In the flowchart, each rectangular box represents a distinct stage in the production of a 50-kilogram batch of a specialty...
GMAT Graphics Interpretation : (GI) Questions
In the flowchart, each rectangular box represents a distinct stage in the production of a 50-kilogram batch of a specialty chemical. Decision points, which are not distinct stages, are represented by diamond shapes. The time required for each stage is indicated in minutes (min). There is no waiting time between stages. Three quarters of all batches do not require additional heating, while half of all batches require a second mixing with hydrochloric acid (HCL); none require a third.
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 Component | Literal Content | Interpretation |
|---|---|---|
| Process Description | production of a 50-kilogram batch of a specialty chemical | Batch size and product |
| Stage Representation | each rectangular box represents a distinct stage | Rectangles = production steps |
| Decision Representation | diamond shapes = decision points, not distinct stages | Diamonds = quality checks |
| Time Measurement | time for each stage in minutes | All stage times in minutes |
| Flow Between Stages | no waiting time between stages | Stages are contiguous |
| Additional Heating Requirement | Three quarters of all batches do not require additional heating | 25% require additional heating |
| Second HCL Mixing Requirement | Half of all batches require a second mixing with hydrochloric acid (HCL); none require a third | 50% require a second HCL mixing, never a third |
Table 2: Chart Analysis
| Chart Component | Shown In Chart | What It Means |
|---|---|---|
| Rectangular Stages | Heating (30min), Additional Heating (20min), Sifting (5min), HCL Mixing (20min), Filtration (10min), Drying (60min) | Up to 6 process stages (but not all used per batch) |
| Diamonds (Decisions) | Adequately degasified? ; Adequately reacted? | Determine extra processing (heating or extra mixing) |
| Conditional Branches | Arrows based on Yes/No at diamonds | Failing a check adds that extra step |
| Minimum Steps | Heating → Sifting → HCL Mixing → Filtration → Drying | Base process: 125 minutes |
| Optional Steps | Additional Heating and/or second HCL Mixing | Add 20 mins (heating) and/or 20 mins (mixing) as needed |
Key Insights
There are four possible process paths: (1) base process with no optional steps (125 min, 37.5%), (2) additional heating only (145 min, 12.5%), (3) second HCL mixing only (145 min, 37.5%), and (4) both additional steps (165 min, 12.5%). The average total process time is 140 minutes. On average, a batch passes through 5.75 distinct process stages, reflecting the probabilistic addition of heating and mixing steps.
Step-by-Step Solution
Question 1: Average Process Time
Complete Statement:
The average time in minutes that a batch of ingredients to make it all the way through the process shown is:
Breaking Down the Statement
- Statement Breakdown 1:
- Key Phrase: average time in minutes
- Meaning: We are being asked for the expected amount of time a batch spends in the entire process.
- Relation to Chart: This involves summing up the times for all steps (rectangles) along every possible process path in the flowchart, weighted by the probability of each path.
- Important Implications: We must account for branches in the process (e.g., extra HCL mixing or heating required for only a portion of batches), not just the minimum or maximum time.
- Key Phrase: average time in minutes
- Statement Breakdown 2:
- Key Phrase: make it all the way through the process
- Meaning: From the initial to the final step, regardless of whether the batch takes extra steps.
- Relation to Chart: The full path includes all required and possible additional steps as dictated by decision (diamond) boxes.
- Important Implications: Some batches will take longer if they require extra heating or a second HCL mixing; these must be part of the average.
- Key Phrase: make it all the way through the process
- What is needed: The expected (average) total time, in minutes, for a batch of ingredients to complete the entire process, accounting for every possible route.
Solution:
- Condensed Solution Implementation:
List every possible path and its probability, calculate the total time for each path, then add each path's time times its probability. - Necessary Data points:
Base path (no extras): 125 min; Path with only extra HCL: 145 min; Path with only extra heating: 145 min; Path with both extras: 165 min. Probabilities: 37.5% (no extras), 37.5% (extra HCL only), 12.5% (extra heating only), 12.5% (both extras).- Calculations Estimations:
\((0.375 \times 125) + (0.375 \times 145) + (0.125 \times 145) + (0.125 \times 165) = 46.875 + 54.375 + 18.125 + 20.625 = 140\) minutes. - Comparison to Answer Choices:
The calculation matches answer choice '140'.
- Calculations Estimations:
FINAL ANSWER Blank 1: 140
Question 2: Average Number of Stages
Complete Statement:
The average number of stages that a batch undergoes is:
Breaking Down the Statement
- Statement Breakdown 1:
- Key Phrase: average number of stages
- Meaning: We want the expected (mean) number of separate process steps (rectangles) each batch experiences.
- Relation to Chart: Count the number of rectangular stages on each possible path for a batch.
- Key Phrase: average number of stages
- Statement Breakdown 2:
- Key Phrase: a batch undergoes
- Meaning: For each possible process route, determine the total number of boxes the batch passes through.
- Relation to Chart: Identify the count of rectangles for each pathway, considering all extra steps if taken.
- Key Phrase: a batch undergoes
- What is needed: The expected (average) count of process steps (rectangles) experienced by a batch from start to finish.
Solution:
- Condensed Solution Implementation:
For each possible path, count the stages (rectangles), multiply by the path's probability, and sum to find the average. - Necessary Data points:
Base path: 5 stages; Path with only extra HCL: 6 stages; Path with only extra heating: 6 stages; Path with both extras: 7 stages. Probabilities as above.- Calculations Estimations:
\((0.375 \times 5) + (0.375 \times 6) + (0.125 \times 6) + (0.125 \times 7) = 1.875 + 2.25 + 0.75 + 0.875 = 5.75\) stages. - Comparison to Answer Choices:
The calculation matches answer choice '5.75'.
- Calculations Estimations:
FINAL ANSWER Blank 2: 5.75
Summary
Both questions relied on calculating a weighted average using the probabilities of taking each possible process path. The solution to the first blank focused on average process time, while the second blank focused on average number of stages completed. Both required understanding the process flow, decision points, and how different pathways affect the overall average. The answers are 140 minutes and 5.75 stages, respectively.
Question Independence Analysis
The two blanks are independent: one asks for average time and the other for the average number of stages. Both use the same probabilities, but solving one does not directly yield the solution for the other.