Debatable Math Question on Practice SAT (help needed)

Test Preparation SAT Preparation
1

<p>I was doing a practice test today when I came across this question:</p>

<p>Four blocks are placed side-by-side.
**STARTING POSITION [W] [Y] [Z] **
A full cycle is completed when the block in the furthest most right position is moved to the furthest most left position. But the full cycle must be completed using the specific steps below.
Step 1: [W] [X] [Z] [Y]
Step 2: [W] [Z] [X] [Y]
Step 3: [Z] [W] [X] [Y]
Begin at the Starting Position. Using this process, how many steps are needed to return the blocks to the Starting Position position?
A. 3
B. 6
C. 9
D. 12
E. 15</p>

<p>Please help me by answering this question and giving the reason for (or the reasoning behind) your answer. I have my own answer and reasoning, but I would like to hear everyone else’s arguments before I tell mine and post the answer given by the book because I feel that the book’s answer and explanation are incorrect and I don’t want to influence other people by saying what I think first. Thanks a lot for your help!</p>

2

<p>I got 12, choice D. I just wrote out the pattern until it got back to WXYZ then counted the steps.</p>

<p>EG:</p>

<ol>
<li>W X Z Y</li>
<li>W Z X Y</li>
<li>Z W X Y</li>
<li>Z W Y X</li>
<li>Z Y W X</li>
<li>Y Z W X</li>
</ol>

<p>…</p>

<ol>
<li>X W Y Z</li>
<li>W X Y Z</li>
</ol>

<p>There might be a shortcut way of doing this, but I can’t think of what it would be.</p>

3

<p>Oh duh, here’s the shortcut. Notice that after 3 steps, the pattern is the same as the starting position but Z was moved from the end to the beginning of the sequence. Since there are four letters, it will take 4*3 (12) steps in order to cycle through to the starting position.</p>

<p>I really hope I’m not wrong about this.</p>

4

<p>adsfg D: I just realized what I was doing wrong. Your first post made sense…the book gave a similar answer but was a little fuzzy. I’m not sure about the shortcut myself but it makes sense to me. Thanks!</p>