<p>Here’s a couple questions from the blue book that I don’t understand and would appreciate some help with.</p>
<li><p>The average (arithmetic mean) of x and y is 5 and the average of x, y, and z is 8. What is the value of z?
The answer was 14. What I tried to do did not work at all.</p></li>
<li><pre><code> 3, 5, -5,…
</code></pre>
<p>The first term in the sequence of numbers show above is 3. Each even-numbered term is 2 more than the previous term and each odd-numbered term, after the first, is -1 times the previous term. For example, the second term is 3+2, and the third term is (-1) x 5. What is the 55th term of the sequence.
The possible answers were -5, -3, -1, 3, 5. The correct answer was -5.</p></li>
</ol>
<p>Can someone help or explain to me how to do these problems?</p>
<ol>
<li>You have to look for patterns
3, 5, -5, -3, 3, 5, -5, -3, 3, 5, -5, -3,- etc
It repeats every 4 so, closest multiple of 4 is 52 (starts again here, 52 being -3)
3 more digits so (3, 5, -5<— )</li>
</ol>
<p>Significa thanks. I realized on #1 when I went to do the average of z i was dividing by 2 not 3. ugh, I always make stupid mistakes.</p>
<p>Care to explain 2 more?</p>
<ol>
<li>If (a+b)^1/2=(a-b)^(-1/2) than [answer E] a^2 - b^2 = 1
I don’t get that at all…</li>
</ol>
<p>4.Set X has x members and set Y has Y members. Set Z consists of all members that are in either set X or set Y with the exception of the k common members (k>0). Which of the following represents the number of members in set Z.
The answer was x + y - 2k. I thought it would have been x + y - k</p>
<p>3 is a bit confusing, I think this is how it goes
You know that the power of 1/2 is the sqrt so put it in sqrt form. And that negative exponents can be nullifed by putting it over one.
So, (sqrt a+b) = 1/(sqrt a-b)
Then I cross multiplied, so (sqrt a+b) (sqrt a-b) = 1
Then I squared both sides, (a+b)(a-b) = 1
Foil, and you get a^2 - b^2 = 1</p>
<p>4, think of it as a venn diagram, if there are common members, you have to subtract it from both sides (They are in both X and Y)</p>
<p>Yep, interesting thing, I was just doing the probability/statistics section in my Math L2 book, there was a formula that you might be interested in</p>
<p>Was that formula a joke? 'Cuz if it wasn’t that only confuses me.</p>
<p>But seriously, I suck at applying math knowledge, like that sqrt problem; although I know that ^1/2 is the same as sqrt I wouldn’t have thought of that</p>
<p>4.Set X has x members and set Y has Y members. Set Z consists of all members that are in either set X or set Y with the exception of the k common members (k>0). Which of the following represents the number of members in set Z.</p>
<p>x = pureXmembers + k common members
y = pureYmembers + k common members
so purelyX = x - k
and purelyY = y-k
so Z = purelyx + purelyY = x-k + y-k = x+y -2k</p>
<p>For the first one, if you don’t like using formulas and just want quick thinking, you can just assume that x and y are 5 for this problem, and since there are 3 numbers in the second equation, you multiply 8 by 3. You get 24. Subtract the 10 that you got from the last equation, and you get 14. If you are more of a formula kind of guy/girl, Significa’s method would be best, but this is faster than an actual formula, taking as little as 10 seconds.
They are technically the same thing, just you do all the work automatically in your head. :)</p>
<p>I may be going about it the wrong way, but I just plugged in numbers for x and y. I used 4 and 6 (the average of 4 and 6 is 5). Then it is easy to determine that z must be 14… 4+6+z must equal 24 in order for the average to be 8, therefore z must be 14.</p>
<p>Yeah, I should have gotten the first one right, except I’m an idiot and I forgot when you find the average of 3 numbers you divide by 3, not 2.</p>
<p>3 more problems. Yeah, I’m really taking advantage of people being able to explain these to me, so what? Sue me.</p>
<ol>
<li><p>Dwayne has a newspaper route for which he collects k dollars each day. From this amount he pays out k/3 dollars per day for the cost of the papers and he saves the rest of the money. In terms of k, how many days will it take Dwayne to save $1000.
The answer was 1500/k</p></li>
<li><p>In the xy-coordinate plane the graph of x = y^2 - 4 intersects line L at (0,p) and (5,t). What is the greatest possible value of the slope of L.
The answer was 1.</p></li>
<li><p>Esther drove to work in the morning at an average speed of 45 mph. She returned home in the evening alone the same route and averaged 30 mph. If Esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning?
The answer was 18.</p></li>
</ol>
<p>I find the easiest method for the first problem of your new list to be just plugging in numbers, it’s simple and not time consuming at all. So let’s assume he makes $300 dollars a day. K=300. 300/3=100. $100 dollars goes towards the cost of the paper. So, in order to make $1000, it would take him 1000/200. So, it would take him 5 days. Now find the same result… 1500/300=5. Thereya go.
It seems like it would take a little while, but it honestly only takes like 20 seconds if you are fast.
There probably is a better way, I just find this method gets the job done for me. </p>
<p>And don’t feel bad for asking questions, it’s what improves your score!</p>
<ol>
<li><p>Blah, ignore this. Look at spideys</p></li>
<li><p>What page? Need to see the diagram.</p></li>
<li><p>Use Xiggi’s speed formula
2<em>rate1</em>rate2 / ( rate1+rate 2) =average speed per hour
2(45) (30) / ((45) + (30))
36 miles per hour. 30minutes = 1/2 hour
So 1/2 x 36 = 18 miles.</p></li>
</ol>
<ol>
<li><p>Dwayne has a newspaper route for which he collects k dollars each day. From this amount he pays out k/3 dollars per day for the cost of the papers and he saves the rest of the money. In terms of k, how many days will it take Dwayne to save $1000.
Let the number of days taken = n
n(k - k/3) = 1000
n.2k/3 = 1000
n = 1500/k</p></li>
<li><p>In the xy-coordinate plane the graph of x = y^2 - 4 intersects line L at (0,p) and (5,t). What is the greatest possible value of the slope of L.
The answer was 1.</p></li>
</ol>
<p>For (0,p) … x = y^2 - 4
0 = p^2 - 4
p = ±2</p>
<p>Also, for (5,t)
5 = t^2 - 4
9 = t^2
t = ±3</p>
<p>The slope of L is given by (t-p)/(5-0) = t-p/5
t-p will be max for t = +3 and p=-2
slope = +3 - (-2) / 5 = 5/5 = 1 </p>
<ol>
<li>Esther drove to work in the morning at an average speed of 45 mph. She returned home in the evening alone the same route and averaged 30 mph. If Esther spent a total of one hour commuting to and from work, how many miles did Esther drive to work in the morning?
The answer was 18.
Let the distance = x
Time = Distance/speed
1 = x/45 + x/30
1 = x[2 + 3 / 90]
1 = x.5/90
x = 18</li>
</ol>
