Data Analysis - ISEE Lower Level Quantitative Reasoning
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If Jill likes blue, yellow, tan and green, and Doug likes red, tan, black and green, which Venn diagram is correct?
If Jill likes blue, yellow, tan and green, and Doug likes red, tan, black and green, which Venn diagram is correct?
The middle portion of the diagram is the area that both circles share, so the color name that belongs in both circles should go in the middle area. Doug and Jill both like green and tan, so those colors should go in the middle. Only Jill likes blue and yellow, so these go on Jill's side. Only Doug likes red and black, so these go on Doug's side.
The middle portion of the diagram is the area that both circles share, so the color name that belongs in both circles should go in the middle area. Doug and Jill both like green and tan, so those colors should go in the middle. Only Jill likes blue and yellow, so these go on Jill's side. Only Doug likes red and black, so these go on Doug's side.
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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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Thirty people are surveyed concerning their color preference. Eighteen people like blue, twenty-one like pink, and six don't like either color. How many people like both colors?
Thirty people are surveyed concerning their color preference. Eighteen people like blue, twenty-one like pink, and six don't like either color. How many people like both colors?
Start by removing the number who don't like either from the total number of peole surveyed:
Using set notation we get:
, or the number of people who like both colors, 
, is equal to the number of people who like blue, 
, plus the number of people who like pink, 
, minus the number of people who like both blue and pink, 
.
Start by removing the number who don't like either from the total number of peole surveyed:
Using set notation we get:
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Twenty-five students were surveyed concerning a classroom pet. Thirteen students wanted a lizard, fifteen wanted a frog, and five didnt want a pet at all. How many students wanted both a lizard and a frog?
Twenty-five students were surveyed concerning a classroom pet. Thirteen students wanted a lizard, fifteen wanted a frog, and five didnt want a pet at all. How many students wanted both a lizard and a frog?
Start by removing the number who don't like either from the total number of students surveyed:
Using set notation we get:
, or the number of people who like both pets, 
, is equal to the number of people who like frogs, 
, plus the number of people who like lizards, 
, minus the number of people who like both frogs and lizards, 
.
Start by removing the number who don't like either from the total number of students surveyed:
Using set notation we get:
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Fifty people were surveyed. Twenty-three people liked the baseball team from Chicago, thirty-five like the baseball team from St. Louis, and ten don't like either team. How many people like both teams?
Fifty people were surveyed. Twenty-three people liked the baseball team from Chicago, thirty-five like the baseball team from St. Louis, and ten don't like either team. How many people like both teams?
Start by removing the number who don't like either team from the total number of people surveyed:
Using set notation we get:
, or the number of people who like both teams, 
, is equal to the number of people who like the Cubs, 
, plus the number of people who like the Cardinals, 
, minus the number of people who like both teams, 
.
Start by removing the number who don't like either team from the total number of people surveyed:
Using set notation we get:
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Twenty-five students are surveyed. Twelve students like math, fifteen like science, and six don't like either subject. How many students like both math and science?
Twenty-five students are surveyed. Twelve students like math, fifteen like science, and six don't like either subject. How many students like both math and science?
Start by removing the number who don't like either from the total number of students surveyed:
Using set notation we have:
, or the number of people who like both subjects, 
, is equal to the number of people who like math, 
, plus the number of people who like science, 
, minus the number of people who like both math and science 
.
Start by removing the number who don't like either from the total number of students surveyed:
Using set notation we have:
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Fifty people are surveyed at the zoo. Thirty-seven liked the Great Apes, twenty-two liked the Reptile House, and eleven didn't like either. How many people liked both the Great Apes and the Reptile House?
Fifty people are surveyed at the zoo. Thirty-seven liked the Great Apes, twenty-two liked the Reptile House, and eleven didn't like either. How many people liked both the Great Apes and the Reptile House?
Start by removing the number who don't like either from the total number of people surveyed:
Using set notation we have:
, or the number of people who like both animals, 
, is equal to the number of people who like apes, 
, plus the number of people who like reptiles, 
, minus the number of people who like both apes and lizards, 
.
Start by removing the number who don't like either from the total number of people surveyed:
Using set notation we have:
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Use the following Venn Diagram to answer the question.
What hobbies to both Andy and Mary enjoy?
Use the following Venn Diagram to answer the question.
What hobbies to both Andy and Mary enjoy?
A Venn Diagram is made up of two circles. Each circle represents something, and the section where they intersect shows what those two circles have in common. So, in the Venn Diagram
we can see Andy's hobbies on the left and Mary's hobbies on the right. The section in the middle shows the hobbies Andy and Mary have in common.
So, to answer the question, what hobbies do Andy and Mary have in common, we can see that they both enjoy eating and singing.
A Venn Diagram is made up of two circles. Each circle represents something, and the section where they intersect shows what those two circles have in common. So, in the Venn Diagram
we can see Andy's hobbies on the left and Mary's hobbies on the right. The section in the middle shows the hobbies Andy and Mary have in common.
So, to answer the question, what hobbies do Andy and Mary have in common, we can see that they both enjoy eating and singing.
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Use the following Venn Diagram to answer the question.
What hobbies do Andy and Mary have in common?
Use the following Venn Diagram to answer the question.
What hobbies do Andy and Mary have in common?
Let's look at the Venn Diagram.
We can see the first circle contains Andy's hobbies, and the second circle contains Mary's hobbies. The place in the middle, where the 2 circles intersect, shows the hobbies that both Andy and Mary enjoy. Or the hobbies they have in common. You can see they are a part of each person's circle.
So, the hobbies that are in the middle are eating and singing. Therefore, the hobbies that Andy and Mary have in common are eating and singing.
Let's look at the Venn Diagram.
We can see the first circle contains Andy's hobbies, and the second circle contains Mary's hobbies. The place in the middle, where the 2 circles intersect, shows the hobbies that both Andy and Mary enjoy. Or the hobbies they have in common. You can see they are a part of each person's circle.
So, the hobbies that are in the middle are eating and singing. Therefore, the hobbies that Andy and Mary have in common are eating and singing.
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Grocery Item Price per Unit Number of Units Needed Total Amount Apples \$0.99 per pound 5 x Pie crust \$2.49 per package 2 \$4.98 Butter \$3.29 for 2 sticks 2 \$6.58
Use the table to solve. Luke went to the store to buy several items to make apple pie. How much will 5 pounds of apples cost him?
| Grocery Item | Price per Unit | Number of Units Needed | Total Amount |
|---|---|---|---|
| Apples | \$0.99 per pound | 5 | x |
| Pie crust | \$2.49 per package | 2 | \$4.98 |
| Butter | \$3.29 for 2 sticks | 2 | \$6.58 |
Use the table to solve. Luke went to the store to buy several items to make apple pie. How much will 5 pounds of apples cost him?
According to the table, each pound of apples costs 99 cents. He needs 5 pounds.
We can find the total cost by multiplying the cost per pound and the total number of pounds.
We can also find the answer by adding the cost of five individual pounds of apples.
According to the table, each pound of apples costs 99 cents. He needs 5 pounds.
We can find the total cost by multiplying the cost per pound and the total number of pounds.
We can also find the answer by adding the cost of five individual pounds of apples.
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Grocery Item Price per Unit Number of Units Needed Total Amount Apples \$0.99 per pound 5 x Pie crust \$2.49 per package 2 \$4.98 Butter \$3.29 for 2 sticks 2 \$6.58
Use the table to solve. If Luke needed to buy 2 more sticks of butter, for a total of 6 sticks of butter, how much money would he need to bring to the store to buy all the items? Round to the nearest dollar.
| Grocery Item | Price per Unit | Number of Units Needed | Total Amount |
|---|---|---|---|
| Apples | \$0.99 per pound | 5 | x |
| Pie crust | \$2.49 per package | 2 | \$4.98 |
| Butter | \$3.29 for 2 sticks | 2 | \$6.58 |
Use the table to solve. If Luke needed to buy 2 more sticks of butter, for a total of 6 sticks of butter, how much money would he need to bring to the store to buy all the items? Round to the nearest dollar.
To buy all the items listed, he will need the sum of all the costs.
For apples, the cost is \$0.99 per pound and he needs 5 pounds.
The apples will cost \$4.95.
The total amount for the pie crusts is \$4.98 in the table.
For butter, we need to find the cost of 6 sticks. In the table, 2 sticks of butter cost \$3.29. Six sticks will cost three times as much.
The butter will cost \$9.87.
Now, we need to add all the costs together.
When you add these items up, you get \$19.80. Then, round to the nearest whole dollar. We need to round up, giving us \$20.
Luke will need to bring \$20 to buy all the items he needs for the apple pies.
To buy all the items listed, he will need the sum of all the costs.
For apples, the cost is \$0.99 per pound and he needs 5 pounds.
The apples will cost \$4.95.
The total amount for the pie crusts is \$4.98 in the table.
For butter, we need to find the cost of 6 sticks. In the table, 2 sticks of butter cost \$3.29. Six sticks will cost three times as much.
The butter will cost \$9.87.
Now, we need to add all the costs together.
When you add these items up, you get \$19.80. Then, round to the nearest whole dollar. We need to round up, giving us \$20.
Luke will need to bring \$20 to buy all the items he needs for the apple pies.
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On 9 tests, Jeff scores 97, 91, 100, 85, 95, 87, 90, 98, and 84. What is the median of his test scores?
On 9 tests, Jeff scores 97, 91, 100, 85, 95, 87, 90, 98, and 84. What is the median of his test scores?
The median is the number that is in the middle when all of the elements are arranged in order from low to high:
84 85 87 90 91 95 97 98 100
(Note: remember that if there are an even number of elements, you average the two that are in the middle).
The median is the number that is in the middle when all of the elements are arranged in order from low to high:
84 85 87 90 91 95 97 98 100
(Note: remember that if there are an even number of elements, you average the two that are in the middle).
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The following table depicts the scores that a class of students receives on a math test. If scores of 92% or greater result in an A, how many students receive an A?
The following table depicts the scores that a class of students receives on a math test. If scores of 92% or greater result in an A, how many students receive an A?
3 students scored in the 
range, and 9 students scored in the 
range. To find the number of students who received an A, we need to add the number of students in each group.
3 students scored in the
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Two teams—one with three boys, one with three girls—are competing to sell the most magazine subscriptions. Below is the table listing the number of subscriptions each student has sold so far.
The boys' team:
The girls' team:
Which of the following is true right now?
Two teams—one with three boys, one with three girls—are competing to sell the most magazine subscriptions. Below is the table listing the number of subscriptions each student has sold so far.
The boys' team:
The girls' team:
Which of the following is true right now?
The girls have sold 
subscriptions; the boys have sold 
subscriptions. The girls are leading by 2.
The girls have sold
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Three teams, each with three Girl Scouts, are competing to sell the most boxes of cookies. Below is the table listing the number of boxes each girl has sold so far.
Badger Team:
Bear Team:
Cougar Team:
From most boxes sold to fewest boxes sold, order the three teams of Girl Scouts.
Three teams, each with three Girl Scouts, are competing to sell the most boxes of cookies. Below is the table listing the number of boxes each girl has sold so far.
Badger Team:
Bear Team:
Cougar Team:
From most boxes sold to fewest boxes sold, order the three teams of Girl Scouts.
Add the numbers of boxes of cookies sold:
Badger Team: 
Bear Team: 
Cougar Team: 
The rank, from most boxes sold to least: Badger Team, Cougar Team, Bear Team
Add the numbers of boxes of cookies sold:
Badger Team:
Bear Team:
Cougar Team:
The rank, from most boxes sold to least: Badger Team, Cougar Team, Bear Team
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Which city has the greatest range of the number of cats and dogs?
Which city has the greatest range of the number of cats and dogs?
Cats are represented by the blue bar, and dogs are represented by the orange bar. Therefore, we're looking for the biggest difference, or range, in the heights of the two bars. This occurs in Miami.
Cats are represented by the blue bar, and dogs are represented by the orange bar. Therefore, we're looking for the biggest difference, or range, in the heights of the two bars. This occurs in Miami.
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How many cities have more cats than dogs?
How many cities have more cats than dogs?
To find the cities with more cats than dogs, look at the chart and see where the blue bar (cats) is greater than the orange bar (dogs). This only happens in Duluth and Pawnee, so the answer is 2.
To find the cities with more cats than dogs, look at the chart and see where the blue bar (cats) is greater than the orange bar (dogs). This only happens in Duluth and Pawnee, so the answer is 2.
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Between what two days did George's speed decrease?
Between what two days did George's speed decrease?
On February 12, George's speed was 19.4 seconds, while on February 13, it was 19.3 seconds. This is the only decrease in the chart.
On February 12, George's speed was 19.4 seconds, while on February 13, it was 19.3 seconds. This is the only decrease in the chart.
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By how many seconds did George's speed increase between February 8 and February 17?
By how many seconds did George's speed increase between February 8 and February 17?
To find the increase, subtract February 8's speed from February 17's speed: 21.2 seconds - 18.2 seconds = 3 seconds
To find the increase, subtract February 8's speed from February 17's speed: 21.2 seconds - 18.2 seconds = 3 seconds
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Based on the graph, which question can be answered?
Based on the graph, which question can be answered?
The bar chart only tells us the number of cats and dogs in each city. It doesn't tell us how many people live in each city, so nothing can be said about the number of dogs or cats per person.
The bar chart only tells us the number of cats and dogs in each city. It doesn't tell us how many people live in each city, so nothing can be said about the number of dogs or cats per person.
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