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The table below shows a gradebook. Letter grades of A, B, C, and D represent numerical grades of 4, 3, 2, and 1, respectively. Each student's overall grade was determined by computing the average (arithmetic mean) of their grades on the first paper, the first quiz, the second paper, the second quiz, and the final project, and then rounding to the nearest whole number. If the average is exactly halfway between whole numbers, the grade will be rounded up.
| Student | Paper 1 | Quiz 1 | Paper 2 | Quiz 2 | Final project |
|---|---|---|---|---|---|
| Phoebe | A | B | B | A | A |
| Stanley | A | B | A | C | A |
| Linette | B | A | B | C | A |
| Mia | B | C | C | D | A |
| Sietske | B | B | C | C | A |
| Sigrid | B | C | C | B | B |
| Vig | B | D | C | D | B |
| Jean | C | C | B | A | B |
| Robin | D | A | A | D | A |
| Yolette | D | C | C | A | A |
For each of the following statements, select Yes if the statement is true based on the information presented in the table. Otherwise, select No.
Each student who did not receive an A on the final project did not receive an A on either quiz.
Each student who did not receive an A on either quiz did not receive an A on the final project.
Each student who got an A on Paper 1 got an A in the course.
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:
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.
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:
In other words: Do all non-A final project students also have non-A quiz grades?
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:
Scanning through these three students, we immediately notice that Jean received:
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.
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:
In other words: Do all non-A quiz students also have non-A final projects?
Let's reverse our sorting strategy from Statement 1:
Scanning through the A-Final-Project students, we immediately spot Stanley:
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.
Original: "Each student who received an A on Paper 1 also received an A as an overall grade."
What we're looking for:
In other words: Do all A-Paper-1 students also have A overall grades?
Let's sort by Paper 1 to quickly identify relevant students:
Looking at these two students:
Let's calculate Stanley's overall grade:
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.
Let's compile our findings:
The correct answer is E) All three statements are No.
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!
Each student who did not receive an A on the final project did not receive an A on either quiz.
Each student who did not receive an A on either quiz did not receive an A on the final project.
Each student who got an A on Paper 1 got an A in the course.