Question

Matthew, Jared, and Richard all bought flowers. The number of flowers Matthew purchased was equal to a single digit. Of the numbers of flowers purchased by Matthew, Jared, and Richard, only one was divisible by 3. The number of flowers one of them bought was an even number. Which of the following could represent the numbers of flowers each purchased?

• A. 3, 8, 24
• B. 7, 9, 17
• C. 6, 9, 12
• D. 5, 15, 18
• E. 9, 10, 13

Hint:

When faced with multiple conditions, use a process of elimination. Test each option against the conditions one by one. As soon as an option fails to meet a condition, you can discard it and move to the next, saving time.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
This question tests your understanding of basic number properties: single-digit numbers, divisibility by 3, and even/odd numbers. We need to evaluate each set of numbers against three given conditions.

Step 2: Key Formula or Approach:
We will check each option against the three conditions provided in the question: \begin{enumerate} \item Matthew's number is a single digit (1-9). \item Exactly one of the three numbers is divisible by 3. \item Exactly one of the three numbers is even. \end{enumerate}

Step 3: Detailed Explanation:
Let's analyze each option:
(A) 3, 8, 24:
\[\begin{array}{rl} \bullet & \text{Single digit: Yes, 3.} \\ \bullet & \text{Divisible by 3: 3 is divisible by 3. 24 is also divisible by 3 (24 = 3 \times 8). This violates the condition that only one number is divisible by 3.} \\ \end{array}\] (B) 7, 9, 17:
\[\begin{array}{rl} \bullet & \text{Single digit: Yes, 7 and 9.} \\ \bullet & \text{Divisible by 3: Only 9 is divisible by 3. This condition is met.} \\ \bullet & \text{Even number: 7, 9, and 17 are all odd. This violates the condition that one of them bought an even number of flowers.} \\ \end{array}\] (C) 6, 9, 12:
\[\begin{array}{rl} \bullet & \text{Single digit: Yes, 6 and 9.} \\ \bullet & \text{Divisible by 3: 6, 9, and 12 are all divisible by 3. This violates the condition that only one number is divisible by 3.} \\ \end{array}\] (D) 5, 15, 18:
\[\begin{array}{rl} \bullet & \text{Single digit: Yes, 5.} \\ \bullet & \text{Divisible by 3: 15 is divisible by 3. 18 is also divisible by 3 (18 = 3 \times 6). This violates the condition that only one number is divisible by 3.} \\ \end{array}\] (E) 9, 10, 13:
\[\begin{array}{rl} \bullet & \text{Single digit: Yes, 9. (This can be Matthew's number). This condition is met.} \\ \bullet & \text{Divisible by 3: Only 9 is divisible by 3. 10 and 13 are not. This condition is met.} \\ \bullet & \text{Even number: Only 10 is an even number. 9 and 13 are odd. This condition is met.} \\ \end{array}\] All three conditions are satisfied by the set {9, 10, 13}.
Step 4: Final Answer
The set of numbers that could represent the flowers purchased is 9, 10, 13.