Question

The electrical engineering department at a certain graduate school in the United States (US) has a total of 36 students. The department has twice as many male students as female students and three times as many international students as students who are US citizens. Quantity A: The number of students who are US citizens \newline Quantity B: The number of female students

• A. The relationship cannot be determined from the information given
• B. Quantity A is greater
• C. The two quantities are equal
• D. Quantity B is greater

Hint:

When working with multiple relationships in a word problem, assign variables, translate each constraint into an equation, and solve systematically.

Answer 1

The Correct Option is B

Step 1: Assign variables.
Let the number of female students be \( f \). Then male students = \( 2f \). Let the number of US citizen students be \( x \), then international students = \( 3x \).
Step 2: Total students equation.
\[ f + 2f = 3f = \text{total students} = 36 \Rightarrow f = 12, \quad 2f = 24. \] So, female students = 12.
Step 3: Now apply the international/US citizen relationship.
\[ x + 3x = 4x = 36 \Rightarrow x = 9. \] So, US citizen students = 9.
Step 4: Comparison.
Quantity A = 9, Quantity B = 12 \[ \Rightarrow \text{Quantity B is greater.} \] Wait! There seems to be a contradiction. Since both variables depend on the same total of 36, and give different values (female = 12, US = 9), we must **reconcile the constraint**. Let's try solving the equation combining both relationships: - Let \( f \) be number of female students, - Then male = \( 2f \) - Total students = \( f + 2f = 3f \) - Also, let US students = \( x \), international = \( 3x \) - Total students = \( x + 3x = 4x \) So, both \( 3f = 36 \) and \( 4x = 36 \) hold. \[ f = 12, \quad x = 9 \Rightarrow \text{Quantity A (US) = 9, Quantity B (female) = 12.} \]
Step 5: Final conclusion.
So, \[ \boxed{\text{Quantity B is greater.}} \]