arbortrees06

hey, can you guys help me out with these problems:
pg. 411 number 13
pg. 412 number 18
pg. 426-427 numbers 14 and 16
thanks!!!!!!!!!!

Harvard_Genius

Ok 411 #13

What is the value of h(1)
Plug 1 into the original equation, so
g(2)+2. Then look at the graph. What happens when x=2 for y=g(x)... y=1. But because it says to add to, it becomes y=3. Answer should be 3. (Checked it and it is)

p. 412 #18

This is on the most fun problems :P. So she drove a 45 MPH in the morning and returned home at 30 MPH in the afternoon. Now obviously you need the formula, Distance = Rate x Time. She spent a lot of 1 hour going to and from work. So pretend as if the entire distance to work was first driven a 45 MPH and then she decided to drive an equal distance at 30 mph. 45 = 1.5 (30). So set 30 equal to x. You then get x+1.5x (the rate) = 1 Hr. So 2.5x = 1 and x = .4. Now multiply .4 by 60 to find out how many minutes = 24. So 1.5 of .4 is .6 and .6 of 60 should add up with 24 to equal 60 minutes or an hour. It does (36 minutes) and 36+24 = 60 mins = 1 hour.

P.426 #14

Ok this is not something you want to work with. So square both sides. You will get (a+b) = (a-b)^-1. This equals (a+b) = 1/(a-b). Now multiply both sides by a-b and you get (a+b)(a-b) = 1. That is answer choice E.

P. 427 #16

This is definetly hard to explain. To approach this problem you first want to make sure you know exactly what it is asking you and translate it in your own words (in your head). Basically, you want to find the union of the 2 sets with the exception of the intersection of the two sets (members that are in either set but not in both sets). Now you are probably wondering why it is 2k instead of 1k. Well once again, translate what K represnets. The common members of a set. But these members are in both sets Pretend set X has the numbeers {1,4,7,9,11} and set Y has the members {1,5,6,7,10,12}. Set Z will have the membesr that are in either set... so {1,1,4,5,6,7,7,9,10,11,12} minus the common membesr {1,1,7,7}. As you can see... it is 2k instead of just k.

Any other math questions you have you can direct to me. Im quite good at SAT math. Hope this helps

arbortrees06

thank you thank you thank you!!! the solutions were so much simpler than i realized! i just printed it out too haha. you are awesome....

Harvard_Genius

No problem, message me if you need more help

gcf101

It's amazing (and frustrating) how many times the same questions gets thoroughly discussed on this forum only to pop up again some time later without anybody bothering (or remembering) to direct to the older threads.

Hard Math Problem =(
SAT math question help
Related thread:
Math Help =/

Look for "Xiggi formula" in all three threads.

jen3248

Harvard genius--are you really a genius who goes to Harvard? If so, what was your secret to getting in ?? : ) thanks.

Harvard_Genius

4 years of hard ass work

SoConfused

Harvard_Genius, can you help me with this problem?

THe average (arithmetic mean) of the test scores of a class of p students is 70, and the average of the test scores of a class of n students is 92. When the scores of both classes are combined, the average score is 86. What is the value of p/n (p over n)?

The answer is 3/8 (3 over 8) but I have no idea how they got that. I tried to set it up like [(70 * P) + (92 * n)]/(p+n) = 86 but I can't seem to solve it.

I went to Studyhall.com but they didn't seem to have solutions to the grid-in problems. Anyway, this problem is #25 on p. 465 in the Red Book. (Third Edition)

Thanks in advance!

obsessedAndre

You had the formula right. All you had to do is solve it:

[70 * P) + (92 * n)]/(p+n) = 86 (why so many parantheses? TI-89?)
=
70P + 92N/p+n = 86
Remember the Distributive Property!

70P + 92N=86(p+n) =

70P+92N=86p+86n

That looks solvable right?

-70p, -86n

6n = 16p

Now here is the tricky part where a lot of people will make a mistake --
because 6n = 16p you will probably be tempted to say p/n = 16/6 which reduces to 8/3. But that is WRONG. Why? Well, consider: if 6*N of something = 16*P of something, which is the greater unit of measure? The N unit.

Therefore, the fact that P has the GREATER coefficient actually means each P is LESS than the each of the variable with the lesser coefficient. So you invert the fraction:
instead of 8/3, p/n actually = 3/8.

It is worth noting that there was no way for me to solve for what P or N is actually equal to (numerically). But it doesn't stop me for answering the question: what is p/n?

SoConfused

Thank you so much! I get it now. It actually seems easy.

I got to the 6N=16P part but I just couldn't do anything with it..LOL It was early this morning and I guess my head just wasn't working properly.

But now it makes sense. Thanks!

xiggi

Humm, not exactly sure why someone would do that ... because
6n = 16 p or 5 = 16p/n or 6/16 = p/n

Just a little aside, one could take the time to write and solve the perfect equation, but a little reasoning could also help in this case.
Draw a diagram for the test scores and CHANGES in scores

70................86......92
...........16...........6

Well we KNOW that the gain of p students HAS to equal the loss of students of n students (no points vanish when averaging the scores).
So we now know that 6*n = 16*p and as result p/n = 6/16.

All you really needed to do was to draw the diagram and "see" the rates of change.

To visualize this better, look at the same problem with easier numbers,

78.........................98..100
................20.............2

In this class, the average of p students went up 20 points and the average of n students went down 2 points. This means that a number of students lost 2 points to a number of students who gained 20 points. The ratio is obviously 10 to 1. Notice how ONE student gaining 20 points requires TEN students losing 2 points each. So there are 1 p students for each 10 n student. This makes p/n = 1/10.

PS To "make sure" to have your ratio in the "right" order, look at the "distance" from the new average. The smaller distance has to be a result of LARGER group (more people losing less on an individual basis). After a while, thsi becomes second nature.

SoConfused

thanks, Xiggi.

I'm trying to follow your method in prepping for the upcoming SAT.

carlbug88

Hi everyone,

I'm new here, and I'm writing the SAT this Saturday. I have a blue book question that I don't think has been answered here before.

It is page 721 #16. There is a picture of a square, with side length 3, with a shaded square lying inside diagonally. The question reads: In the figure above, what is the area of the shaded square?

Any help would be much appreciated.

Thanks.

Carly

seth blue

The tirangles are equilateral, so the hypoteneuse of each tirangle is the root of 5. Squaring the root of 5, you get 5 for the area of the square.

privileged

Hi, if you grid in 6/16 instead of 3/8 will it be regarded as correct?