What is the average weight of the class? (1) The class has ten students. (2) If one more student, whose weight is twice the average weight of the class, joins the class, the average increases by 2.
Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
Statement 1 gives the count but not the weights. Statement 2 relates the new average to the old average but requires the number of students to solve for the specific average value. Together, we have n=10, and if the new student weight is 2A, the new average is (10A + 2A)/11 = A + 2. This allows solving for A.
Let the average weight of the class be A and the number of students be N. Using the second statement alone, if a student weighing twice the average joins, the new sum is NA plus 2A, and the new average is (NA plus 2A) divided by (N plus 1), which equals A plus 2. This equation yields the total number of students N as 9.5, but you still cannot find A. Using the first statement gives the exact value of N as 10, which when plugged into the equation from the second statement allows you to solve for A, showing both statements together are sufficient.