<p>75 television viewers offered their opinions about program A and program B. Of those viewers, 18 liked neither Program A nor Program B, while 25 liked both programs. If 22 viewers liked program A only, how many viewers liked program B?</p>
<p>I can't get it to equal 10 like it should :( I even drew Venn diagrams and it's just not working out</p>
<p>Of the 75 viewers, 18 abstained.
57 viewers remain that voted.
22 liked Program A.
That means 35 viewers liked Program B only or Program A and B.
If 25 viewers liked Program A, that means 10 viewers liked only Program B.</p>
<p>Why doesn’t it work with the group forumla? 75 = 22 + x + 18 - 25 where x should be program B’s amount</p>
<p>There are 75 people total, so the number of individuals in each group, when added together, will equal 75.
This is the formula: 18 + 25 + 22 + x = 75;</p>
<p>I think the formula you’re thinking about is group overlap, which is actually: [elements in set A] + [elements in set B] - 2[elements in both set A and B]</p>
<p>That’s irrelevant though.</p>
<p>How come there is no group overlap here? We have a number of people that like both? Thus, the intersection of two sets?</p>
<p>Group overlap would be for something like 100 people like cheese and 30 people like macaroni. If 10 people like both cheese and macaroni, how many people like only one? Then you would do 100 + 30 - 20 = 110.</p>
<p>This is an entirely different type of problem. It’s not that there is no group overlap. Rather, the group overlap is already accounted for. If the answer really is 10, the question is also slightly flawed in that it should specify “how many viewers liked ONLY program B?”</p>
<p>For the math portion of the SAT, it’s good not to think in terms of the formulas, but to actually get a sense of why you solve things they way you do.</p>
<p>[People Who Like Program B] = [Total Group] - [People Who Like Program A] - [People Who Like Program A and B]. There is no unknown overlap that you have to solve for here to speak of.</p>