<p>i have trouble going about how to do these problems. the ones where you have to see if I, II, or III is true and I have a feeling one o them will appear on the SAT. How do you go about these and other ones like this?</p>
<p>e.g. If x, y, and z are positive and xy^3z^2> x^2y^2z^2, which of the following are true? </p>
<p>I. x<y
II. x<z
III. y<z </p>
<p>answer is I</p>
<p>two things: is the question written correctly? And where is it from?</p>
<p>PS: i am trying to help. It is a very hard problem. If you affirm that it is correct, I will figure it out with an explanation</p>
<p>this would be a problem for spidey.
I'll try to see if I can do it. lol</p>
<p>sorry I don't understand what's so hard about it...</p>
<p>basically:</p>
<p>(x)(y^3)(z^2)>(x^2)(y^2)(z^2)</p>
<p>you can divide both sides by (z^2)</p>
<p>so it's:</p>
<p>(x)(y^3) >(x^2)(y^2)</p>
<p>then you divide both sides by (x)(y^2)</p>
<p>which leaves you w/:</p>
<p>y>x</p>
<p>the way he wrote it made me think of</p>
<p>(xy)^((3z)^2)) > x^(2y^((2z)^z))</p>
<p>yeah. with the way he wrote it, i was completely confused. that's why I asked him if he wrote it correctly, because SAT math problems are generally really easy, its just that the pressure and time can get you a question or two wrong.</p>
<p>Meadow: I'm still unsure if it was written correctly. If it is, I think you're explanation may be wrong.</p>
<p>Meadows method is correct. heres an alternative method, its called logical reasoning. </p>
<p>(x)(y^3)(z^2) > (x^2)(y^2)(z^2) </p>
<p>We're told that all x y and z are positive, and the left side is bigger than the right. Both sides have z^2 but the left is bigger simply because of its y^3 . Now, if its bigger simply because the X was replaced by a Y, that means Y must be bigger than X. Bam, there's your answer.</p>
<p>yeah, it's possible.
but if he didn't put parenthesis they probably don't exist? Plus, you get the right answer so I'm assuming that's the way its supposed to be written...</p>
<p>yeah and Quix's way is better way, but when i'm taking the SAT's I tend to not want to think and reason things out due to pressure.</p>
<p>Yeah I understand that. But the problem is incorrectly written. The way its written now, it would simplify to xy^6z > x^8yz. Try doing that one. </p>
<p>Quix and Meadows methods are great if that is the problem. My assumption is that they both are correct, because they way I have it would be way too hard for an SAT question.</p>
<p>xy^6z > x^8yz ? Ok, sure.
xy^6z > x^8 y z</p>
<p>we cancel out the z's, and your left with
x y ^6 > x^8 y</p>
<p>divide the right by y </p>
<p>x y ^5 > x^8 </p>
<p>Divide both by x</p>
<p>y^5>x^7 </p>
<p>Y is obviously bigger than X. Same answer, same methodology.</p>
<p>the problem is from a 2006 PSAT booklet and I just did practice problems for the SAT from this.</p>
<p>(x)(y^3)(z^2)>(x^2)(y^2)(z^2)</p>
<p>^ so I was right...</p>
<p>lol i picked up my pen, wrote an X, then i got stuck! i couldn't understand the Q! lol i know theres something wrong cuz no parentheses, so i scroll down, ehh look wat i found, a bunch of people confused like meh!</p>
<p>Oh. To answer the OP's question, to do these questions, you simply have to use logic and POE. That's it. No tricks.</p>
<p>This isn't a "trick"
but I always tell my students to try to make the question more approachable by substituting in real values. You'll know that you can do this anytime you see variables in the question and in the answer choices.</p>
<p>-For all algebraic questions one of the first things you do is look for ways to simplify---are there any terms that can be canceled out? Can you reduce a fraction any further?<br>
With this question you should see immediately that z^2 can be canceled out.</p>
<p>-Now you are left with just x and y variables. Try to substitute in your own values that work,...just to make the question more 'concrete.' You will quickly realize that y must be greater than z for this to work.</p>