Maths Question

Test Preparation SAT Preparation
1

<p>If each of 8 boys played a game of chess with each of the 6 girls and then each girl played with each of the other girls, which of the following could be the total number of games played?</p>

<p>A 63
B 65
C 69
D 75
E 78</p>

<p>I don't understand why there should be 48 games between 8 boys and 6 girls, and 15 games between the girls.</p>

<p>Please help me!</p>

2

<p>This is two counting problems in one:</p>

<p>The 48 is easier: you have 8 boys to choose from and 6 girls. Just multiply.</p>

<p>The second part is trickier: you have 6 girls to choose from, and then 5 possible opponents. 6 x 5 = 30…but wait – that would count A plays B and B plays A as two different games! In other words, the answer is too big by a factor of 2. So it’s 30 / 2 = 15 more games. (If you know combinations and permutations, this is also 6C2 because the order you pick the girls does not matter.)</p>

3

<p>^
or you can say that each of 8 boys plays one game with each of 6 girls. So that that’s why you multiply 8 x 6 which is equal 48.
For the second one, in order not to get confused, I would have done the following:
So 6 girls play n games with each other.
Let the letters represend each girl.</p>

<p>A B C D E F
5 4 3 2 1 0 </p>

<p>5+4+3+2+1=15 OR you may write this</p>

<p>1) A-B
2) A-C
3) A-D
4) A-E
5) A-F
6) B-C
7) B-D
8) B-E
9) B-F
10) C-D
11) C-E
12) C-F
13) D-E
14) D-F
15) E-F</p>

<p>So 48+15=63
Hope that helps!</p>

4

<p>Thanks alot! I got it now… I have another question.</p>

<p>The quadratic function graphed above has an equation of f(x)= ax^2 + bx + c. (Its an inverse U shaped parabola, with a positive y intercept when x = 0, and the maximum point is to the right of the y intercept). Which of the following must be true?</p>

<p>A) a> 0
B) b> 0
c) b< 0
d) c<0
e) c is even</p>

<p>My answer was C, because -b/2a > 0, a< 0, therefore b must be negative in order for the function to materialize.</p>

<p>The answer is B. I looked through it again and realized my error was in taking the original sign of b as negative, in which case the function would not exist because that would have made b positive after applying -b/2a. Am I right? I asked because the explanation I got was:</p>

<p>axis of symmetry = -b/2a> 0, where a < 0.
f(0)= c> 0, therefore b> 0.</p>

5

<p>^
Where did you find that question? Or at least give us its photo.</p>

6

<p>Mirage2000, here’s the link: [ImageShack&#174</a>; - Online Photo and Video Hosting](<a href=“http://img62.imageshack.us/i/inverseparabola.jpg/]ImageShack®”>ImageShack - Best place for all of your image hosting and image sharing needs)</p>

<p>As you can see, its really a simple inverse of the usual parabola, no values were given. </p>

<p>Hope this helps you in understanding the question.</p>

7

<p>Ok. The equation for the graph you draw is approximately: y= -0.5x^2+1.5x+7
And this tells us that </p>

<p>A) a>0 ( wrong because if a>o then the graph wouldn’t be an inverse; and here a is -0.5)
B) b>0
C) b<0
D) c<0 ( C is 7 which is greater than zero.)
E) c is even (7 is odd. and practically it doesn’t matter at all.)</p>

<p>So I eliminated A, D, and E. I would choose B. (if your graph is correct of course)</p>

<p>If b<0 then it your graph would be like <a href=“http://img220.imageshack.us/i/thatx.jpg/[/url]”>http://img220.imageshack.us/i/thatx.jpg/&lt;/a&gt;
In your drawing the b is definetly more than zero.</p>

8

<p>Here’s why this problem is not an SAT problem:</p>

<p>On the SAT, when it comes to parabolas in the form y=ax2 + bx + c, they NEVER ask about the b value. They want you to be able to look at this parabola and deduce that the a value is negative (b/c it opens downward) and the c value is positive (b/c it’s the y intercept. They just don’t ask about the b value. </p>

<p>BUT IF THEY DID…</p>

<p>Since the x coordinate of the vertex is positive, and since it = -b/2a, where we already know that a is negative, b must be positive.</p>

<p>But again, if this comes from an actual college board test, then it is a first.</p>

9

<p>^
Yeah. It was a tough one. However, I made correct equations :)</p>

10

<p>hey mirage</p>

<p>in your graph, the axis of symmetry is in the left quadrant (-x, y) while the axis in my graph is in the right quadrant (x,y). is that (the location of the axis of symmetry) the reason for the change from b>0 (in my graph) to b<0 (in your graph?</p>

11

<p>-b/2a > 0, right?
a has to be negative, because it is an inverted parabola, so for example fill in -2.
-b / -4 = b / 4 > 0, so b has to be positive. Answer B.</p>

12

<p>

</p>

<p>Yes! </p>

<p>10char</p>

13

<p>A simple question of Combinations.</p>

<p>1) 8 Boys with 6 Girls: Total Options: 6 x 8 = 48</p>

<p>Here’s the Math: 8C1 * 6C1 (choosing 1 out of 8 x choosing 1 out of 6)</p>

<p>2) 6 Girls play with each other:</p>

<p>Imagine these as the 6 girls: ! @ # $ % ^</p>

<p>! plays with (@ # $ % ^) [5 games]
@ plays with (# $ % ^) [4 games]</p>

<h1>plays with ($ % ^) [3 games]</h1>

<p>$ plays with (% ^) [2 games]
% plays with (^) [1 game]</p>

<p>Count the number of games. 5+4+3+2+1 = 15</p>

<p>(note: since it is a question of combination - counting - it will be erroneous to “double-count” the games girls play among themselves)</p>

14

<p>Coming to your second question, it is also quite simple. I solved the question first and later realized that you had provided with an image also. But nonetheless, I arrived on the correct answer. I think that it will be better if I explain to you with pictures. So, here’s your original image, with answers:</p>

<p>[Parabola</a> - Answers](<a href=“http://img824.imageshack.us/i/parabolao.jpg/]Parabola”>ImageShack - Best place for all of your image hosting and image sharing needs)</p>

<p>PS. Pckeller, I’ve since quite a few questions asking about the b value of a graph on the SAT.</p>

15

<p>^ Which tests?</p>

16

<p>^
Tizil7, what is point in explaining something that has been already explained?</p>

17

<p>Hmm, Maybe Kaplan? Or was it Princeton Review? Or maybe Barron’s 2400. I’m sorry, can’t recall exactly which book(s) I saw it in.</p>

18

<p>Right, but those are not real collegeboard tests. Not a big deal though.</p>