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　　Data Sufficiency

　　What is the average (arithmetic mean) of a, b, and c ?

　　(1)a + 2b + 3c = 10

　　(2)3a + 2b + c = 14

　　Answer Choices

　　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:

　　C

　　Explanation:

　　The average of a, b, and c is a+b+c/3. Statement (1) says that a+2b+3c = 10, but there is not enough information to determine the value of a+b+c. Thus, statement (1) alone is not sufficient. Similarly, the equation statement (2) also fails to give enough information, so statement (2) alone is not sufficient. If the equations in statements (1) and (2) are added together, term by term, the result is 4a+4b+4c=24, which means that a+b+c = 6. The average is therefore 6/3 = 2. Thus, BOTH statements TOGETHER are sufficient to answer the question. The best answer is C.