SAT Math Multiple Choice Practice Question 175: Answer and Explanation
21. Ms. Belton's class and Ms. Jimenez's class have no students in common. If 45 percent of Ms. Belton's students play a sport, 30 percent of Ms. Jimenez's students play a sport, and 40 percent of the students in the two classes combined play a sport, which statement must be true?
A. The two classes have the same number of students.
B. The two classes have 30 students total.
C. Ms. Belton's class has exactly 20 students.
D. Ms. Jimenez's class has twice as many students as Ms. Belton's.
E. Ms. Belton's class has twice as many students as Ms. Jimenez's.
Correct Answer: E
E. Let b equal the number of students in Ms. Belton's class and j equal the number in Ms. Jimenez's class. Now you can write 0.45b + 0.30j = 0.40(b + j). Distributing gives you 0.45b + 0.30j = 0.40b + 0.40j, and combining like terms gives you 0.05b = 0.10j. Dividing by 0.05 (or multiplying by 20) gives you b = 2j, so Ms. Belton's class has twice as many students as Ms. Jimenez's.