Question

	Number Studying Biology	Number Not Studying Biology	Tota
Number of Boys			18
Number of Girls
Tota	26

The table above shows the number of students in a certain high school class who are boys and the number of students in the class who are studying biology. What is the total number of students in the class?
(1) Of the boys in the class, 15 are studying biology.
(2) The number of girls in the class is twice the number of students in the class who are not studying biology.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is B Statement (2) alone is sufficient, but statement (1) alone is not sufficient.

1. For Statement 1.
   

   	No. of studying Biology	No. not studying Biology	Total
   No. of Boys	$15$	$3$	$18$
   No. of Girls	$11$	$x$
   Total	$26$	$3+x$	$29+x$

   For statement 2.
   

   	No. of studying Biology	No. not studying Biology	Total
   No. of Boys			$18$
   No. of Girls			$2y$
   Total	$26$	$y$

   Given that there are 15 boys in the class studying biology, the table can be completed as shown below, where x can be any nonnegative integer. Because the value of x in the table can be any nonnegative integer, the total number of students in the class, which equals 29 + x, cannot be determined; NOT sufficient.
2. Given that the number of girls in the class is twice the number of students in the class not studying biology, the table can be completed as shown below, where y is the number of students in the class not studying biology. Because the total number of students in the class can be computed in two ways, either as the number of boys in the class added to the number of girls in the class or as the number of students in the class studying biology and the number of students in the class not studying biology, it follows that 18 + 2y = 26 + y, or y = 8. Therefore, the total number of students in the class is 18 + 2(8) = 26 + 8 = 34; SUFFICIENT.

• The correct answer is B; statement (2) alone is sufficient.