Researchers carried out a study of the calorie content of meals in 89 fast food restaurants, using a diverse group...
GMAT Two Part Analysis : (TPA) Questions
Researchers carried out a study of the calorie content of meals in 89 fast food restaurants, using a diverse group of approximately 3,300 participants. The researchers collected receipts from the participants to calculate the calorie content of their meals, and then they administered a short questionnaire asking participants to estimate the calorie content of their meals. The average (arithmetic mean) calorie content of the meals was 775, and the participants underestimated the calorie content of their meals by an average of 200 calories. Two-thirds of all participants underestimated the calorie content of their meals, with approximately one-quarter of all participants underestimating the calorie content by at least 500 calories.
Consider the following incomplete sentence: Approximately 1 of the participants underestimated the calorie content of their meals, and approximately 2 of the participants underestimated the calorie content by at least 500 calories. Select for 1 and for 2 the values that complete the sentence in a manner consistent with the information provided. Make only two selections, one in each column.
Phase 1: Owning the Dataset
Understanding the Given Information
We have a study with:
- Total participants: 3,300
- Two-thirds underestimated their meal calories
- One-quarter underestimated by at least 500 calories
Visual Representation
Let's create a number line showing participant groups:
Total Participants: 3,300
|----------------------------------------|
Underestimated (any amount): \(\frac{2}{3}\) of all
|------------------------|
Underestimated by \(\geq 500\) cal: \(\frac{1}{4}\) of all
|------|
Phase 2: Understanding the Question
We need to complete:
- Blank 1: Number of participants who underestimated (any amount)
- Blank 2: Number of participants who underestimated by at least 500 calories
The key insight: Both fractions refer to "of all participants" (the full 3,300).
Phase 3: Finding the Answer
Calculating Blank 1
Participants who underestimated = \(\frac{2}{3} \times 3,300\)
= 2,200 participants
Calculating Blank 2
Participants who underestimated by \(\geq 500\) calories = \(\frac{1}{4} \times 3,300\)
= 825 participants
Both calculations are straightforward multiplications that can be done mentally or with a calculator.
Phase 4: Solution
Final Answer:
- Statement 1: 2,200
- Statement 2: 825
These values complete the sentence: "Approximately 2,200 of the participants underestimated the calorie content of their meals, and approximately 825 of the participants underestimated the calorie content by at least 500 calories."