<p>well tough for me at least</p>
<p>Each of the following inequalities is true for some values of X except</p>
<p>A. x< x^2< x^3
B. x< x^3 < x^2
C. x^2< x^3< x
D. x^3< x< x^2
E. x^3< x^2< x</p>
<p>and how would you approach such a problem?</p>
<p>thanks</p>
<p>e? x^2 will always be greater than x.</p>
<p>Ahh this one, just keep plugging in different numbers like .5 or -.5 and whole numbers. </p>
<p>A Works
B Works Plug in -1/2 -1/2<-1/8<1/4
C Doesn't work
D Works Plug in -2
E Works Plug in 1/2</p>
<p>oh, i forgot about fractions...</p>
<p>shiomi- I did that and eventually got it, but I just felt so ****ed after this question. I was wondering if there was any more practical way.</p>
<p>ans is C..........</p>
<p>plugging in and eliminating...i saw this prob like few days ago,i dont remember from which, may jan 08 or 10 RS, but its not hard if u plug in~~</p>
<p>i would like to share my way of solving....</p>
<p>a) when u look at choice a,u know in ur heart that it is true
b)look at hte second part of the inequalities.... x^3<x^2...so x^3-x^2<0....therefor="" x^2(x-1)<0....so="" x-1<0....x<1......now="" the="" first="" part="" of="" inequlity="" x<x^3....so="" x-x^3<0.......x(1-x^2)<0......1-x^2<0.....1<x^2......x="">-1........so pick a value like -.75 and test the inequality.....this option is correct
c) this 1 is the answer.....x^2<x^3...x^2(1-x)<0....x>1.... the second part of inequality is x^3<x....x(x^2-1)<0.....x^2<1........x<1.....no number can be bigger than 1 and smller than 1 at a time..........so it is the choice
d) & e) u know with ur heart that these two option are correct</x^3...x^2(1-x)<0....x></x^2...so></p>
<p>hope it helps</p>
<p>haha thanks gluttony. </p>
<p>yes i knew in my heart and soul that those three were true.</p>
<p>In general, the best way to handle these is to plug in values.
But you have to be very clear on what numbers you can plug in.
If there are no stated parameters in the question then realize that any type of number is fair game: positive, negative, fractions, whole numbers, even or odd.
Sometimes parameters are stated: only positive integers or only even integers, or only integers. Always zone in on these!
Some useful tips to remeber:
0 is an integer--but it is neither positive nor negative. So if the question asks for integers, then 0 is included. But if it asks for only positive integers, then it isn't included.
Also, 0 is an even integer.
1 is not prime.
2 is prime (the only even prime number).</p>
<p>End of section questions like to ask tricky questions that require knowledge of rarely thought about 'rules' of numbers. Know these!</p>
<p>okay, thanks a lot anita. Ill keep the last few rules in mind.</p>
<p>You're right nbafan. There is a more efficient solution. Rather than plug-in numbers aimlessly, look at each answer choice and ask yourself what KIND of number the inequality is describing.</p>
<p>For (A), it's fairly obvious...what kind of number gets bigger when it's squared, even bigger when it's cubed? That's any pos. number greater than 1. Eliminate the obvious choices first before wrestling with the hard ones. (E) is another fairly easy one - a positive fraction gets smaller when squared and even smaller when cubed.</p>
<p>(B) is probably the trickiest one to prove, it's what kind of number gets bigger when you cube it, but even bigger when you square it? It's the one you least expect I guess, the lowly negative fraction. Let's use -½. When you square it, you get positive ¼, obviously bigger. And when you cube it you get -¹⁄₈, still negative, but closer on the numberline to zero than our original ½.</p>
<p>This question tests your understanding of the basic properties of numbers: the negatives, the positives, the wholes and the fractional numbers. So those are the basic types you must consider for this question.</p>
<p>alright, so you're saying instead of just plug in right from start, spend few seconds just thinking. But you're definitely rghtt. It also helps that there are only 4 types of real numbers we really have to know and 5 choices. positive/negative integer, and positive/negative fraction</p>