<p>So the question is: </p>
<p>On her biology test, Cathy answered 5/6 of the questions correctly. If Cathy answered 18 of the first 27 questions correctly, then the total number of questions on the test must be at least…</p>
<p>(A) 32
(B) 36
(C) 45
(D) 48
(E) 54</p>
<p>Does anyone have a simple method to solving this? </p>
<p>The answer is (E)…</p>
<p>Since it’s MC, you can just work backwards. Since it’s asking for the least total of questions, you can assume he gets the rest of them right. 54-27=27, add 27 to 18 and you get 45/54, which equals 5/6.</p>
<p>well (18/27)+x=(5/6)
x=(1/6)
the only way you can make denominators equal and get the same MC answer is for all denominators to be 54 as denominators number represents the total questions and numerator is correct ones</p>
<p>First, lets consider the given information. We know that she answered 5/6 of the answers correctly. This implies that she answered 1/6 of the questions incorrectly. Also, we know that she answered 18 of the first 27 questions correctly, which also means she got 9 wrong.</p>
<p>Since we need to find the LEAST possible number of questions on the test, we have to assume that she answers every single one of the next questions correctly. Why? Because if she answered some of the next questions incorrectly then she would have to answer more questions correctly to make up for it and thus it would no longer be the least number of questions.</p>
<p>Since we know that she got 9 questions wrong and answered 1/6 of the questions incorrectly, 9 must be 1/6 of the total number of questions on the test. Why? Because she can no longer, as shown in the above paragraph, get any questions wrong to find the LEAST number of problems on the test. </p>
<p>Hence:
Let q be the number of questions on the test.</p>
<p>(1/6)q=9</p>
<p>(1/6)q * 6 = 9 * 6</p>
<p>q=54</p>
<p>Hope this helps!</p>
<p>Thank you so much! That was indeed very helpful! :-)</p>