Esoteric Math Questions

<p>I devote this thread to the math questions I find too hard to be self-explanatory. I'll be updating it daily (unless I suddenly become adept in SAT math, which is very, very unlikely).</p>

<p>The thread contains only HARD questions that APPEAR on the SAT.</p>

<p>And the first batch for today 08.02.2012:</p>

<p>1.A group of people were standing single file in a line to buy movie tickets.As Juan stood in the line , he noticed that there were 9 more people behind him than there were in front of him.He also noticed that the total number of people in the line was 3 times the number of people in front of him. </p>

<p>... I actually solved this as I was writing it..intially I made a mistake by frogetting to include Juan in the total number of people .. oh well, I'd be happy if someone sets up an equation for this.</p>

<p>2.In the xy-plane , a point with coordinates (a,b) lies on both of the lines y=2x+3 and y=1-3x . Which of the following equations must be true?</p>

<p>A) a = b
B) a=b+4
C) a=2b
D) a=2b+4
E) a=4-2b</p>

<p>This is a much simpler, straight on question.The problem is that I don't really get what am I actually searching for. I acknowledge that a should be something in terms of b and both should be substituted into both of the equations..but what's the desired result?Equations must be equal?Please explain.</p>

<p>Way to use the big sat word: Esoteric...
1.) F=front B=back T=total
T=3F B=F+9 and then him:
3F=F+9+F+1
F=10
B=19
T=19+10+1(Juan)=30
2.)Plug in Coordinates for X and Y:
b=2a+3 b=1-3a; from there you have all you need...
The equations are equal (because they intersect at (a,b)), from there it is a matter of doing math:
a=-2/5 so b=11/5
then just plug, A is wrong, B is wrong, C is wrong, D is wrong, E is correct
IN FACT, once you get a's value, all of the equations adding something to b must be wrong, making e the only plausible answer...</p>

<p>Thanks a lot ! :)
With the consideration the delectable explanation of yours I even found a shortcut for the 2nd:
since
b=2a+3
b=1-3a ,
adding the two equations will result:
2b=a+4 -> a=4-2b</p>

<h1>1. Cool question!</h1>

<p>First, create your variables!
i = people in front;
b = people behind;</p>

<p>b = i + 9;
3i = 2i + 10; //because he's in line too</p>

<p>Therefore,
i = 10;
b = 19;</p>

<p>I forgot what you're solving for, but that should be sufficient.
...oh god too much coding.</p>

<h1>2.</h1>

<p>y = 2x +3 and y = -3x +1
Now, find the intersection. //I usually just draw it
a = -2/5 and b = 11/5
Which answer expresses this relationship.
You will find that E is, in fact, correct:
(20/5) - (22/5) = -2/5</p>

<p>For that first one...</p>

<p>When I see a problem like that, I know that I'm "supposed to" set up equations. But I can't resist trying the lazy way first. I make up some numbers and see what happens. This time, it took three tries:</p>

<p>Are there 3 kids in front? If so, there'd be 12 in back. Plus 3 +12 + me = 16. 3x3 is not 16.</p>

<p>Are there 5 kids in front? 5 + 9 = 14 in back. 5 + 14 + 1 = 20. 5 x 3 is not 20.</p>

<p>Are there 10 kids in front? 10 + 9 = 19 in back. 10 + 19 + 1 = 30...which is also 3 x 10</p>

<p>I know this is not the mathy way. But I still have yet to see a real SAT problem that requires solving a system of 2 eqns and 2 unknowns. I've seen plenty that SEEM to require this, but they always have turned out to be vulnerable to this kind of laziness.</p>

<p>Yeah, I'm using a similar method. Just wanted to see how an equation of such a question looks.</p>

<p>And the questions to chew on today:</p>

<p>1.If a and b are integers such that a+b< 1000 and a/b=0.625 , what is the greatest value of b?</p>

<ol>
<li></li>
</ol>

<p>y, 2y+7 , y+6...</p>

<p>In the increasing sequence above, the first term is y and the difference between any two consecutive terms is 3.What is the value of the fourth term in the sequence?</p>

<p>A) -4
B) 2
C) 5
D )13
E) 19</p>

<p>These two left me completely clueless.I confess I'm really bad at sequences and "what's the greatest number/ what's the smallest number?" questions</p>

<p>A=.625B
.625B+B<1000
1.625B<1000
B<615.38
so B=615</p>

<p>The second is a matter of plugging in, I'm sure there's easier ways but I don't feel like figuring out:
A= 3rd term is -7, 2nd -10, and 1st -13 (won't work when you plug in y)
B=3rd Term is -1, 2nd -4, 1st -7 (won't work again)
C=3rd term is 2, 2nd is -1, 1st -4 (IT WORKS)!!!
SO C IS CORRECT!</p>

<ol>
<li>I worked in exactly the same way. Turns out the answer is 608 :/ </li>
</ol>

<p>Consequently, A must be 380 . I guess figuring out B is just to get a general direction , then the rest is trial and error.For example you can check and see that 384/615 is 0.62(rounded)</p>

<p>2.Once again ,thanks!It really turns out to be an easy question once you figure it out! :)</p>

<p>Another one coming right up. Guess what? Sequences again..</p>

<p>The nth term of a sequence is given by the formula n^2 + 2n . How much larger is the 10th term of the sequence than the 9th term?</p>

<p>The lack of numbers in a grid in clearly confounds me.Plugging in gave me varying results...what should be done?</p>

<p>Answer is 21, you get 10^2+2<em>10 and 9^2+2</em>9 and that's 120 and 99 difference between them is 21</p>

<p>The nth term of a sequence is given by the formula n^2 + 2n . How much larger is the 10th term of the sequence than the 9th term?</p>

<p>This is literally just a matter of plugging things into f(n) = n^2 + 2n solving for f(10) - f(9);
f(9) = 81 + 18 = 99;
f(10) = 100 + 20 = 120;
f(10) - f(9) = 21;</p>

<p>Thanks !Well..that's.. a no-brainer seems like. I should really practice sequences..failing on level 3s is definitely a bad omen.</p>

<p>And today's questions come as a photo!</p>

<p><a href="http://i.imgur.com/zv8rs.jpg%5B/url%5D"&gt;http://i.imgur.com/zv8rs.jpg&lt;/a&gt;&lt;/p>

<p>Sorry for the mess on the last grid-in. If you have hard time viewing it with all the ink on it , I'll redraw it.</p>

<p>7th Question. I'll be frank - I never did graphs of quad function at high school. They only teached us the formulas for it , and that it.They didn't teach us how to move graphs or anything more explicit.I studied them myself, and I'm not entirely sure how this makes sense. When a>0 the graph should be concave up and when a<0 , concave down? Then why is the answer a? It has something to do with foiling? (x- )(x+ ) ?</p>

<p>18th My progress so far:</p>

<p>ABC is a 3-4-5 right triangle, similar to O (y-intercept) C. And..that's it.</p>

<p>A positive A shifts the graph however units upward. The -x^2 flips it so it points downward.
It's like this: (-Ax^2 -M) + B
So the negative flips a graph, the A will make it more narrow if it is a number greater to 1, -1 (like 2,-2) and it will make it wider if it is less then 1,-1 (like 1/4, -1/4) and M will move the graph to the right however units (if it is like x^2-3) or to the right however units if it is -M (x^2+3) and B will move the graph to the up (+) or down (-) BUT NOTE PARENTHESIS. Outside is up down inside is left right. I hope I made sense...</p>

<p>Okay. 18. 3-4-5 triangle. You know that AB is 4 so B is 1,4 then, you know AC is 3 do C is (4,0) you use point slope form and get y=-4/3x+16/3 y-int is 16/3, or 5.33</p>

<p>Esoteric really isn't the right word to describe these types of questions...</p>