The table below shows a gradebook. Letter grades of A, B, C, and D represent numerical grades of 4, 3,...

OWNING THE DATASET

Let's start by understanding what we're working with. This table shows grades for 10 students across multiple assessments: Quiz 1, Quiz 2, Paper 1, Final Project, and Overall Grade.

Looking at the grading system, we see letter grades (A, B, C) where:

• \(\mathrm{A} = 4.0\)
• \(\mathrm{B} = 3.0\)
• \(\mathrm{C} = 2.0\)

Key insight: For "each student who..." statements, we only need ONE counterexample to disprove the claim. This means we can stop our analysis as soon as we find a single exception.

Before calculating anything, let's think strategically about how to approach each statement. The most efficient way to analyze this data will be to sort the table based on relevant columns for each statement.

ANALYZING STATEMENT 1

Statement 1 Translation:

Original: "Each student who did not receive an A on the final project also did not receive an A on either quiz."

What we're looking for:

• Students without an A on the final project
• Check if ANY of them got an A on Quiz 1 OR Quiz 2

In other words: Do all non-A final project students also have non-A quiz grades?

Strategic Approach

The most efficient way to test this is to sort by Final Project grades and focus only on students without an A.

Let's sort by Final Project column:

1. Sort by Final Project grades (ascending)
2. Identify non-A students: Sigrid, Vig, and Jean
3. Check their Quiz 1 and Quiz 2 grades

Scanning through these three students, we immediately notice that Jean received:

• Final Project: B
• Quiz 2: A

We've found our counterexample! Jean didn't get an A on the final project but did get an A on Quiz 2.

Statement 1 is No.

Teaching callout: Notice how sorting helped us quickly focus only on relevant students (those without an A on the final project). This is much faster than checking all 10 students one by one. As soon as we found one counterexample, we could stop our analysis.

ANALYZING STATEMENT 2

Statement 2 Translation:

Original: "Each student who did not receive an A on either quiz also did not receive an A on the final project."

What we're looking for:

• Students without an A on Quiz 1 AND without an A on Quiz 2
• Check if ANY of them got an A on the Final Project

In other words: Do all non-A quiz students also have non-A final projects?

Strategic Approach

Let's reverse our sorting strategy from Statement 1:

1. Sort by Final Project grades (descending to show A's first)
2. Identify students with an A on Final Project
3. Check if any of these students didn't get an A on either quiz

Scanning through the A-Final-Project students, we immediately spot Stanley:

• Final Project: A
• Quiz 1: B
• Quiz 2: C

Perfect! Stanley received an A on the Final Project despite not receiving an A on either quiz.

Statement 2 is No.

Teaching callout: By sorting strategically, we narrowed our focus to only those students who could potentially disprove the statement. This "counterexample hunting" approach is much more efficient than checking every student in the table.

ANALYZING STATEMENT 3

Statement 3 Translation:

Original: "Each student who received an A on Paper 1 also received an A as an overall grade."

What we're looking for:

• Students with an A on Paper 1
• Check if ALL of them got an A overall

In other words: Do all A-Paper-1 students also have A overall grades?

Strategic Approach

Let's sort by Paper 1 to quickly identify relevant students:

1. Sort by Paper 1 grades (descending to show A's first)
2. Identify students with an A on Paper 1: Phoebe and Stanley
3. Check their Overall grades

Looking at these two students:

• Phoebe: Paper 1 (A), need to check Overall
• Stanley: Paper 1 (A), need to check Overall

Let's calculate Stanley's overall grade:

• Quiz 1: B (3.0)
• Quiz 2: C (2.0)
• Paper 1: A (4.0)
• Final Project: A (4.0)
• Overall: \(\frac{3.0 + 2.0 + 4.0 + 4.0 + 4.0}{5} = \frac{17}{5} = 3.4\)

A 3.4 translates to a B overall grade. We found our counterexample!

Statement 3 is No.

Teaching callout: We only needed to calculate one student's overall grade to disprove the statement. Once we found that Stanley's overall grade was a B (not an A), we could immediately determine the statement was false without calculating Phoebe's grade.

FINAL ANSWER COMPILATION

Let's compile our findings:

• Statement 1: No (Jean had no A on Final Project but had an A on Quiz 2)
• Statement 2: No (Stanley had no A on either quiz but had an A on Final Project)
• Statement 3: No (Stanley had an A on Paper 1 but a B Overall)

The correct answer is E) All three statements are No.

LEARNING SUMMARY

Skills We Used

• Efficient Sorting: We sorted the data differently for each statement to focus only on relevant students
• Counterexample Strategy: For "each student who..." statements, we hunted for just one exception
• Minimum Calculation: We only calculated what was absolutely necessary (just one overall grade)

Strategic Insights

1. Sort first, calculate later: Sorting instantly revealed patterns and helped us focus on just the data we needed
2. For universal claims, hunt for exceptions: Just one counterexample disproves "each" or "all" statements
3. Calculate only what's absolutely necessary: We didn't need to convert the entire table to numbers

Common Mistakes We Avoided

• Calculating all 10 students' overall grades when we only needed to check 1-2 students
• Checking every student for every statement when sorting could narrow our focus
• Continuing analysis after finding a clear counterexample

Remember, on GMAT table questions, your goal isn't to analyze all the data—it's to find the fastest path to the correct answer. Sorting and focusing on potential counterexamples will save you valuable time on test day!