Start by working through the problem yourself
The following teaching exercise is about a weighted average. Before opening the explanation, write down the operation you chose and the unit of the result. A correct guess and a well-justified method call for different kinds of review.
Un service traite 30 dossiers lundi, en consacrant 6 minutes à chacun, puis 20 dossiers mardi, en consacrant 9 minutes à chacun. Quelle est la durée moyenne de traitement par dossier sur les deux jours ?
Choose an answer.
The solution, step by step
A. 7,2 minutes.
The method in action
- Monday accounts for 30 × 6 = 180 minutes; Tuesday accounts for 20 × 9 = 180 minutes.
- That is 360 minutes for 50 cases, so 360 ÷ 50 = 7.2 minutes per case.
- B treats the two groups as though they had the same number of cases. C adds the two per-case times without calculating an average.
Compare a formula alone with an explanation of the decision
One worked solution might simply say “(30 × 6 + 20 × 9) ÷ 50 = 7.2, answer A.” The calculation is correct. But if you answered 7.5, this line does not yet show why averaging the two times is wrong. It gives the result without necessarily resolving your confusion.
A second worked solution starts with what is being asked: time per case across all cases. It converts each group into total time, adds those times, and divides by the total number of cases. It explains that the groups are different sizes and checks that the result falls between 6 and 9, closer to 6 because more cases took that long.
The second worked solution is useful because it makes the connections visible, not simply because it is longer. If you already understand all this, the short formula may be enough to check your work. What you need depends on your error and level of independence; a detailed worked solution should make it easy to find the relevant part.
Look for what connects the prompt to a reusable method
ETS describes quantitative reasoning as involving understanding, choosing a strategy, and checking the result. GMAC also encourages studying answer explanations during preparation. The five criteria below are our teaching framework for reviewing an explanation; they are not an official certification of study materials.
| Criterion | What the explanation should help you understand | How it applies in this example |
|---|---|---|
| Rationale | Why this operation answers the question. | Time per case is total time divided by the number of cases. |
| Steps | How the information is transformed. | Calculate the total time for each day before adding them. |
| Plausible error | Where an incorrect method changes the meaning. | Averaging 6 and 9 gives equal weight to both groups. |
| Transfer | What other situations use the same method. | Cost, weight, or time per item across groups of different sizes. |
| What to check | How to spot an implausible result. | Check the unit and that the result falls between the extreme values. |
The pitfall
The pitfall is mistaking a familiar explanation for a mastered method
When all the steps are visible, they may seem obvious. Close the explanation and say what information led you to choose the operation. If you can recall only the numbers or answer letter, revisit the rationale before moving on to a longer set.
A check does not replace a demonstration. In the first exercise, 7.5 also falls between 6 and 9, so this check alone cannot rule it out. You must consider the weight of each group. A good explanation shows what a check can confirm and what it cannot establish on its own.
Change the context to check that you understood the relationship
Now solve this new exercise without copying the previous formula. The context changes, but the question still concerns all the items together. After reviewing your answer, explain in one sentence what stays the same between the two methods.
Un envoi contient 12 colis de 2 kg chacun et 8 colis de 4,5 kg chacun. Quelle est la masse moyenne d’un colis de cet envoi ?
Enter your answer before viewing the review.
The solution, step by step
3 kg per package.
The method in action
- The total weight is 12 × 2 + 8 × 4.5 = 24 + 36 = 60 kg.
- The 20 packages therefore have an average weight of 60 ÷ 20 = 3 kg.
- The simple average of 2 and 4.5 would be 3.25 kg; that would apply to equally sized groups, which is not the case here.
Keep the useful decision instead of copying the entire worked solution
In your notes, record the initial confusion, the information that resolved it, and a new exercise to try. For this example: “I averaged the two times; first I need to determine how many cases each time applies to.” This note leads to action. Copying the full explanation may remain passive.
The same framework works for verbal questions: a good explanation cites evidence from the passage, justifies eliminating choices, and shows why an appealing answer goes beyond the text. Choose study materials based on what they help you understand; do not confuse the number of explanations with independence.
Key takeaways
- A useful worked solution justifies the approach and addresses a plausible error.
- A consistency check supplements the reasoning but does not replace it.
- Applying the method unaided to a new problem is a better check of understanding.