<p>To those who can’t look through the entire thread of the “OFFICAL MAY SAT DISCUSSION”, then if you’re interested in the answers to the math section, I have compiled all the individual posts explaining the answers for each specific question asked within the thread. </p>
<p>I hope this alleviates all of your worries!</p>
<li><p>There are 23 with oats and 25 with rice and 16 only oats so…</p>
<p>23-16 = 7 that have both</p>
<p>25-7 = 18 that only have rice </p></li>
<li><br>
<br></li>
<li><p>10 possibilities between 4000-5000 ascending from left to right:</p></li>
</ol>
<p>4567
4568
4569
4578
4579
4589
4678
4679
4689
4789</p>
<li>x < 2 < 2x OR 2x < 2 <3x ?
<ul>
<li> 2x < 2 < 3x</li>
</ul></li>
</ol>
<p>2x < 2 < 3x … I put .8 because .8 * 3 = 2.4 and .8 * 2 = 1.6</p>
<p>Anything from .7 to .9 is OK.</p>
<li><p>Yeah, I put 31 also because the third one has to be between the difference and the sum of the other 2 sides and the sum is 32 so the greatest possible value is 31 which is an option.</p></li>
<li><p>The sum of the digits of all even numbers is even: 2011!</p></li>
<li><p>The two-gallon problem was tricky. Here’s my solution to it:</p>
<p>(Name) has a scooter (motorbike?) that runs m miles per 1 gallon. Her scooter can hold 2 gallons of gas and gas costs $1.25 per gallon. If she pays d dollars to fill her tank, how much gas was there in the scooter/motorbike initially?</p>
<p>The hardest thing about this problem was realizing which variables are relevant.</p>
<p>Using an equation involving cost, I came to my answer.</p>
<p>$d + $1.25g = $2.5, where g is the gallons needed to fill the tank.</p>
<p>d + 1.25g = 2.5
2.5 - d = 1.25g
g = (2.5-d)/1.25
g = 2 - d/1.25</p></li>
<li><p>What about the one with “t” as the third number and the first and second added to 180? [D]</p></li>
<li><p>What about that question with two lines that were tangent to a circle and it asked which other angle equalled it?</p>
<p>It was a quadralateral… opposite sides were equal… it gave you theat two of the sides were tangent (so, they were 90 deg… and not coincidentally, they were opposite each other)… thus, based on the property of quad… the opposite angle was equal.</p></li>
<li><p>Can you guys explain to me that math question where two lines were tangent to a circle at point A and B.</p>
<p>It kind of formed a triangle looking thing with a perpendicular line from the radius going straight up.</p>
<p>It asked what angle that the angle on the far left equalled.</p>
<p>= [What it created was not a triangle - but a quadrilateral… In the quadrialteral, opposite sides are congruent … thus angle B was congruent to the angle opposite it…]</p></li>
<li><p>PRD = All of the other choices had only 2 dividends (was that the word)
15- 5<em>3
21- 7</em>3
27- 9<em>3
18- 6</em>2*3- which is greater than 18</p></li>
<li><p>There was only one math I remember with Roman numerals (hate those ones)</p>
<p>Was the answer II and III? [Only II]</p></li>
<li><p>If a and b are numbers on a number line more than 100 apart, which of the following MUST be true?</p></li>
</ol>
<p>I. |a| - |b| > 100</p>
<p>II. |a - b| > 100</p>
<p>III. |a| * |b| > 100</p>
<hr>
<pre><code> I. If a and b are more than 100 apart, a and b could be -50 and 51, respectively. |-50| - |51| = 50 - 51 = -1. -1 is NOT greater than 100, so I is NOT always true.
II. If a and b are more than 100 apart, a and b could be -50 and 51, or 200 and 99, or 1066 and 742, or -500 and -620, respectively, for example. In each case, the difference between each is greater than 100. Remember that when subtracting negative numbers, the sign changes and you are actually adding, eg. 50 - (-51) = 101. If you are subtracting a positive number from a negative one, remember that you must take the absolute value. This is ALWAYS true.
III. If a and b are more than 100 apart, a and b could be 100 and -1, or 101 and 0, respectively. |100| x |-1| = 100. |101| x |0| = 0. Neither of these is greater than 100. This is NOT always true.
THE ANSWER: II ONLY.
</code></pre>
<li><p>The surface area problem but I got the cylinder problem. The answer was [16/9].</p></li>
<li><p>3, 4, 6 Triangle: </p>
<p>If you know Laws of Cosines…that’s how 3,4,6 could be done</p>
<p>c^2 = a^2 + b^2 - 2(a)(b)*cos(angle c)</p>
<p>So, if you set a = 3, b = 4, c = 6, you can find angle c > 90.</p></li>
<li><p>Here are some answers I remember putting down for the grid-ins:</p>
<p>15, 4, 115, 1600, 3/4, 10, 9?, 18, .8, .167 (.6666)</p></li>
</ol>
<p>1) 15
2) 4
3) 1/6
4) .66 - .9
5) 115
6) 18
7) 9
8) 1600
9) 3/4
10) 10</p>
<pre><code> For the grid-in involving the bar graph, I put 1600 because it asked for the total amount among the ones above the median, which was 350.
[2, 15, 30, 2000, 47.5, 5, 3, 2.5, .75, 10]
^ I had the test that had entomology as one of the vocab answers for study of insects.
</code></pre>
<li><p>^ .8 was x < 2 < 3x</p></li>
<li><p>"a^x/a^y = a^-6</p>
<p>a^x times a^y = a^12</p>
<p>What’s y?"</p>
<hr>
<p>Simplifying, a^(x-y) = x^-6
x - y = -6</p>
<p>a^(x+y) = a^12
x + y = 12,</p>
<p>Add both equations together:</p>
<p>2x = 6
x = 3. </p>
<p>Plug back in:</p>
<p>3 + y = 12</p>
<p>Y = 9</p></li>
<li><p>People studying music and art? </p>
<p>I got 16 for that, 48 students, 9 study neither, 30 study music, 25 study art, 48-9-39; 55-39=16 that study both.</p></li>
<li><p>In a series, each term was n(n+1); how much greater was the 20th term than the 19th? 20(21)=420; 19*20=380, 420-380= [40]</p></li>
<li><p>g(x)=-f(x); its the same shape except downward.</p></li>
<li><p>The other choices were about intercepts or something. I extended the line in both directions and I dont thing any of them were true, besides the point seemed to have a somewhat negative slope, for the one with the triangle (grid in) was the slope is [3/4].</p></li>
<li><p>Did anyone get 51 for the musical note question on the Math section?</p>
<p>[51] only one divisible by 3.</p>
<p>Yeah, the music one was 51. My reasoning:</p>
<p>There were four notes on the diagram and the third note was the one the musician would stop on. If you make a pattern, you’ll see the following:</p>
<p>He must stop on 3, or 7, or 11, etc., or more accurately, a number of the form 4k-1 where k is some number. 51 was the only choice that satisfied this condition.</p></li>
<li><p>I got 13 (b or c) for the area of the square when given the two numbers of the sides of the triangle. Rounded off from 12.96 something. </p>
<p>Square was 13, as the length of the triangle sides were 3 and 2 the hypothenus was sqrt(13).</p>
<p>3^2=9… 2^2=4, 9+4=13 square root of 13 squared is 13.</p>
<p>If your triangle sides were 2 and 3, it was 13
If your triangle sides were 3 and 4, it was 25</p></li>
<li><p>3 sq. and 4 sq is 25 rad 25 is 5…then 5 *5 for area gets 25.</p></li>
<li><p>Oranges - 1.80</p></li>
<li><p>I got a 47.5 on grid.</p></li>
<li><p>The one with the parallelogram the answer is 240.</p></li>
<li><p>Are you talking about the one thats solve for x with the triangle? There was a right angle, a triangle and 2 x’s. For that one, the triangle’s third angle was 40, the right angle was 90 so thats 130 together. 360-130 = 230, divide that by 2 to get 115 degrees for x.</p></li>
<li><p>x^2+kx+15 = (x+t)(x+5) </p>
<p>a) 8
b) 9
c) 10
d) 15</p>
<p>The answer was 8, b/c it must be 3, 3*5 = 15.</p>
<p>k^2x=kx
k can be 0 or 1</p>
<p>x^2 + kx + 15= (x+t)(x+5)</p>
<p>It must equal to 3 since 5*3=15
Thus when u FOIL out the factors the equation becomes. x^2 + 8x + 15.
so k=8</p></li>
<li><p>It was like…“x” represents the amount of books. </p>
<p>3/4 are paperback (or something).how many paperbacks are there in terms of x?</p>
<p>So yeah… [3x/4]</p></li>
<li><p>What is the answer to the math problem where you have an 3 hours and 3 breaks 12 minutes each…how long was each session?</p></li>
<li><p>It was 36 minutes because it said that the 3 breaks were between consecutive sessions. So it would be like this:</p>
<p>Session, break, session, break, session, break, session</p>
<p>3 * 60 = 180 minutes
180 - (3*12) = 144
144/4 = 36 minutes</p>
<p>There were 3 breaks, not sessions. Look at it like this:</p>
<p>|start| SESSION (break) SESSION (break) SESSION (break) SESSION </p>
<p>|finish|</p>
<p>If it were just a break for each session there wouldn’t really be either a start or a finish because there would be a break next to a finish:</p>
<p>|start| SESSION (break) SESSION (break) SESSION (break) |finish|</p></li>
<li><p>0 is neither negative or positive.</p>
<p>If xy=2, yz=5, xz=10, and x>0, what is the value of xyz?</p>
<p>If you multiply all three expressions together, you get:</p>
<p>(xy)(yz)(xz) = (2)(5)(10)
(x^2)(y^2)(z^2) = 100
(xyz)^2 = 100
xyz = 10</p>
<p>The reason xyz cannot be negative is because:</p>
<p>We know x>0, so if xy = 2, y >0 and if yz=5, z> 0.
Because all three are greater than 0, their product must be positive.</p></li>
<li><p>On line l, A is located at (2,7) and B is located at (12, 1).
What is f(7).</p>
<p>Okay, so you find the slope of the line.
Slope = -6/10 (or -3/5)</p>
<p>Using -3/5, if you move from A down 3 and then right 5, you wind up at the x-coordinate of 7, and the y coordinate 4.</p>
<p>Therefore the answer is 4.
I believe it was C or D.</p></li>
</ol>