  # SAT math questions

<p>This is my first time posting a question here so sorry if I am doing this wrong. Anyway I have two questions from the math portion of my SAT practice test.</p>

<ol>
<li>If the average (arithmetic mean) of t and t+2 is x and if the average of t and t-2 is y, what is the average of x and y?</li>
</ol>

<p>(a) 1
(b) t/2
(c) t
(d) t+1/2
(e) 2t</p>

<ol>
<li>For all numbers x and y, let x△y be defined as x△y=x^2+xy+y^2. What is the value of (3△1)△1?</li>
</ol>

<p>(a) 5
(b) 13
(c) 27
(d) 170
(e) 183</p>

<p>Any help with these would be greatly appreciated. Thanks!</p>

<ol>
<li>X and Y are averages, so x equals (2t+2)/2 and Y equals (2t-2)/2. To find the average of x and y, add up (2t+2)/2 and (2t-2)/2, and divide the answer by two, which equals t. The answer is C. </li>
<li>plug in the numbers accordingly to get 3^2+(3)(1)+1^2= 13. Now find 13△1, which is 13^2+(13)(1)+1= 183. The answer is E.</li>
</ol>

<p>Here's a write up of something very similar to what confused said.</p>

<ol>
<li>If the average (arithmetic mean) of t and t+2 is x and if the average of t and t-2 is y, what is the average of x and y?</li>
</ol>

<p>(a) 1
(b) t/2
(c) t
(d) t+1/2
(e) 2t</p>

<p>If the math confuses you, you can convert the algebra into arithmetic.</p>

<p>Step 1: Give 't' a value (t = 4)
Step 2: Solve the problem using that real value:
(4 + 6) / 2 = x = 5</p>

<p>(4 + 2) / 2 = y = 3</p>

<p>(5 + 3) / 2 = solution = 4</p>

<p>Step 3: Use the solution and those #s we've found and put those back into the answer choices.</p>

<p>(a) 1 X
(b) t/2X 4/2 = 2
(c) t YES 4 = 4
(d) t+1/2X 4 + 2 = 6
(e) 2tX 8=8</p>

<p>I'll answer #8 on the next post.</p>

<p>Craig Gonzales</p>

<ol>
<li>For all numbers x and y, let x△y be defined as x△y=x^2+xy+y^2. What is the value of (3△1)△1?</li>
</ol>

<p>(a) 5
(b) 13
(c) 27
(d) 170
(e) 183</p>

<hr>

<p>For this one, yes, you just enter the values into the problem. SATSSB was pretty spot on, and his scan was really nice.</p>

<p>The thing to note is that whenever you see funky shapes on the sat, they are just mind-tricks to confuse you. Think of them like functions (because that's what they are) and plug-in accordingly.</p>

<p>If I had f(x) = 2x + 3, and I asked you to solve f(f(3)), all I'd want is you to run through the function twice: f(3) = 2(3) + 3 = 9 | f(9) = 2(9) + 3 = 21 <-- Solution</p>

<p>So, for this one, you just follow the rules and the rules of PEMDAS (IE Do the parentheses first)</p>

<p>So, Step 1:</p>

<p>3△1 = x^2+xy+y^2 = 3^2 + 3(1) + 1^2 = 9 + 3 + 1 = 13</p>

<p>So, Step 2: You want to bring down that '13' that you just found:</p>

<p>13△1 = x^2+xy+y^2 = 13^2 + 13(1) + 1^2 = 169 + 13 + 1 = 183</p>

<p>Now, that's your solution: 183 (E)</p>

<hr>

<p>The key here is to know how to do these types of questions in the future. They look scary, because you were never taught "the triangle method to math" because that stuff does not really exist. </p>

<p>So whenever you see something like this that does not really exist. Just beat it and move on.</p>

<p>Craig Gonzales</p>

<p>
[quote]
7. If the average (arithmetic mean) of t and t+2 is x and if the average of t and t-2 is y, what is the average of x and y?

[/quote]

We'll use the fact that the average of two numbers is represented by a mid-point between those numbers on the number line.</p>

<p>Mark t-2, y, t, x, and t+2 on the number line. They are evenly spread.
Since t is a mid-point between x and y, t is their average.</p>

<p>Thanks for all the help!</p>