<p>Did a practice test today and I felt relatively good about it: I was expecting 2280 or higher. Unfortunately, I got only 2240 :(. Upon reviewing the test, I found 2 questions I had absolutely no idea how to do. Was the answer key messed up or something? Help would be appreciated.</p>
<p>Here are the questions (one is CR, other is Math...my only mistake -_-):</p>
<p>Math:
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
A. 6
B.9
C.15
D.21
E.24</p>
<p>I put A. 6 - 6 Italians means 9 Germans, means 15 both= 30</p>
<p>Apparently the answer is 9. What.</p>
<p>Critical Reading:
In line 42, the word "mean" most closely means what?:
A. Base
B. xxx
C. xxx
D. xxx
E. Stingy</p>
<p>The passage was discussing how powerful and noble rulers inspire more than powerful and mean rulers. Apparently "mean" most closely means base, rather than stingy. What even.</p>
<p>Are you sure 9 is the right answer? If this is from a prep book, there’s a good chance this is wrong because I got 6 as well mathematically</p>
<p>Okay that was dumb. I read it wrong. My bad! LOL yeah the answer is 6.</p>
<p>Wait so what about the critical reading question?</p>
<p>“Mean” has an alternate meaning of “lowly” (in morality, dignity, or honor), so “base” is the correct answer. While one might argue that “stingy” is immoral, it is too narrow and specific.</p>
<p>For the math question, I got 9 students studying only Italian.
That “If the number of students that study both subjects is the same as the number of students that study exactly one subject” has to be divided into 2 cases, because we dont know which is “one subject”, german or italian, right?
One of the cases have the result of 9
Take g,i,x as the number of students studying only german, italian and both, consecutively.
So we have :
g+i+x = 30
g+x=3+x
g=x
→ g=11,i=8,x=11</p>
<p>Oops, the second equation is g+x=3+i+x </p>
<p>btw, how do you guys got 6? Pls explain for me!!!
Thks in advance</p>
<p>You do NOT need any algebra for this. Take it in two steps:</p>
<p>First, just look at whether kids took one subject or both. If there are 30 kids, and the same number took both as took just one, it means that it has to be 15 who took both and 15 who took just one.</p>
<p>[But @hanggo I do see how you read it: you thought that the number that took both was the same as the number who took just German or the same as the number who took just Italian. But by saying “the number who studied exactly one subject”, they make it clear that you count anyone who studies exactly one subject – not just the ones who studied one PARTICULAR subject or the other.}</p>
<p>In any case, once you know that 15 kids took just one subject, you just have to break it up so that 3 more took one than the other. 6 and 9 are easy to find just by playing with numbers…</p>
<p>Here are my solutions copied over from another thread (note that I start with exactly what pckeller did):</p>
<p>Since there are 30 students, and the number that study both subjects equals the number that study only one subject, there are 15 students that study only one subject. So we want to split up 15 as a sum of two numbers such that one is 3 more than the other - we have 9 + 6 = 15 (we can get this using “informal” or “formal” algebra). So 6 students study Italian only.</p>
<p>Notes: (1) Here is the “formal” algebra in case you need it: Let x be the number of students that study Italian only. Then the number of students that study German only is x+3. So x + (x+3) = 15. Thus, 2x + 3 = 15. So 2x = 12, and x = 6.</p>
<p>(2) To do this with a Venn diagram, you would draw 2 overlapping circles labelling the first G and the second I. The intersection gets 15 right away, and then we need to put a total of 15 in the other two regions such that region G has 3 more than region I (by G, I actually mean “G only,” and similarly for I) . This should clearly be 9 and 6, respectively. (Remark: note that I am strongly assuming that there are no students that do not study either language - this should have been mentioned in the problem. Technically ther should be a recatangle surrounding the two overlapping circles. It is consistent with the given information that we could put 4 in the rectangle outside the two circles, 13 in the intersection, 8 in region G and 5 in region I.)</p>
<p>(3) To solve this algebraically, we can let x be the number of students that study German only, y the number of students that study both, and z the number of students that study Italian only. Then we get the system of equations:</p>
<p>x+y+z=30
x+z=y
x+y=y+z+3</p>
<p>This system simplifies to:</p>
<p>x+y+z=30
x-y+z=0
x-z=3</p>
<p>You can solve this system pretty quickly by hand using the elimination method, or you can do Gauss Jordan Reduction pretty quickly in your graphing calculator by inputting a matrix and using the rref( feature.</p>
<p>@pckeller and DrSteve
I got it
Thank you guys so muchhhhhhhh</p>