SAT Math HELP

Test Preparation SAT Preparation
1

<p>Please help I do not understand the following questions, and if you can please explain too how you got the answer.</p>

<ol>
<li>A computer is programmed to read a positive integer n and carry out the following intrauctions repeatedly until a value of 1 is obtained.</li>
</ol>

<p>If n is even, then the new value of n is n/2.
If n is odd, then the new value of n is 3n+1.</p>

<p>For instance if the first value of n is 14 the second value of n is 7 and the third value is 22, and this is continued until a value of 1 is obtained.</p>

<p>*When the first value of n is 27, the 112th value is 1. When the first value of n is 54, which value is 1?</p>

<p>A. 56 B. 58 C. 111 D. 113 E. 224
(My guess was either A or E since it has to be either twice or half of the 112th value... but im not sure)</p>

<ol>
<li><p>If x and y are positive integers, x divided by 7 leaves a remainder of 3, and y divided by 7 leaves a remainder of 4, what is the remainder when xy is divided by 7?
A. 0 B. 1 C. 2 D. 5 E.6</p></li>
<li><p>A trains leaves the station at 11:00 a.m. traveling at the rate of 40 miles per hour. A faster train leaves the same station at 1 p.m. that afternoon and travels in the same direction on a parallel track at a rate of 60 miles per hour. At what time will the faster train overtake the slower one?</p></li>
</ol>

<p>A. 3pm B. 4pm C. 5pm D. 6pm E. 7pm</p>

<ol>
<li>For any real number x, define {x} as the least non-negative number such that x+{x} is an integer. For example, {2.8}=0.2, since 2.8+0.2=3. What is the value of 0.4-{0.4}?</li>
</ol>

<p>A. -0.6 B. -0.2 C. 0 D. 0.6 E. 1</p>

<ol>
<li>If n is a positive integer, then (4^n)^2 = ?
A. 2^4n B. 2^2n^2 C 4^n+2 D 4^n^2 E. 16n^2
(2 to the (2 to the 2n (4 to the (4 to the n (16n squared)
four n power to the n+2 power) squared
power) 2nd power) power)</li>
</ol>

2

<p>Damn, I had eloquent explanations, but my internet timed out and it didn’t post. So here are brief rewritten explanations.</p>

<p>1) The first step of 54 is to divide by two since it is even. That gives us 27. We can now follow all the steps of 27. So the answer is 112 + 1. (the 112 steps from 27 and the 1 extra step we took) D</p>

<p>2)</p>

<p>Let x = 10
and y = 11, both satisfy the requirements.</p>

<p>therefore 110 / 7 = 15 r 5.</p>

<p>Answer is 5, D</p>

<ol>
<li>map it out, work it out by thinking, or use equation. </li>
</ol>

<p>80 + 40t = 60t,
t=4.
t = time in hours after second train leaves</p>

<p>therefore answer is 1:00pm + 4 hours = 5:00pm – C</p>

<p>4) B
{0.4} = 0.6
0.4 - 0.6 = -0.2</p>

<p>5) Simplify: (4^n)^2 = 16^n </p>

<p>2^4 = 16, so we should keep a look out for answer choices with such.</p>

<p>We can see A has 2^4, so lets check.</p>

<p>2^4n = 16^n voila. answer is A.</p>

3

<p>omg everything makes so much sense ;~; thank you, but the one question i still dont quite get is 4, how is it -0.2??</p>

4

<p>For number 4,</p>

<p>You know that {anything inside these curly brackets} = any random POSITIVE number that will make it {whats in here, without the curly brackets} = a integer. </p>

<p>Kinda weird explanation, sorry, but here are some examples:</p>

<p>{5.7} = 0.3 ---- 5.7 + 0.3 = 6 (an integer)
{4.4} = 0.6 ---- 4.4 + 0.6 = 5 (an integer)</p>

<p>Also, {4.4} cannot equal -0.4 because the question specifies that it is non negative. </p>

<p>So therefore {0.4} = 0.6 – since 0.4 + 0.6 = 1 (an integer)</p>

<p>So in the equation 0.4 - {0.4} = ?
we simply plug in 0.6 for {0.4} to make 0.4 - 0.6 = ?
solve this and we get -0.2.</p>

<p>Hope that was a bit clearer. (also hope i’m right (didn’t overlook some fine detail of the problem))</p>

5

<p>Yes thats much clearer to me now, I really appreciate your help</p>

6

<p>Wouldn’t 4 be C, since 0 is the closest non-negative number, not 1?</p>

7

<p>^ i was thinking that, but </p>

<p>“define {x} as the least non-negative number such that x+{x} is an integer”
So i thought this means that {x} is non negative (not least non negative number that x is closest to, which in this case is 0) and therefore {0.4} cannot = -0.4</p>

<p>Anyway, if you did closest to integer, following your train of thought, you would get:
{0.4} = -(0.4)</p>

<p>0.4 - -(0.4) = 0.8 (not in the answer choices)</p>

<p>sorry if this doesn’t make sense :S - I confused myself ( hate technicalities )</p>

8

<p>It does make sense, I just don’t understand why it’s not 0.8</p>

9

<p>because {x} cannot be negative. So the closest integer that would keep {0.4} positive is 1. Not 0.</p>