Machines A, B, and C each manufacture car parts at distinct constant

Question Explanation
This is a Yes/No Data Sufficiency question with variables in the question and in the statements, so Plug In values for Ar and Br. The task of a Yes/No Data Sufficiency is to determine whether the information in the statements produces a consistent Yes or No response for any number that satisfies the statement(s). Evaluate the statements one at a time.

Evaluate Statement (1), which states that Ar, the ratio of Machine A's rate to Machine C's rate, is greater than 1. Plug In values for the machines' rates that satisfy the statement and determine the answer to the question. If Ar = 10, then Machine A's rate could be 10 parts per minute and Machine B's rate would be 1 part per minute, and the answer to the question is “No” because Machine A does not have the slowest constant rate. Now, Plug In again, to see whether there is a way to produce a "Yes" answer. If Ar = 1.1, then Machine A's rate could be 11 parts per minute and Machine B's rate would be 10 parts per minute, and the answer to the question is still “No” because Machine A does not have the slowest constant rate. Since a ratio greater than 1 means Machine A must have a greater rate than Machine C, all possible values that satisfy this statement will produce a response of “No.” When all values that satisfy a statement produce a consistent response to the question, the statement is sufficient. Write down AD.

Now, evaluate Statement (2). Statement (2) states that Br > Ar, so Plug In values that satisfy the statement and determine the answer to the question. If Ar = 2 and Br = 10 and Machine C's rate is 1 part per minute, then Machine A's rate would be 2 parts per minute and Machine B's rate would be 10 parts per minute. Therefore, the answer to the question is “No” because Machine A does not have the slowest constant rate. Now, Plug In again, to see whether there is a way to produce a "Yes" answer. If Ar = 0.5 and Br = 10 and Machine C's rate is 1 part per minute, then Machine A's rate would be 0.5 parts per minute and Machine B's rate would be 10 parts per minute, and the answer to the question is “Yes” because Machine A has the slowest rate. When two sets of values that satisfy the statement produce different responses to the question, the statement is insufficient. The correct answer is choice A