math questions from the oct05 sat

Test Preparation SAT Preparation
1

<p>would like to hear the various approaches people have for these problems:</p>

<li>Let @x be defined as x + 1/x for all nonzero integers x. If @x=t, where t is an integer, which of the following is a possible value of t?</li>
</ol>

<p>a) 1
b) 0
c) -1
d) -2
e) -3</p>

<li>If p and n are integers such that p > n > 0 and p^2 - n^2 = 12, which of the following can be the value of p-n?</li>
</ol>

<p>I. 1
II. 2
III. 4</p>

<p>a) I only
b) II only
c) I and II only
d) II and III only
e) I, II and III</p>

<p>3.Each of the following inequalities is true for some
values of x EXCEPT</p>

<p>(A) x < x^2 < x^3</p>

<p>(B) x < x^3 < x^2</p>

<p>(C) x^2< x^3 < x</p>

<p>(D) x^3 < x < x^2</p>

<p>(E) x^3 < x^2< x</p>

<p>This last one is from the March05 exam.</p>

<p>Thanks!</p>

2

<h1>2. (p+n)(p-n)=12</h1>

<p>so p-n can be equal to either 12, 6, 4, 3, 2, 1 (factors of 12)</p>

<p>now they tell you 1, 2, or 4 as possible values of p-n.
if p-n is 4, then p+n is 3. if p and n are greater than zero, then that is not possible.
if p-n is 2, then p+n is 6. that is possible (p=4, n=2)
if p-n is 1, then p+n= 12. not possible
is the answer B?</p>

3

<h1>1 The only way for 't' to be an integer, assuming x is an integer, is if 1/x is also an integer. The only way for 1/x to be an integer is for x to be 1 or -1. If x=1, t=2 (not an option). If x=-1, t=-2, which is choice (d).</h1>

4

<p>Maea, if X=-1, that would be -1+1/-1, which is 0/-1 which equals 0. Is it it (x+1)/x or x+(1/x)?</p>

5

<ol>
<li><p>Should be B 0 </p></li>
<li><p>Should be C</p></li>
</ol>

<p>not sure what do u all think?</p>

6

<p>rahoul. its x + (1/x).</p>

<p>answers:
1.c
2.b
3.c</p>

7

<p>Rahoul (and everyone else), if x=-1, it would indeed be -1+1/-1. Order of operations states that you do the division before the addition, which makes it -1+(1/-1). This equals -1+(-1)=-1-1=-2. My answer stands, d.</p>

<p>[soulofwit - you put 'c', which was probably either a typo or you answered the wrong question - they were looking for t's value, not x]</p>

8

<p>How do you do 3?</p>

9

<p>maea, yes that was a typo. the correct answer for #1 is choice D.</p>

10

<p>any alternate approaches for #2, and anyone who can explain #3?</p>

11

<p>I'm pretty sure that #2 is answer b)</p>

<p>I really can't explain it, it's in my mind but i can't find a way to take it out of my brain and put it in this Message box.</p>

12

<h1>3.</h1>

<h1><a href="http://talk.collegeconfidential.com/sat-preparation/418815-fast-way-approach-problem.html?%5D%5B/url"&gt;http://talk.collegeconfidential.com/sat-preparation/418815-fast-way-approach-problem.html?][/url&lt;/a&gt;]&lt;/h1>

<h1>2 alternate (not faster).</h1>

<p>Knowing the formula a^2-b^2=(a-b)(a+b) is pretty much mandatory for the SAT.</p>

<p>If p-n =
I. 1
II. 2
III. 4
then p=
I. n+1
II. n+2
III. n+4</p>

<p>p^2 - n^2 =
I. (n+1)^2 - n^2 = 2n+1, can not =12 for integer n.
II. (n+2)^2 - n^2 = 2(2n+2) = 12 for n=2.
III. (n+4)^2 - n^2 = 4(2n+4), can not =12 for integer n.</p>

<p>II only is answer B.</p>

13

<p>good stuff; thanks everyone for the helpful info!</p>

14

<p>Thanks for the link, gcf101</p>

15

<p>Namaste, tetrisfan</p>

16

<p>namaste to you gcf101 lol</p>