Ambiguous Math question?

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1

<p>Each student in a group of 30 students studies German, Italian or both. The total number of students studying German is three more than the total number of students studying Italian. If the number of students that study both subjects is the same as the number of students that study exactly one subject, how many students in the group study only Italian?</p>

<p>A) 6</p>

<p>B) 9</p>

<p>C) 15</p>

<p>D) 21</p>

<p>E) 24</p>

<p>What confuses me is the phrasing. When the question says "total number of students studying German" and "total number of students studying Italian" does that include people that study both? Does the category of people studying German include people studying German and Italian? It says TOTAL so...</p>

<p>The third sentence is also confusing. When the question says "number of students that study exactly one subject", I figured that exactly one subject meant either German or Italian. It turns out that "exactly one subject" turns out to be the collective group of students that take 1 subject. Does anyone else find this ambiguous?</p>

2

<p>The phrasing looks fine to me.</p>

<p>

If you’re a kid with both German and Italian on his/her schedule, than you are both in a German class and in an Italian class at some point during the day. So yes, you are included in the total number of students studying German, as well as the total number of students studying Italian.</p>

<p>

This also seems very clear to me-- “exactly one subject”-- it doesn’t specify German or Italian, so how would they expect you to know if the subject was German or Italian, if they didn’t just mean “one” subject, period?</p>

3

<p>The phrasing seems fine. I believe the answer is 6.</p>

<p>Here’s how I got this answer </p>

<ol>
<li>“number of students that study both subjects is the same as the number of students that study exactly one subject”</li>
</ol>

<p>That means 15 students take both languages and 15 students take only one.</p>

<ol>
<li>“The total number of students studying German is three more than the total number of students studying Italian”</li>
</ol>

<p>Break down 15 so it fits this statement. you get 6 and 9. italian taking students are 3 less than the german ones which means 6 students take only Italian.</p>

<p>Edit:
In the end there are</p>

<p>15 students taking both
9 students taking ONLY german
6 students taking ONLY italian</p>

4

<p>How does this tie in with the formula Total= X + Y - Both + Neither?</p>

<p>30=9+6-15+0?</p>

5

<p>I should’ve specified.</p>

<p>15 students taking both
9 students taking ONLY german
6 students taking ONLY italian</p>

<p>so it’s 15 + 6+ 9 =30</p>

6

<p>That’s exactly where I got confused. I wasn’t sure if they were talking about the individual class (one subject) or the just 1 class in general. </p>

<p>Purpleacorn, the first part of your explanation is not right. The question means to say that German+Italian+Both=30. NOT German+Italian=30</p>

7

<p>Thanks Monk, I was just a little confused on the phrasing.</p>

8

<p>Slasheer, in this problem the “X and Y” do not overlap with the “both” so that equation wouldn’t work. It’s German only+Italian only+both. I just had some trouble with the phrasing</p>

9

<p>@CimmerianMonk</p>

<p>I think you are misinterpreting the question. There are 3 groups; Italians, Germans, or both. BOTH is a group by itself, both does not mean Italians + Germans. In a group of 30 kids 6 take Italian, 18 takes German, and 6 takes both. </p>

<p>Further explanation:
Let’s just say:</p>

<p>Italian students = x
German students = y
Students of both languages = z</p>

<p>From the question, we know two things:</p>

<p>3x = y
z = x OR z = y</p>

<p>From the answer choices, we know that z does not equal to y or else it will go past the limit of 30 students, therefore, z = x. Either way, the answer is A.</p>

10

<p>

</p>

<p>Technically, yes it does, but it doesn’t matter whether you see that or not.</p>

<p>If you see that, then you should also see the following:</p>

<p>(German only) + (both) = (Italian only) + (both) +3. Subtract (both) on both sides.</p>

<p>(German only) = (Italian only) + 3</p>

<p>We know that out of the 30 students, the number who take only one language is the same as the number who take both. That means there are 15 single-language students, and 15 double-language students.</p>

<p>(German only) + (Italian only) = 15. But we said before, (German only) = (Italian only) + 3. So substitute:</p>

<p><a href=“Italian%20only”>B</a> + 3** + (Italian only) = 15</p>

<p>2(Italian only) = 12</p>

<p>(Italian only) = 6.</p>

<p>If you didn’t recognize that the total number of students for each language includes those who take both, you’d cut (incorrectly, but without getting the wrong answer) immediately to (German only) = (Italian only) +3. But you’d probably think of it as simply (German) = (Italian) + 3.</p>

<p>In other words, while the question isn’t ambiguous, if you thought it was, and you chose the wrong interpretation, you should still get the right answer unless you make some other mistake too.</p>

<p>And I hate to name names, but JohnTee is way off base.</p>