A certain publishing company surveyed readers of three books it publishes (Books A, B, and C). In the diagram, each...
GMAT Graphics Interpretation : (GI) Questions
A certain publishing company surveyed readers of three books it publishes (Books A, B, and C). In the diagram, each circle represents one of these books. Next to the label for each circle is the proportion of the total number of survey respondents who had read the corresponding book. Each number in the diagram shows the proportion of the total number of respondents who had read the book(s) represented by the circle or circles in which it appears. For example, the proportion of the number of respondents who had read Book C was 0.72, and the proportion who had read Books B and C but not Book A was 0.20.
Select from each drop-down menu the option that completes the statement so that it most accurately reflects the information provided.
Owning the Dataset
Table 1: Text Analysis
| Text Component | Content | Simple Interpretation |
|---|---|---|
| Survey Context | A publisher surveyed readers of three books it publishes (Books A, B, and C). | Readers were surveyed about which of three books they had read. |
| Circle Representation | Each circle in the diagram represents one of these books. | Venn diagram circles = each book |
| Circle Labels | Next to each circle is the proportion of the total number of respondents who had read that particular book. | Number by each circle = total fraction who've read that book |
| Venn Region Numbers | Each number in the diagram shows the proportion of total respondents who read the specific group(s) represented by overlapping circles. | Numbers inside diagram = fraction for each exact combination of books read |
| Example Interpretation | E.g., the proportion of respondents who had read Book C was 0.72, and the proportion who had read Books B and C but not Book A was 0.20. | 72% read Book C; 20% read B and C but not A |
Table 2: Chart Analysis
| Chart Component | Value/Pattern | What It Reveals |
|---|---|---|
| Book A readers | 0.58 | 58% of respondents read Book A |
| Book B readers | 0.81 | 81% of respondents read Book B (most popular) |
| Book C readers | 0.72 | 72% of respondents read Book C |
| Only A | 0.05 | Very few read only Book A |
| Only B | 0.08 | Only 8% read just Book B |
| Only C | 0.14 | 14% read only Book C |
| A and B only | 0.15 | Some (15%) read A and B but not C |
| B and C only | 0.20 | 20% read B and C but not A |
| A and C only | 0.00 | No one read A and C but not B |
| All three (A, B, C) | 0.38 | 38% of respondents read all three books |
| Empty A∩C region | 0.00 | All who read both A and C also read B |
Key Insights
- The largest single group among respondents (38%) is those who read all three books.
- Book B is the most-read and central: everyone who read both A and C also read B, evidenced by the zero in the 'A and C only' region.
- Over 60% of Book A readers read all three books \(\mathrm{(0.38/0.58 ≈ 0.655)}\), confirming the high overlap among A readers.
- The probability a randomly selected respondent read only A and C is zero, since the 'A and C only' region is empty.
Step-by-Step Solution
Question 1: Conditional Probability of Reading All Three Books Among Readers of a Specific Book
Complete Statement:
Among the respondents who had read [BLANK], the probability that one selected at random had read all three books is greater than 0.60.
Breaking Down the Statement
- Statement Breakdown 1:
- Key Phrase: Among the respondents who had read [BLANK]
- Meaning: We are considering only those people who read a particular book.
- Relation to Chart: We look at the total percentage next to each book in the Venn diagram.
- Important Implications: This sets the 'given that' condition for a conditional probability calculation.
- Key Phrase: Among the respondents who had read [BLANK]
- Statement Breakdown 2:
- Key Phrase: probability that one selected at random had read all three books
- Meaning: Out of those who read the chosen book, what fraction also read all three books?
- Relation to Chart: This is the proportion at the intersection of all three circles — the middle of the Venn diagram.
- Important Implications: We're looking for \(\mathrm{P(all\ three\ |\ specific\ book) = P(all\ three) ÷ P(that\ book)}\).
- Key Phrase: probability that one selected at random had read all three books
- What is needed: Which single book, when chosen as the [BLANK], gives \(\mathrm{P(all\ three\ |\ that\ book) \gt 0.60}\).
Solution:
- Condensed Solution Implementation:
Compute the conditional probability for each book: \(\mathrm{P(all\ three\ |\ A)}\), \(\mathrm{P(all\ three\ |\ B)}\), and \(\mathrm{P(all\ three\ |\ C)}\). Choose the book with a result above 0.60. - Necessary Data points:
\(\mathrm{P(all\ three\ books) = 0.38}\); \(\mathrm{P(Book\ A) = 0.58}\); \(\mathrm{P(Book\ B) = 0.81}\); \(\mathrm{P(Book\ C) = 0.72}\).- Calculations Estimations:
\(\mathrm{P(all\ three\ |\ A) = 0.38 ÷ 0.58 ≈ 0.655}\); \(\mathrm{P(all\ three\ |\ B) = 0.38 ÷ 0.81 ≈ 0.469}\); \(\mathrm{P(all\ three\ |\ C) = 0.38 ÷ 0.72 ≈ 0.528}\). - Comparison to Answer Choices:
Only Book A has \(\mathrm{P \gt 0.60}\) (about 0.655).
- Calculations Estimations:
FINAL ANSWER Blank 1: Book A
Question 2: Probability That a Random Survey Respondent Read Only Books A and C
Complete Statement:
The probability that a randomly selected respondent had read only Books A and C is [BLANK].
Breaking Down the Statement
- Statement Breakdown 1:
- Key Phrase: randomly selected respondent
- Meaning: We are considering the entire survey population.
- Relation to Chart: Use the Venn diagram's proportions directly.
- Key Phrase: randomly selected respondent
- Statement Breakdown 2:
- Key Phrase: had read only Books A and C
- Meaning: These respondents read both A and C but NOT Book B.
- Relation to Chart: This refers to the A∩C region of the diagram outside B's circle.
- Key Phrase: had read only Books A and C
- What is needed: The proportion represented by just the overlap of A and C (excluding B).
Solution:
- Condensed Solution Implementation:
Read the value in the Venn diagram representing 'only A and C.' - Necessary Data points:
From the diagram, the region representing 'only A and C' is labeled as 0.00.- Calculations Estimations:
No calculation is required: the diagram shows this value is 0.00. - Comparison to Answer Choices:
0.00 is an option, and matches exactly.
- Calculations Estimations:
FINAL ANSWER Blank 2: 0.00
Summary
For Blank 1, only Book A satisfies the condition that more than 60% of its readers read all three books, since \(\mathrm{0.38/0.58 ≈ 0.655}\). For Blank 2, the probability a randomly chosen respondent read only A and C is 0.00, directly given by the Venn diagram. So, the answers are: Book A and 0.00.
Question Independence Analysis
The two questions are independent. The first requires a conditional probability calculation about all three books among readers of a specific book, while the second only requires direct reading of a single region in the Venn diagram. The answer to one does not affect the solution to the other.