Explanation

Calling S and P the number of people on Susan's team and on Phillip's team, we can write the information given as , and we want to know whether . Now that you've done a bunch of word problems, you may be wondering whether there is any significance to whether a question is about people or ages or some other type of thing. Often it makes no difference, but one thing to keep an eye out for is that certain word problems inherently limit the possibilities to integers. That's the case here, since the teams are measured in the number of people, and we should understand that people come only in whole integer numbers. On to the statements, separately first.

Statement (1) tells us that . And we already know that . Let's analyze by cases. An easy-to-construct case from the equation, call it Case I, is that both variables are 10: . In this case, the answer to the question is, "No, there are not fewer people on Susan's team." Can we generate a case with an opposite result? Case II: . That case is allowed because and . In this case, the answer to the question is "yes." Therefore, we don't have sufficient information to answer the question definitively, and Statement (1) is insufficient.

Statement (2) indicates that . Our previously examined Case II is admissible here, since and for that case, and it gives us a "yes." Can we come up with a case that yields a no? By and , and working our way up from , we have the following allowed pairs: ; ; . There is no case allowed by Statement (2) and the prompt in which S is equal to or greater than P, so we have sufficient information to answer the question definitively (in the affirmative). Statement (2) is sufficient and the correct answer is (B).

Note: there is a somewhat faster way to analyze this question using algebra. This method, in fact, applies to most questions that involve two linear equations (or in this case, one equation and an inequality). If we think of S as y and P as x we can write as and plot it in the xy-plane. As you can see, it starts negative, with a y-intercept at -10. It will be true that as long as this line is to the right of , which is Therefore, the answer is "yes" from the origin all the way up until the lines cross, which is where and are both true, at . This method may be better for you if you are truly faster at it. The optimal case for most people will be to use analysis by cases as the first line of business but go to algebraic methods when they seem easier, when analysis by cases is running into problems, and/or in order to confirm an answer.

Again, the correct answer is (B).