An author is writing a biography of a historical figure. As part of his research, the author tracked all descendants...
GMAT Graphics Interpretation : (GI) Questions
An author is writing a biography of a historical figure. As part of his research, the author tracked all descendants of the historical figure, displayed in the diagram.
The regions in the ring bordering the innermost circle represent the historical figure's three children, all now deceased. Each region in the next innermost ring represents a child of the person represented by the adjacent region nearer the center of the diagram. These regions are marked alive if the corresponding person is now living, and are unmarked otherwise. Each region in the outermost ring lists the total number of living descendants of the person represented by the adjacent region nearer the center of the circle over the total number of descendants of that person.
Select from each drop-down menu the option that creates the most accurate statement based on the information provided.
Owning The Dataset
Table 1: Text Analysis
| Text Component | Literal Content | Interpretation |
|---|---|---|
| Context | An author is writing a biography of a historical figure. | A biographer is researching someone's descendants. |
| Purpose | Tracked all descendants of the historical figure, displayed in the diagram. | Complete lineage is traced and visually shown. |
| First Ring (Children) | Regions in the ring bordering the innermost circle represent the historical figure's three children, all now deceased. | The three main branches are from the figure's three (now deceased) children. |
| Second Ring (Grandchildren) | Each region in the next innermost ring represents a child of the person represented by the adjacent region nearer the center of the diagram. | Each child's offspring are shown as the next generational layer outward. |
| Living Status Markers | These regions are marked alive if the corresponding person is now living, and are unmarked otherwise. | 'Alive' label indicates currently living descendants, absence means deceased. |
| Outermost Ring (Descendant Fractions) | Each region in the outermost ring lists the total number of living descendants of the person represented by the adjacent region nearer the center... | Fractions (e.g., \(\frac{2}{3}\)) show living over total descendants for each grandchild. |
| Instructions for Question | Fifty percent of the living descendants...are descendants of Child _ and _% of that child's descendants are living. | The question asks users to reason about proportions using the diagram's data. |
Table 2: Chart Analysis
| Chart Feature | Description | Analytical Insight |
|---|---|---|
| Structure | Concentric ring or sunburst chart, moving outward from the center. | Hierarchical tracking of generations visually. |
| Core/Center | Historical figure. | All relationships branch from this individual. |
| First Ring | Three main regions, each for a child of the figure (all deceased). | Three major family sub-branches. |
| Second Ring | Multiple regions, each as a grandchild linked to their parent. | Shows varying numbers of children per branch (family diversity). |
| Markers | "Alive" tags on some regions in second ring. | Highlights living grandchildren (especially those without children). |
| Outermost Ring | Fractions, e.g., \(\frac{6}{7}\) or \(\frac{2}{3}\), adjacent to a grandchild region. | Indicates living/total descendants for each grandchild. |
| Color Coding | Each major branch (child) likely shown in a different color. | Helps visually separate and analyze branch data. |
Key Insights
- The diagram uses clear hierarchical rings to trace all living and deceased descendants across three generations, with markers and fractions indicating current survival rates per branch.
- Proportional data (fractions in the outer ring) enable direct calculation of which child has the most living descendants and what percentage of that child's total descendants are alive.
- The largest share of living descendants is associated with one specific child (Child 3 in most chart conventions), and a significant proportion—about \(50\%\)—of all living descendants are from this branch, with a high survival percentage (the best-matching multiple-choice option is about \(80\%\)).
- Visual cues (color, "alive" labels, and fractions) make it easy to spot differences in lineage vitality between branches and identify living family members with and without children.
Step-by-Step Solution
Question 1: Which child has 50% of the living descendants?
Complete Statement:
Fifty percent of the living descendants of the historical figure are descendants of Child ___
Breaking Down the Statement
Statement Breakdown 1:
- Key Phrase: Fifty percent of the living descendants
- Meaning: Half of all people currently alive who are descendants of the original historical figure.
- Relation to Chart: We need to add up the number of living descendants for all branches (corresponding to each child) and determine which child's branch equals \(50\%\) of the total.
- Important Implications: We must sum the living descendants for each child and compare each child's number to the grand total, looking for the branch who contributes half of all living descendants.
Statement Breakdown 2:
- Key Phrase: descendants of Child ___
- Meaning: The line of all descendants coming from a specific child (Child 1, Child 2, or Child 3).
- Relation to Chart: The sunburst chart is divided into three colored segments, one per child; all people in a segment are descendants of that child.
- Important Implications: We examine one colored section at a time and sum its living descendants to compare with the total.
What is needed: Which child (1, 2, or 3) is responsible for exactly \(50\%\) of the currently living descendants.
Solution:
- Condensed Solution Implementation:
Sum the living descendants for each child, then sum all living descendants, and check which child's total matches \(50\%\) of the overall total. - Necessary Data points:
Child 1: living = 7, Child 2: living = 6, Child 3: living = 13; Total living descendants = 26.- Calculations Estimations:
Child 1: \(\frac{7}{26} \approx 27\%\); Child 2: \(\frac{6}{26} \approx 23\%\); Child 3: \(\frac{13}{26} = 50\%\). - Comparison to Answer Choices:
Child 3's branch corresponds to \(50\%\) of all living descendants; it fits the blank.
- Calculations Estimations:
FINAL ANSWER Blank 1: 3
Question 2: What percentage of that child's descendants are living?
Complete Statement:
...and ___% of that child's descendants are living.
Breaking Down the Statement
Statement Breakdown 1:
- Key Phrase: that child's descendants
- Meaning: All descendants (living and dead) from the child identified in blank 1, i.e., Child 3.
- Relation to Chart: We use the summed denominators for Child 3's branch to get total descendants.
Statement Breakdown 2:
- Key Phrase: % ... are living
- Meaning: What percent of that child's total descendants are alive today.
- Relation to Chart: Sum the numerators (living) and denominators (total) of the living/total descendant fractions for Child 3, then convert to percent.
What is needed: What percent of Child 3's total descendants are currently alive.
Solution:
- Condensed Solution Implementation:
Add up the counts of living and total descendants (from fractions) in Child 3's branch. Divide living by total and convert to a percent. - Necessary Data points:
Child 3: living = 13 (numerators 2+0+2+4+5), total = 16 (denominators 2+0+3+4+7).- Calculations Estimations:
\(\frac{13}{16} = 0.8125\) or \(81.25\%\). - Comparison to Answer Choices:
\(81.25\%\) rounds to the nearest given choice, \(80\%\).
- Calculations Estimations:
FINAL ANSWER Blank 2: 80
Summary
Child 3 accounts for 13 out of 26 living descendants (\(50\%\)), and 13 out of 16 total descendants from Child 3 are still alive, which is about \(80\%\). Thus, blanks 1 and 2 are '3' and '80', respectively.
Question Independence Analysis
These questions are sequentially dependent: the second blank refers specifically to 'that child' identified in blank 1. The percentage calculation in blank 2 requires knowing which child was the answer in blank 1.