A sales representative based in City A is about to begin a journey, by car, to Cities B, C, D,...

OWNING THE DATASET

Let's examine this table showing the probability of encountering traffic when traveling between consecutive locations (A through G). The key to solving this problem efficiently is to quickly identify patterns in the data.

Key insights from scanning the table:

• Some segments have \(0.0\) probability values (\(\mathrm{A \rightarrow B}\), \(\mathrm{B \rightarrow C}\), and \(\mathrm{E \rightarrow F}\)) - these jump out immediately
• The remaining segments (\(\mathrm{C \rightarrow D}\), \(\mathrm{D \rightarrow E}\), and \(\mathrm{F \rightarrow G}\)) all have the same probability value: \(0.7\)
• The table shows direct segments only, but questions may involve routes with multiple segments

Data structure understanding: Each cell represents the probability of encountering traffic on that specific segment. A value of \(0.0\) means no chance of traffic, while higher values indicate greater likelihood of traffic.

ANALYZING STATEMENT 1

Statement 1 Translation:
Original: "The minimum probability of encountering traffic on the optimal route from D to E is 0.7."
What we're looking for:

• What is the probability of encountering traffic on the direct \(\mathrm{D \rightarrow E}\) segment?
• Is this value equal to \(0.7\)?

In other words: Is \(0.7\) the lowest possible probability of traffic when traveling from D to E?

Let's approach this strategically. When finding the optimal route between two points, we want to focus only on the relevant segment.

Looking at our table, we need to check only the \(\mathrm{D \rightarrow E}\) column:

• Direct route \(\mathrm{D \rightarrow E}\) has probability \(0.7\)

Since there's only one direct path from D to E with probability \(0.7\), this is indeed the minimum probability.

Statement 1 is YES.

Teaching callout: Notice how we didn't need to analyze any other segments in the table. By focusing only on the specific segment mentioned in the statement, we save significant time and avoid unnecessary work.

ANALYZING STATEMENT 2

Statement 2 Translation:
Original: "The probability of not encountering traffic on the optimal route from F to G is 0.7."
What we're looking for:

• What is the probability of encountering traffic on the \(\mathrm{F \rightarrow G}\) segment?
• Is the probability of NOT encountering traffic equal to \(0.7\)?

In other words: Is there a \(0.7\) probability of a traffic-free journey from F to G?

For this statement, we need to:

1. Find the probability of encountering traffic on \(\mathrm{F \rightarrow G}\)
2. Calculate the complement to find the probability of NOT encountering traffic

Looking at our table, the \(\mathrm{F \rightarrow G}\) segment has a \(0.7\) probability of encountering traffic.
Therefore, the probability of NOT encountering traffic = \(1 - 0.7 = 0.3\)

Since \(0.3 \neq 0.7\), this statement is false.

Statement 2 is NO.

Teaching callout: The complement principle is crucial here. When a statement refers to "not encountering" something, we need to subtract the original probability from 1. Always watch for negation in probability questions!

ANALYZING STATEMENT 3

Statement 3 Translation:
Original: "The probability of not encountering traffic on any segment of the route from A to G is approximately 0.03."
What we're looking for:

• What is the probability of NOT encountering traffic on ANY segment from A to G?
• Is this combined probability approximately \(0.03\)?

In other words: If we travel the entire route from A to G, is there about a 3% chance of encountering no traffic at all?

This requires a more comprehensive approach. We need to:

1. Find the probability of not encountering traffic for each segment
2. Multiply these probabilities together (since we need ALL segments to be traffic-free)

Let's break this down strategically:

Step 1: Identify the probability of NOT encountering traffic for each segment:

• \(\mathrm{A \rightarrow B}\): Probability of traffic = \(0.0\), so probability of NO traffic = \(1.0\)
• \(\mathrm{B \rightarrow C}\): Probability of traffic = \(0.0\), so probability of NO traffic = \(1.0\)
• \(\mathrm{C \rightarrow D}\): Probability of traffic = \(0.7\), so probability of NO traffic = \(0.3\)
• \(\mathrm{D \rightarrow E}\): Probability of traffic = \(0.7\), so probability of NO traffic = \(0.3\)
• \(\mathrm{E \rightarrow F}\): Probability of traffic = \(0.0\), so probability of NO traffic = \(1.0\)
• \(\mathrm{F \rightarrow G}\): Probability of traffic = \(0.7\), so probability of NO traffic = \(0.3\)

Step 2: Multiply all probabilities together:
\(1.0 \times 1.0 \times 0.3 \times 0.3 \times 1.0 \times 0.3 = 0.3^3 = 0.027 \approx 0.03\)

Key insight: We can simplify this calculation! Since segments with \(0.0\) probability of traffic contribute a factor of \(1.0\) to our multiplication, they don't change the result. We only need to focus on the three segments with non-zero probabilities.

Simplified calculation: \(0.3 \times 0.3 \times 0.3 = 0.3^3 = 0.027 \approx 0.03\)

Statement 3 is YES.

Teaching callout: Notice how we eliminated segments with zero impact (those with \(1.0\) probability of no traffic). This pattern recognition allowed us to simplify our calculation to just three identical values, making the math much easier.

FINAL ANSWER COMPILATION

After analyzing each statement:

• Statement 1: YES - The minimum probability of traffic on \(\mathrm{D \rightarrow E}\) is indeed \(0.7\)
• Statement 2: NO - The probability of no traffic on \(\mathrm{F \rightarrow G}\) is \(0.3\), not \(0.7\)
• Statement 3: YES - The probability of no traffic across the entire route is approximately \(0.03\)

The correct answer is B (Statements 1 and 3 are true, Statement 2 is false).

LEARNING SUMMARY

Skills We Used:

• Segment Isolation: We focused only on relevant columns for each statement, avoiding unnecessary analysis
• Zero-Impact Elimination: We recognized that segments with \(0.0\) traffic probability (\(1.0\) no-traffic probability) don't affect our multiplication
• Pattern Recognition: We identified that all non-zero segments had the same probability value (\(0.7\)), simplifying our calculation

Strategic Insights:

• Always scan for extreme values (like \(0.0\)) first - they often create shortcuts
• When calculating probabilities across multiple segments, look for values that don't affect the result (like \(1.0\) in multiplication)
• For "not encountering" probabilities, remember to use the complement (\(1 - p\))

Common Mistakes We Avoided:

• Building a complete "optimal route" table before addressing specific statements
• Calculating probabilities for segments that weren't relevant to the statements
• Performing lengthy calculations when pattern recognition could simplify the work

Remember that in GMAT table analysis, the fastest solution always does the minimum necessary work to verify or falsify each statement. Build only what you need when you need it!