SAT Math Multiple Choice Question 465: Answer and Explanation

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Question: 465

15. A college cafeteria received a petition from students to offer healthier meat, vegetarian, and vegan dishes. In response to the petition, the cafeteria conducted an analysis of its existing menu to determine the current state of those options. The results are summarized in the table below. The analyst used a sliding scale based on the nutrient levels compared against calorie, sugar, and sodium counts to determine the health score, a score of 1 being the least healthy and 5 being the healthiest.

Health Score Meat Dishes Vegetarian Dishes Vegan Dishes
1 3 1 1
2 4 3 1
3 8 5 4
4 5 4 2
5 0 1 0

If a student chooses a dish at random for lunch one day, what is the probability that it will be a meat dish with a health score of at least 4?

  • A.
  • B.
  • C.
  • D.

Correct Answer: A

Explanation:

A

Difficulty: Medium

Category: Problem Solving and Data Analysis / Statistics and Probability

Strategic Advice: Sometimes, rewording a probability question makes it clearer, particularly when there is a lot of information given in a table.

Getting to the Answer: Reword the question: Find the probability that the student randomly chooses a dish that is both meat and has a health score of at least 4. This tells you that you are only interested in the combinations meat/4 and meat/5. The probability of randomly selecting one of these two combinations is (number of meat/4 + number of meat/5) divided by (number of all dishes). Now read the table and do the math. To save a bit of time, recall that you already found the total number of vegetarian and vegan dishes (22) in the previous question, so all you need to do is add the meat dishes:

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