How many students do not have a dog?
A class of
First, calculate the number of students with a dog:
Next, subtract the number of students with a dog from the total number of students.
First, calculate the number of students with a dog:
Next, subtract the number of students with a dog from the total number of students.
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If a standard die is rolled, what is the probability of getting a 1 or a 2?
If a standard die is rolled, what is the probability of getting a 1 or a 2?
We need to know the total number of possibilities, and the total number of ways to achieve our goal.
A standard die has 6 faces, so there are a total of 6 numbers that we could roll.
We want to roll a 1 or a 2, which means there are 2 ways that we can succeed (rolling a 1 or a 2).
Thus, we have a probability of success as $\frac{2}{6}$ which reduces to $\frac{1}{3}$.
We need to know the total number of possibilities, and the total number of ways to achieve our goal.
A standard die has 6 faces, so there are a total of 6 numbers that we could roll.
We want to roll a 1 or a 2, which means there are 2 ways that we can succeed (rolling a 1 or a 2).
Thus, we have a probability of success as $\frac{2}{6}$ which reduces to $\frac{1}{3}$.
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The beverage menu from a restaurant reads as follows:
Ten friends go out for drinks. They order four sodas, two coffees, two iced teas, a milk, and a hot tea. One of the ten agrees to leave the entire amount of the tip, which is to be 20% of the check. What is the amount of the tip (round to the nearest dime)?
The beverage menu from a restaurant reads as follows:
Ten friends go out for drinks. They order four sodas, two coffees, two iced teas, a milk, and a hot tea. One of the ten agrees to leave the entire amount of the tip, which is to be 20% of the check. What is the amount of the tip (round to the nearest dime)?
The costs of the beverages will be as follows:
Add these amounts:
20% of $14.40 is 
, or $2.90 when rounded to the nearest dime.
The costs of the beverages will be as follows:
Add these amounts:
20% of $14.40 is
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The following is a portion of the menu at a coffee shop:
A boss treats her employees to coffee at this coffee shop. She orders three lattes, three Americanos, two espressos, a cappucino, and a Turkish coffee. The tax is 
. The boss hands the cashier a 
bill. How much change will she get back?
The following is a portion of the menu at a coffee shop:
A boss treats her employees to coffee at this coffee shop. She orders three lattes, three Americanos, two espressos, a cappucino, and a Turkish coffee. The tax is
Add the prices of the ten items:
of this is 
, so the tax is 
The price of the beverages after tax is 
.
The change out of a 
bill is 
.
Add the prices of the ten items:
The price of the beverages after tax is
The change out of a
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Refer to the above circle graph. There are 
voters registered as independents in Smith County; to the nearest hundred, how many voters in all are registered?
Refer to the above circle graph. There are
Set 
to the number of voters total. 
of them are independent - these number 
, so we can set up the equation:
, so the correct choice is 
.
Set
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Refer to the above graph, which shows the high temperatures in the town of Smithville over seven days.
Which day of this week saw the highest peak temperature?
Refer to the above graph, which shows the high temperatures in the town of Smithville over seven days.
Which day of this week saw the highest peak temperature?
The highest point on the line graph is located at Tuesday.
The highest point on the line graph is located at Tuesday.
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Refer to the above graph, which shows the high temperatures in the town of Smithville over seven days.
On how many days that week did Smithville see a peak temperature 75 degrees or greater?
Refer to the above graph, which shows the high temperatures in the town of Smithville over seven days.
On how many days that week did Smithville see a peak temperature 75 degrees or greater?
There were four days that saw a peak temperature of 75 degrees or greater:
Monday: 76 degrees
Tuesday: 80 degrees
Wednesday: 77 degrees
Friday: 78 degrees
There were four days that saw a peak temperature of 75 degrees or greater:
Monday: 76 degrees
Tuesday: 80 degrees
Wednesday: 77 degrees
Friday: 78 degrees
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Nine students are running for student council; each member of the student body will vote for four. Freida's boyfriend Greg is running and she wants to vote for him. How many ways can she cast a ballot so that she can include Greg among her choices?
Nine students are running for student council; each member of the student body will vote for four. Freida's boyfriend Greg is running and she wants to vote for him. How many ways can she cast a ballot so that she can include Greg among her choices?
Since Freida has already chosen one of the nine candidates, she will choose three of the remaining eight, Since order is unimportant, the number of ways to do this is the number of combinations of three chosen from eight.
Since Freida has already chosen one of the nine candidates, she will choose three of the remaining eight, Since order is unimportant, the number of ways to do this is the number of combinations of three chosen from eight.
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The above is an annual income tax table for a given state. Married couples will pay the tax rate for the tax bracket in which their entire income falls.
Mr. Jackson earned $34,287 last year; Mrs. Jackson earned $25,879. How much will the couple pay in income tax for that year (nearest hundred dollars)?
The above is an annual income tax table for a given state. Married couples will pay the tax rate for the tax bracket in which their entire income falls.
Mr. Jackson earned $34,287 last year; Mrs. Jackson earned $25,879. How much will the couple pay in income tax for that year (nearest hundred dollars)?
The Jackson's income totaled
.
This puts them in the 1.7% tax bracket, so they will pay
in taxes.
The correct response is $1,000.
The Jackson's income totaled
This puts them in the 1.7% tax bracket, so they will pay
The correct response is $1,000.
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Washington Elementary School has seven eighth-grade teachers; each teacher has the number of boys and girls listed above.
An eighth-grade girl has transferred from another school. It is desired that no teacher have more than thirty students overall or eighteen girls in his or her class. Of the seven teachers, how many could accept the girl into his or her class?
Washington Elementary School has seven eighth-grade teachers; each teacher has the number of boys and girls listed above.
An eighth-grade girl has transferred from another school. It is desired that no teacher have more than thirty students overall or eighteen girls in his or her class. Of the seven teachers, how many could accept the girl into his or her class?
We can eliminate Cermak and Georghiou immediately since each has eighteen girls in his class. Of the other five:
Adams has 
students;
Boyer has 
students;
Donovan has 
students;
Esterhaus has 
students;
Finnegan has 
students.
Only Mrs. Finnegan's class could accept the new girl without going against the wishes of the school. The correct response is one.
We can eliminate Cermak and Georghiou immediately since each has eighteen girls in his class. Of the other five:
Adams has
Boyer has
Donovan has
Esterhaus has
Finnegan has
Only Mrs. Finnegan's class could accept the new girl without going against the wishes of the school. The correct response is one.
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Jefferson Elementary School has seven eighth-grade teachers; each teacher has the number of boys and girls listed above.
How many teachers have classes in which at least 40% of the students are boys?
Jefferson Elementary School has seven eighth-grade teachers; each teacher has the number of boys and girls listed above.
How many teachers have classes in which at least 40% of the students are boys?
Five teachers each have 30 students, and 40% of 30 is
.
Two teachers each have 29 students, and 40% of 29 is
.
Therefore, to have a class that is at least 40% boys, a teacher must have 12 boys at minimum. Only Mr. Georghiou does not have at least 12 boys, so the correct response is six.
Five teachers each have 30 students, and 40% of 30 is
Two teachers each have 29 students, and 40% of 29 is
Therefore, to have a class that is at least 40% boys, a teacher must have 12 boys at minimum. Only Mr. Georghiou does not have at least 12 boys, so the correct response is six.
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Determine the median of the following seven test scores:
Determine the median of the following seven test scores:
To determine the median of a set of numbers, you first need to order them from least to greatest:
Since there is an odd number of scores, the median is the score that falls exactly in the middle of the new list. Thus, the median is 88.
To determine the median of a set of numbers, you first need to order them from least to greatest:
Since there is an odd number of scores, the median is the score that falls exactly in the middle of the new list. Thus, the median is 88.
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Adams Elementary School has seven fifth-grade teachers; each teacher has been assigned the number of boys and girls listed above.
However, just before the start of the school year, Mrs. Henry has been hired as an additional fifth-grade teacher. It is desired that some students be reassigned to her class so that each class have the same number of students, or as close to the same number of students as possible. If this is done, how many students will be in Mrs. Henry's class?
Adams Elementary School has seven fifth-grade teachers; each teacher has been assigned the number of boys and girls listed above.
However, just before the start of the school year, Mrs. Henry has been hired as an additional fifth-grade teacher. It is desired that some students be reassigned to her class so that each class have the same number of students, or as close to the same number of students as possible. If this is done, how many students will be in Mrs. Henry's class?
This problem is essentially figuring out what will be the average number of students in each class if there are eight teachers instead of seven.
Add the fourteen numbers in the table:
students.
If there are eight teachers, then each teacher, including Mrs. Henry, will have
students.
This problem is essentially figuring out what will be the average number of students in each class if there are eight teachers instead of seven.
Add the fourteen numbers in the table:
If there are eight teachers, then each teacher, including Mrs. Henry, will have
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A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.
What percent of the tiles are marked with consonants?
Note: for purposes of this question, "Y" is a consonant.
A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.
What percent of the tiles are marked with consonants?
Note: for purposes of this question, "Y" is a consonant.
Counting the number of tiles with vowels is much easier.
Out of the 100 tiles, there are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles. This is a total of
tiles out of 100.
There are also two blanks, so the number of tiles marked with consonants is
56 out of 100 is 56%.
Counting the number of tiles with vowels is much easier.
Out of the 100 tiles, there are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles. This is a total of
tiles out of 100.
There are also two blanks, so the number of tiles marked with consonants is
56 out of 100 is 56%.
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A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.
What percent of the vowel tiles are marked with an "A"? (Nearest whole percent).
Note: for purposes of this question, "Y" is a consonant.
A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.
What percent of the vowel tiles are marked with an "A"? (Nearest whole percent).
Note: for purposes of this question, "Y" is a consonant.
There are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles. This is a total of
vowel tiles.
Out of these tiles, 9 are marked with an "E"; this is
.
This rounds to 21%.
There are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles. This is a total of
vowel tiles.
Out of these tiles, 9 are marked with an "E"; this is
This rounds to 21%.
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A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.
All of the consonant tiles are placed in a box. It is desired to place just enough of the vowel tiles so that the probability of drawing a vowel is 
. How many vowels must be placed in the box?
Note: for purposes of this question, "Y" is a consonant.
A popular word game uses one hundred tiles, each of which is marked with a letter or a blank. The distribution of the tiles is shown above, with each letter paired with the number of tiles marked with that letter. Notice that there are two blank tiles.
All of the consonant tiles are placed in a box. It is desired to place just enough of the vowel tiles so that the probability of drawing a vowel is
Note: for purposes of this question, "Y" is a consonant.
There are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles. This is a total of
There are also two blanks, so the number of tiles marked with consonants is
.
For the probability of drawing a vowel tile to be 
, the ratio of consonant tiles to vowel tiles must be
- that is, 2 to 1.
If we let 
stand for the number of vowel tiles to be added, then
vowel tiles.
There are nine "A" tiles, twelve "E" tiles, nine "I" tiles, eight "O" tiles, and four "U" tiles. This is a total of
There are also two blanks, so the number of tiles marked with consonants is
For the probability of drawing a vowel tile to be
If we let
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Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period. The temperatures at left are given in degrees Fahrenheit.
Temperatures given in degrees Fahrenheit can be converted to the Celsius scale using the formula
Express the highest temperature of the week in degrees Celsius (nearest whole degree).
Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period. The temperatures at left are given in degrees Fahrenheit.
Temperatures given in degrees Fahrenheit can be converted to the Celsius scale using the formula
Express the highest temperature of the week in degrees Celsius (nearest whole degree).
As can be seen below, the highest temperature for the week was 78 degrees Fahrenheit, on Tuesday.
To convert this to degrees Celsius, set 
and substitute in the given formula:
. The correct choice is 
.
As can be seen below, the highest temperature for the week was 78 degrees Fahrenheit, on Tuesday.
To convert this to degrees Celsius, set
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Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period.
The high temperature on Wednesday occurred at 1:00 PM; the low temperature, at the end of the day (midnight). The temperature drop was steady. What was the average drop in temperature per hour between 1:00 PM and midnight (nearest tenth of a second)?
Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period.
The high temperature on Wednesday occurred at 1:00 PM; the low temperature, at the end of the day (midnight). The temperature drop was steady. What was the average drop in temperature per hour between 1:00 PM and midnight (nearest tenth of a second)?
As can be seen in the diagram below, the high and low temperatures on Wednesday were, respectively, 74 and 60 degrees, for a drop of 
degrees.
This drop occurred over a period of 
hours, for an average drop of
degrees per hour. The quotient of this is seen below:
This rounds to 1.3 seconds.
As can be seen in the diagram below, the high and low temperatures on Wednesday were, respectively, 74 and 60 degrees, for a drop of
This drop occurred over a period of
degrees per hour. The quotient of this is seen below:
This rounds to 1.3 seconds.
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Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period.
Between which two consecutive days did the high temperature show an increase?
Refer to the above graph, which shows the high and low temperatures for Kingdom City over a one-week period.
Between which two consecutive days did the high temperature show an increase?
Examining the high temperature line, it can be seen that, among the four choices given, only the segment connecting Monday to Tuesday has a positive slope (lower left to upper right).
Therefore, of the four choices, Monday to Tuesday is correct.
Examining the high temperature line, it can be seen that, among the four choices given, only the segment connecting Monday to Tuesday has a positive slope (lower left to upper right).
Therefore, of the four choices, Monday to Tuesday is correct.
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