The graph displays experimental data relating the surface area of a snow shovel's blade, in hundreds of square centimeters (100...
GMAT Graphics Interpretation : (GI) Questions
The graph displays experimental data relating the surface area of a snow shovel's blade, in hundreds of square centimeters (\(100 \text{ cm}^2\)), to the time to fatigue: the minimum number of hours of snow shoveling until a healthy adult feels too fatigued to continue. The line shown is a trendline corresponding to the data. From each drop-down menu, select the option that creates the most accurate statement based on the information provided.
Owning the Dataset
Table 1: Text Analysis
Text Analysis Table
| Component | Literal Content | Interpretation |
|---|---|---|
| Subject Matter | Experimental data relating the surface area of a snow shovel's blade to the time to fatigue | Study measures effect of shovel size on time adults can shovel before exhaustion |
| X-axis Variable | Surface area of a snow shovel's blade, in hundreds of square centimeters (\(100\text{ cm}^2\)) | Shovel blade size in units of \(100\text{ cm}^2\) |
| Y-axis Variable | Time to fatigue: the minimum number of hours of snow shoveling until a healthy adult feels too fatigued to continue | Number of hours someone can keep shoveling before being too tired |
| Trendline | The line shown is a trendline corresponding to the data | Visual indication of overall relationship between blade size and time to fatigue |
Table 2: Chart Analysis
Chart Analysis Table
| Chart Feature | Details | Interpretation |
|---|---|---|
| Chart Type | Scatter plot with trendline | Shows individual data and the general trend |
| X-axis Scale | 0–20 (\(100\text{ cm}^2\) units); so range is 0 to \(2000\text{ cm}^2\) | Range of shovel sizes tested |
| Y-axis Scale | 0–2.0 hours | Maximum measured time to fatigue |
| Slope (Trendline) | Negative, approx. \(-0.05\text{ h per }100\text{ cm}^2\) | Increasing blade area decreases the time before exhaustion |
| Data Distribution | Most points near trendline; one outlier at \(x=8\) (\(800\text{ cm}^2\)), \(y≈0.3\text{ h}\) | Experimental results are mostly predictable except for the outlier |
| Notable Outlier | Point at (\(800\text{ cm}^2\), ~0.3h) | One participant fatigued earlier than others with that shovel size |
Key Insights
- There is a clear negative correlation: larger shovel blades consistently lead to quicker fatigue.
- The trendline shows that every increase of \(200\text{ cm}^2\) in blade area reduces fatigue time by about 0.1 hours (trendline slope ≈ \(-0.05\text{ h per }100\text{ cm}^2\)).
- There is a prominent outlier: at \(800\text{ cm}^2\), the time to fatigue is much lower than predicted by the trend (about 0.3 hours), standing out from other results.
Step-by-Step Solution
Question 1: Finding the Greatest Distance from the Trendline
Complete Statement:
The data point for which the distance to the trendline is greatest corresponds to a shovel-blade surface area that is approximately _______ \(\text{cm}^2\).
Breaking Down the Statement
Statement Breakdown 1:
- Key Phrase: distance to the trendline is greatest
- Meaning: We are looking for the biggest outlier—the point that is furthest vertically from the trendline.
- Relation to Chart: This occurs at the data point on the scatter plot that is farthest above or below the trendline.
- Important Implications: We need to visually identify the most extreme outlier from the trend in the chart.
Statement Breakdown 2:
- Key Phrase: shovel-blade surface area
- Meaning: This is the x-axis value (in \(\text{cm}^2\)) for the outlier point.
- Relation to Chart: Read the x-axis coordinate of the farthest point; axis is labeled in units of \(100\text{ cm}^2\).
- Important Implications: Remember to convert from axis units (100s of \(\text{cm}^2\)) to actual \(\text{cm}^2\).
What is needed: The x-axis value (in \(\text{cm}^2\)) of the point farthest from the trendline.
Solution:
Condensed Solution Implementation:
Scan the scatter plot for the point farthest from the trendline. Identify its x-value.
Necessary Data points:
On the plot, the outlier is at \(x = 8\) (representing \(8 × 100 = 800\text{ cm}^2\)).
Calculations Estimations:
\(x = 8\) corresponds to \(800\text{ cm}^2\) (since each unit is \(100\text{ cm}^2\)).
Comparison to Answer Choices:
Possible answers: 400, 600, 800, 1000. 800 is correct.
FINAL ANSWER Blank 1: 800
Question 2: Surface Area Corresponding to Each 0.1-Hour Fatigue Decrease
Complete Statement:
According to the trendline, each 0.1-hour decrease in time to fatigue corresponds to an increase in shovel-blade surface area that is approximately _______ \(\text{cm}^2\).
Breaking Down the Statement
Statement Breakdown 1:
- Key Phrase: according to the trendline
- Meaning: Use the black line's slope (not the outliers or individual data points).
- Relation to Chart: Focus on the negative slope of the trendline.
Statement Breakdown 2:
- Key Phrase: each 0.1-hour decrease in time to fatigue
- Meaning: A vertical drop of 0.1 hours on the y-axis.
- Relation to Chart: How much do you need to increase the blade area to get this drop.
What is needed: The increase in shovel-blade surface area (\(\text{cm}^2\)) that leads to a 0.1-hour decrease in time to fatigue according to the trendline.
Solution:
Condensed Solution Implementation:
Calculate the x-axis change needed for a 0.1-hour decrease, using the trendline slope.
Necessary Data points:
Slope ≈ \(-0.05\text{ hours per }100\text{ cm}^2\) (every increase of \(100\text{ cm}^2\) reduces time by 0.05 hours).
Calculations Estimations:
0.1-hour decrease requires \(2 × 100\text{ cm}^2 = 200\text{ cm}^2\) increase (since 0.05 hours per \(100\text{ cm}^2\), and \(0.1\text{ hours} ÷ 0.05 = 2\)).
Comparison to Answer Choices:
Possible answers: 100, 150, 200, 250. 200 is correct.
FINAL ANSWER Blank 2: 200
Summary
Blank 1 is solved by visually identifying the biggest outlier on the scatterplot (\(800\text{ cm}^2\)). Blank 2 is solved by applying the trendline's slope to see that a 0.1-hour decrease in fatigue corresponds to a \(200\text{ cm}^2\) blade area increase.
Question Independence Analysis
The questions are independent: one requires identifying an outlier and the other is about interpreting the trendline's slope. Solving one does not require solving the other.