GMAT Integrated Reasoning

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1

Screen shot 2016 07 12 at 11.54.31 am
The graph above plots sixteen points that each describe the shoe size of sixteen individual children.

Identify the missing information of the following statement.

The relationship between the age of the child and the child's shoe size is __________.

positive

negative

zero

Explanation

Looking at the graph, first identify the points.

Screen shot 2016 07 12 at 11.54.31 am

There are sixteen points: (2,1), (3,1), (3,2), (4,3), (5,5), (5,6), (6,4), (6, 7), (7,6), (7,7), (8,6), (8,7), (8,9), (9,9), (10,9), (12,9)

The line of best fit can be drawn on the image and it would have a positive slope.

It is seen that as the age of the children increases that the shoe size also increases.

Therefore there is a positive relationship between the child's age and shoe size.

2

The table displays the academic class spread among Dawn County schools in 2005.

Based on the given information in the table, select the options that can be proven to be true.

I. No class is offered in less than one-third of the schools.

II. Every school in the district offers either Gym or at least one Art class (Painting or Sculpting).

III. Math is an academic class that is offered in all schools in Dawn County.

III.

II.

I.

I. and II.

II. and III

Explanation

Examining the table given, the truth of the statements can be identified.

Looking at option I. No class is offered in less than one-third of the schools.

It is seen that Sculpting is offered in 13% of the schools which is less than 33% therefore sculpting is offered in less than one-third of the schools thus making the statement false.

Looking at option II. Every school in the district offers either Gym or an Art class.

The table states that 5 schools offer Gym and a total of three schools offer Art (Painting or Sculpting). This makes a total of 8 schools but it is unknown if there are 8 different school or if the 5 schools that have gym also have an art class. Therefore this statement is false.

Looking at option III. Math is an academic class that all schools in Dawn County offer.

The table shows that the % of schools offering Math is 100% therefore this statement is true.

3

Screen shot 2016 07 12 at 11.54.31 am
The graph above plots sixteen points that each describe the shoe size of sixteen individual children.

Identify the missing information of the following statement.

The relationship between the age of the child and the child's shoe size is __________.

positive

negative

zero

Explanation

Looking at the graph, first identify the points.

Screen shot 2016 07 12 at 11.54.31 am

There are sixteen points: (2,1), (3,1), (3,2), (4,3), (5,5), (5,6), (6,4), (6, 7), (7,6), (7,7), (8,6), (8,7), (8,9), (9,9), (10,9), (12,9)

The line of best fit can be drawn on the image and it would have a positive slope.

It is seen that as the age of the children increases that the shoe size also increases.

Therefore there is a positive relationship between the child's age and shoe size.

4

The table displays the academic class spread among Dawn County schools in 2005.

Based on the given information in the table, select the options that can be proven to be true.

I. No class is offered in less than one-third of the schools.

II. Every school in the district offers either Gym or at least one Art class (Painting or Sculpting).

III. Math is an academic class that is offered in all schools in Dawn County.

III.

II.

I.

I. and II.

II. and III

Explanation

Examining the table given, the truth of the statements can be identified.

Looking at option I. No class is offered in less than one-third of the schools.

It is seen that Sculpting is offered in 13% of the schools which is less than 33% therefore sculpting is offered in less than one-third of the schools thus making the statement false.

Looking at option II. Every school in the district offers either Gym or an Art class.

The table states that 5 schools offer Gym and a total of three schools offer Art (Painting or Sculpting). This makes a total of 8 schools but it is unknown if there are 8 different school or if the 5 schools that have gym also have an art class. Therefore this statement is false.

Looking at option III. Math is an academic class that all schools in Dawn County offer.

The table shows that the % of schools offering Math is 100% therefore this statement is true.

5

The table displays the academic class spread among Dawn County schools in 2005.

Based on the given information in the table, select the options that can be proven to be true.

I. No class is offered in less than one-third of the schools.

II. Every school in the district offers either Gym or at least one Art class (Painting or Sculpting).

III. Math is an academic class that is offered in all schools in Dawn County.

III.

II.

I.

I. and II.

II. and III

Explanation

Examining the table given, the truth of the statements can be identified.

Looking at option I. No class is offered in less than one-third of the schools.

It is seen that Sculpting is offered in 13% of the schools which is less than 33% therefore sculpting is offered in less than one-third of the schools thus making the statement false.

Looking at option II. Every school in the district offers either Gym or an Art class.

The table states that 5 schools offer Gym and a total of three schools offer Art (Painting or Sculpting). This makes a total of 8 schools but it is unknown if there are 8 different school or if the 5 schools that have gym also have an art class. Therefore this statement is false.

Looking at option III. Math is an academic class that all schools in Dawn County offer.

The table shows that the % of schools offering Math is 100% therefore this statement is true.

6

Screen shot 2016 07 12 at 11.54.31 am
The graph above plots sixteen points that each describe the shoe size of sixteen individual children.

Identify the missing information of the following statement.

The relationship between the age of the child and the child's shoe size is __________.

positive

negative

zero

Explanation

Looking at the graph, first identify the points.

Screen shot 2016 07 12 at 11.54.31 am

There are sixteen points: (2,1), (3,1), (3,2), (4,3), (5,5), (5,6), (6,4), (6, 7), (7,6), (7,7), (8,6), (8,7), (8,9), (9,9), (10,9), (12,9)

The line of best fit can be drawn on the image and it would have a positive slope.

It is seen that as the age of the children increases that the shoe size also increases.

Therefore there is a positive relationship between the child's age and shoe size.

7

The table displays the academic class spread among Dawn County schools in 2005.

Based on the given information in the table, select the options that can be proven to be true.

I. At least half the school's in Dawn County support advanced placement courses.

II. The majority of schools's in Dawn County participate in offering a type of foreign language to their students.

III. The core subjects such as English and Math enroll the majority of students.

I. and III.

I., II., and III.

I.

I. and II.

II. and III.

Explanation

Examining the table given, the truth of the statements can be identified.

Looking at option I. At least half the school's in Dawn County support advanced placement courses,

advanced placement courses at AP Calculus and AP English. Since 50% of schools offer each this statement is true.

Looking at option II. The majority of schools's in Dawn County participate in offering a type of foreign language to their students,

the foreign languages are French, Latin, German, and Spanish. French, German, and Spanish are offered in 4 school which is half the schools however, it is not known if they are offered in the same four schools or in different schools. Latin is offered in three schools and again, it is not known if it is offered in the same or different schools as the other foreign languages. Therefore, this statement is false.

Looking at option III. The core subjects such as English and Math enroll the majority of students,

the majority of students will need to be over 50% of the students. Since Math has 100% student enrollment and English has 75% then, the majority of students are enrolled in core subjects. Therefore this statement is true.

8

Over a seven-year period, from 2002 to 2009, the number of babies born to married couples increased despite a decrease in marriages from 17,000 marriages in 2002.

In the given expression, and represent the percent change in the babies and marriages, respectively. represents the number of babies per married couple in 2002. The percent change in a quantity is calculated by the formula:

Identify the following with the given information,

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per family in 2009.

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per married couple in 2009.

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per married couple in 2009.

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per married couple in 2009.

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per married couple in 2009.

I. The expression that represents the number of babies born in 2002.

II. The expression of the number of babies born per married couple in 2009.

Explanation

To identify,

I. The expression that represents the number of babies born in 2002.

Recall the given information in this particular question.

It is known that in 2002 there are 17,000 marriages and represents .

Using this information to create a mathematical expression is as follows.

Now to identify,

II. The expression of the number of babies born per married couple in 2009.

Use the formula given

This part of the problem is asking for a ratio, but the variables that are given are percents.

Therefore, the 100’s are there because M and B are percent quantitie_s._ They are both added because M is a negative number.

So the number in the numerator is the percentage of babies that exist in 2009 compared to 2002 (a number that will be less than 100). The denominator is the percentage of the 2002 marriages that exists in 2009 (a number greater than 100).

Thus the solution is,

9

Gmat integrated reasoning soccer question

Refer to the pictograph that describes all of the students who play soccer at Douglas High School. Each star represents 5 students from a sample of 75 total students.

Identify the missing information in the following statements using the pictograph.

I. If one student is selected at random from the 75, the chance that the student will be older than 17 or on the Varsity team, or both is __________.

II. If one student is selected at random from the 75, the chance that the students is both younger than 17 and on the Varsity Soccer Team is __________.

I. 2 out of 3

II. 1 out of 5

I. 1 out of 5

II. 2 out of 3

I. 1 out of 3

II. 1 out of 5

I. 2 out of 6

II. 2 out of 5

I. 2 out of 5

II. 2 out of 6

Explanation

To identify the missing information in the following statements use the pictograph.

Gmat integrated reasoning soccer question

I. If one student is selected at random from the 75, the chance that the student will be older than 17 or on the Varsity team, or both is __________.

To find the probability of choosing a student that is either older than 17, or on the Varsity team, or both can be written mathematically as follows.

To find the ratio divide the number found above by the total number of students.

In words this is 2 out of 3.

II. If one student is selected at random from the 75, the chance that the students is both younger than 17 and on the Varsity Soccer Team is __________.

In mathematical terms this is written as the following,

To find the ratio divide the number found above by the total number of students.

In words this is 1 out of 5.

10

The table displays the academic class spread among Dawn County schools in 2005.

Based on the given information in the table, select the options that can be proven to be true.

I. At least half the school's in Dawn County support advanced placement courses.

II. The majority of schools's in Dawn County participate in offering a type of foreign language to their students.

III. The core subjects such as English and Math enroll the majority of students.

I. and III.

I., II., and III.

I.

I. and II.

II. and III.

Explanation

Examining the table given, the truth of the statements can be identified.

Looking at option I. At least half the school's in Dawn County support advanced placement courses,

advanced placement courses at AP Calculus and AP English. Since 50% of schools offer each this statement is true.

Looking at option II. The majority of schools's in Dawn County participate in offering a type of foreign language to their students,

the foreign languages are French, Latin, German, and Spanish. French, German, and Spanish are offered in 4 school which is half the schools however, it is not known if they are offered in the same four schools or in different schools. Latin is offered in three schools and again, it is not known if it is offered in the same or different schools as the other foreign languages. Therefore, this statement is false.

Looking at option III. The core subjects such as English and Math enroll the majority of students,

the majority of students will need to be over 50% of the students. Since Math has 100% student enrollment and English has 75% then, the majority of students are enrolled in core subjects. Therefore this statement is true.

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