<p>Each of the following inequalities is true for some
values of x EXCEPT
(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>The answer is C but I cannot find an example for B</p>
<p>Example for B is any no. smaller than 1 but negative, like -0.35</p>
<p>^ Wouldn’t that result in something like D?</p>
<p>OMG NVM I GOT IT. TYVM</p>
<p>Never mind because I got this question wrong myself while practicing. It perhaps is from one of the released past tests… probably SAT test booklet 2007-08</p>
<p>When picking numbers you want to vary the “type” of number you choose. In this case there are 4 types that will eliminate each of 4 of the choices:</p>
<p>(1) A positive integer greater than 1
(2) A negative integer less than -1
(3) A positive fraction between 0 and 1
(4) A negative fraction between -1 and 0.</p>
<p>The numbers I would choose are 2, -2, .5, and -.5.</p>
<p>Be particularly careful when plugging negative numbers into your calculator.</p>
<p>^ Yes! Specifically, all of you graphing calculator users: make sure you keep your brain working…supposed you mean to find the value when -3 is squared. If you enter:</p>
<p>-3^2 </p>
<p>your graphing calculator reports the answer as -9. You KNOW that’s wrong, so what happened? Your calculator followed the rules of order of operation – it squared and then made it negative. </p>
<p>So what do you do? </p>
<p>Either use parenthesis: (-3)^2</p>
<p>or do it in two steps: -3 ENTER followed by ^2 which your calculator will read as ANS^2.</p>
<p>Or just be alert and realize that the negative number squared must be positive. The point is that if you mindlessly follow your calculator, you could get burned.</p>