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# Integrated Reasoning Questions: Graphics Interpretation

This Graphics Interpretation section has twelve questions, just as the next generation GMAT Integrated Reasoning sections will have.  You are allowed to use a calculator, because an on-screen calculator will be available during the Integrated Reasoning section only of the actual exam.

The chart above shows the technology capabilities of the 20 existing high schools in Grangerville.

## Questions

1) If a Grangerville high school is chosen at random, the probability that it will be public high school with a dedicated computer lab is:

(A) 20%

(B) 33.3 %

(C) 40%

(D) 42.9%

(E) 44.4%

2) If a Grangerville high school with either a dedicated computer lab or a computer in every classroom is chosen, the probability that it will be a public school is:

(A) 20%

(B) 33.3 %

(C) 40%

(D) 42.9%

(E) 44.4%

3) If a Grangerville high school with a dedicated computer lab is chosen, the probability that it will be a public school is:

(A) 20%

(B) 33.3 %

(C) 40%

(D) 42.9%

(E) 44.4%

4) If a Grangerville high school with a dedicated computer lab and without a computer in every classroom is chosen, the probability that it will be a public school is:

(A) 20%

(B) 33.3 %

(C) 40%

(D) 42.9%

(E) 44.4%

5) Which of the following statements is true?

I. Independent schools constitute the high percentage of high schools in Grangerville with both a dedicated computer lab and a computer in every classroom

II. Public Schools are tied for the highest percentage of high schools of Grangerville with a dedicated computer lab.

III. Public Schools constitute the highest percentage of high schools of Grangerville with either a dedicated computer lab or a computer in every classroom.

(A) I only

(B) II only

(C) III only

(D) I and II

(E) I and III

6) If a public high school in Grangerville is chosen at random, the probability that it has a dedicated computer lab is:

(A) 16.7%

(B) 33.3%

(C) 66.7%

(D) 80%

(E) 100%

7) If a public high school in Grangerville is chosen at random, the probability that it has a computer in every classroom is:

(A) 16.7%

(B) 33.3%

(C) 66.7%

(D) 80%

(E) 100%

8 ) If a public high school in Grangerville is chosen at random, the probability that it has a dedicated computer lab and does not have a computer in every classroom is:

(A) 16.7%

(B) 33.3%

(C) 66.7%

(D) 80%

(E) 100%

9) If a parochial high school in Grangerville is chosen at random, the probability that it has a dedicated computer lab is:

(A) 16.7%

(B) 33.3%

(C) 66.7%

(D) 80%

(E) 100%

10) If a parochial high school in Grangerville is chosen at random, the probability that it has a dedicated computer lab and does not have a computer in every classroom is:

(A) 16.7%

(B) 33.3%

(C) 66.7%

(D) 80%

(E) 100%

11) If an independent high school in Grangerville is chosen at random, the probability that it has a dedicated computer lab is:

(A) 16.7%

(B) 33.3%

(C) 66.7%

(D) 80%

(E) 100%

12) If an independent high school in Grangerville is chosen at random, the probability that it has a dedicated computer lab and does not have a computer in every classroom is:

(A) 16.7%

(B) 33.3%

(C) 66.7%

(D) 80%

(E) 100%

## Practice Question Answers and Explanations

(1) A; (2) D; (3) B; (4) E; (5) E; (6) B; (7) A; (8) B; (9) E; (10) D; (11) E; (12) B.

1) There are twenty school total. Of those twenty, only four are in the category “public school with a dedicated computer lab” – the four red squares in the Venn circle on the left.  4/20*100 = 20%.  Answer = A.

2) There are 14 schools in one of the two Venn circles – those are the schools either with dedicated computer labs or a computer in every classroom.  Of those schools, 6 are public: the four red squares in the left Venn circle, and the two in the right Venn circle.  6/14*100 = 42.9%.  Answer = D.

3) There are 12 in the left Venn circle (including the overlap region) – those are the schools with dedicated computer labs.  Of those, four are public schools – the four red squares in the Venn circle on the left.  4/12*100 = 33.3%.  Answer = B.

4) When the overlap region is subtracted from the left Venn circle, the resultant lune holds the high schools with a dedicated computer lab and without a computer in every classroom.  There are nine schools in this region, of which 4 are public: the four red squares in that left-most lune.  4/9*100 = 44.4% Answer = E.

5) Evaluate the statements one by one.  Statement I: Independent schools constitute the high percentage of high schools in Grangerville with both a dedicated computer lab and a computer in every classroom.  Schools with both a dedicated computer lab and a computer in every classroom are the overlap region of the two Venn circles.  There are three schools in that region, and two are independent, so independent schools constitute the majority of that region.  Statement I is true.

Statement II: Public Schools are tied for the highest percentage of high schools of Grangerville with a dedicated computer lab. The schools with a dedicated computer lab are the left Venn circle, the whole of the circle including the overlap region.  In this circle, there are 12 schools —- 5 parochial, 4 public, and 3 independent.  Therefore, parochial schools only constitute the highest percentage of that region, and public schools are a clear second.  Statement II is false.

Statement III:  Public Schools constitute the highest percentage of high schools of Grangerville with either a dedicated computer lab or a computer in every classroom.  Schools with either a dedicated computer lab or a computer in every classroom constitute the combined area of the two Venn circles.  There are 14 schools in that region —- 6 public, 5 parochial, and 3 independent.  Public schools constitute the majority of that region.  Statement III is true.

6) There are 12 public high schools – the 12 red squares throughout the diagram, including those at the top.  Of these, four are in the left Venn circle, which represents having a dedicated computer lab.  4/12*100 = 33.3%.  Answer = B.

7) There are 12 public high schools.  Of these, two are in the right Venn circle, which represents having a computer in every classroom.  2/12*100 = 16.7%  Answer = A.

8 ) There are 12 public high schools.  Of these, there are four in the left-most Venn lune (i.e. the left circle with the overlap subtracted).  This region represents the schools that have a dedicated computer lab and do not have a computer in every classroom.  4/12*100 = 33.3%.  Answer = B.

9) There are 5 parochial schools in the diagram – the five blue circles.  All five of these are in the left Venn circle, which represents having a dedicated computer lab.  5/5*100 = 100%.  Answer = E.

10) There are 5 parochial schools in the diagram.  Of these, four of them are in the left-most Venn lune, which represents the schools that have a dedicated computer lab and do not have a computer in every classroom.  4/5*100 = 80%.  Answer = D.

11) There are 3 independent schools in the diagram – the three green triangles.  Of these, all three are in the left Venn circle, which represents having a dedicated computer lab.  3/3*100 = 100%.  Answer = E.

12) There are 3 independent schools in the diagram.  Of these, only one is in the left-most Venn lune, which represents the schools that have a dedicated computer lab and do not have a computer in every classroom.  1/3*100 = 33.3%.  Answer = B.

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### 7 Responses to Integrated Reasoning Questions: Graphics Interpretation

1. lucky1829 March 25, 2015 at 4:56 pm #

In Question 2, we count together every dot in both cycles (including the overlap). However, the question states: “with EITHER a dedicated computer lab OR a computer in every classroom is chosen…”

IMO that does not include the “both” section. My answer would be 6/11 and not 6/14.

2. Avi February 10, 2015 at 7:27 pm #

Hi Mike,

Would you mind suggesting me any good resources for articles with graphs, charts and statistical data.
This will be of great use for tackling the IR.

3. Karen April 30, 2012 at 1:06 pm #

In Question 5, your statement II is: I. Public Schools are tied for the highest percentage of high schools of Grangerville with a dedicated computer lab.

But in your explanation for why number 5 is ‘E’ shows statement II as follows: Public Schools constitute the highest percentage of high schools of Grangerville with a dedicated computer lab.

If you answer question 5 as it reads in the question section, what would the correct answer be?

• Mike April 30, 2012 at 4:17 pm #

Karen: If one group has sole possession of the highest percentage, then it’s false to say that they they were tied for first place. If I have the highest score of 35 on something, and my friend Bert has the second highest score of 33, then it would be false to say that Bert & I are tied for first place. To say someone has sole occupancy of first place or the highest score is to say that there is no tie for first place. Does that make sense? Mike 🙂

• Karen May 1, 2012 at 6:39 am #

No! Well, yes, I understand your explanation, but you didn’t answer my question!
Why is the wording in the question and the wording in your answer for Statement II different from each other?

And does the fact that they are different mean E would not have been the correct answer if you had used the wording in the question?

I would suggest that you make Statement II in your question and explanation be the same to avoid confusion.

• Mike May 1, 2012 at 12:05 pm #

Karen: I’m very sorry! I didn’t realize you were pointing out a typo in the post itself. Of course you’re right — the wording in the explanation should match the question, or it’s no explanation! I just corrected the post, so everything matches. BTW, I’m not sure where I got the alternate version of the wording, but Statement II is still false, and E is still the correct answer. Thank you very much for your help, and once again, I’m sorry I didn’t catch that mistake the first time you asked. Mea culpa!
Mike 🙂

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