What is the weight of Bob, if the average weight of Albert, Bob and Caitlin is 45 pounds? (1) The average weight of Albert and Bob is 40 pounds. (2) The average weight of Bob and Caitlin is 43 pounds.
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.
Let A, B, C be the weights. (A+B+C)/3 = 45 => A+B+C = 135. (1) A+B = 80. (2) B+C = 86. With (1), C = 135-80 = 55. With (2), A = 135-86 = 49. Neither alone gives B, but together we can solve for A and C, then B = 135 - (A+C).
From the main prompt, the total weight of Albert, Bob and Caitlin is 45 multiplied by 3, which equals 135 pounds. Statement (1) provides the combined weight of Albert and Bob as 40 multiplied by 2, or 80 pounds, which leaves Caitlin weighing 135 minus 80, or 55 pounds, but we still cannot isolate Bob's weight. Statement (2) provides the combined weight of Bob and Caitlin as 43 multiplied by 2, or 86 pounds, which leaves Albert weighing 135 minus 86, or 49 pounds, but we still cannot isolate Bob's weight. By using both statements together, we subtract Albert's weight of 49 from the combined Albert and Bob weight of 80 to find that Bob weighs 31 pounds, meaning both statements together are sufficient.