The question asks whether mp is greater than m but doesn't provide any information about either variable. They could be integers or fractions. They could be positive, negative, or zero.
Glance at the statements. The second one has information about only one of the two variables, so start there. Also note that the question never provides real values anywhere for these variables. It's a theory problem. You can test some real numbers (Test Cases) to figure out what's going on.
Finally, this is a Yes/No question, so sufficient information is defined as information that gives you a definitive answer: either Always Yes or Always No. As you test cases, see whether you can find both Yes and No answers to the question: Is mp > m ?
(2) INSUFFICIENT: Test one case of real numbers. If p is less than 1, then p could be 0 and m could be 2. In this case, mp = 0, which is not greater than m = 2. This is a No case: No, mp is not greater than m. Can you get a Yes case when p is less than 1?
Case 2: p = –1, m = –2, mp = 2. In this case, Yes, mp > m.
Since both Yes and No cases are possible, this statement is not sufficient to answer the question.
(1) INSUFFICIENT: Break this inequality into two parts and put it into words. First, m is greater than p. Second, p is greater than 0.
Case #1: p = 1, m = 2, mp = 2. In this case, No, mp is not greater than m.
Case #2: p = 2, m = 3, mp = 6. In this case, Yes, mp is greater than m.
Since both Yes and No cases are possible, this statement is not sufficient to answer the question
(1) AND (2) SUFFICIENT: Put the info together:
m is greater than p
p is greater than 0
p is less than 1
Now, p is required to be a value between 0 and 1. Test some cases.
Case #1: p = 0.5, m = 2, mp = 1. In this case, No, mp is not greater than m.
Case #2: p = 0.5, m = 10, mp = 5. In this case, No, mp is not greater than m.
Case #3: p = 0.5, m = 0.5, mp = 0.25. In this case, No, mp is not greater than m.
What's going on? The value of p must be between 0 and 1 and the value of m must be positive (since it's greater than p). Whenever you multiply a positive number by something between 0 and 1, that number is going to get smaller. It's impossible for mp to be greater than m. The answer is Always No—and that's a definitive answer to the question.
The correct answer is (C). Using the two statements together, it's possible to arrive at a definitive answer (in this case, Always No).
