<p>For positive integers y and z, of z to the 2nd=y to the 3rd and y to the 2nd =16, then y/2 = </p>
<p>a .8
b .5
c .4
d .2
e 2</p>
<p>The units digit of 2 to the 33rd is how much less than the hundredths digit of 567/1000</p>
<p>a 1
b 2
c 3
d 4
e 5</p>
<ol>
<li>y ^ 2 = 16</li>
</ol>
<p>y = 4</p>
<p>4 / 2 = 2. The answer should be E if I read that correctly.</p>
<ol>
<li>Two has a pattern.
2 ^ 1 = 2
2 ^ 2 = 4
2 ^ 3 = 8
2 ^ 4 = 16
2 ^ 5 = 3*2*</li>
</ol>
<p>That means every fourth power ends in six. 2 ^ 34 ends in six. Then, 33 ends in eight. 8 - 6 = 2. So the answer should be B.</p>
<ol>
<li><p>I got E too, but in the book it says that it is B. Is this just a mistake?</p></li>
<li><p>Why do you pick every fourth power?</p></li>
</ol>
<p>34 isn't a multiple of 4. 32 ends in 6 so 33 ends in 2. The correct answer is 6-2 which is 4.</p>
<p>blythe89, it is every 4 because the pattern of 2^n is that every 4 powers, the unit digit repeats itself. 2, 4, 8, 6, 2...</p>
<p>2 ^ 1 = 2
2 ^ 2 = 4
2 ^ 3 = 8
2 ^ 4 = 16
2 ^ 5 = 32</p>
<p>How does it repeat itself?</p>
<p>
[quote]
For positive integers y and z, of z to the 2nd=y to the 3rd and y to the 2nd =16, then y/2 =</p>
<p>a .8
b .5
c .4
d .2
e 2</p>
<ol>
<li>I got E too, but in the book it says that it is B. Is this just a mistake?
[/quote]
</li>
</ol>
<p>Someone made a mistake ... the book or the transcriber. </p>
<p>The REAL question should be, "What is y/Z. </p>
<p>In this case, y is 4 and z is 8. So y/z is 1/2 or .5. The answer is indeed B. </p>
<p>PS Isn't it fun to have to decipher the question to find the correct answer
PPS I blame gcf101 for his theories of extraneous information in SAT problems. In this case, z WAS needed. :D</p>
<p>2 ^ 1 = 2
2 ^ 2 = 4
2 ^ 3 = 8
2 ^ 4 = 16
2 ^ 5 = 32</p>
<p>How does it repeat itself?</p>
<p>2 ^ 1 = 2
2 ^ 2 = 4
2 ^ 3 = 8
2 ^ 4 = 16</p>
<p>2 ^ 5 = 32
2 ^ 6 = 64
2 ^ 7 = 128
2 ^ 8 = 256</p>
<p>2 ^ 9 = 512
2 ^ 10= 1024
2 ^ 11 = 2048
2 ^ 12 = 4096</p>
<p>2 ^ 13 = 8192 --------- see the pattern 2,4,8,6
2 ^ 14 = 16384
2 ^ 15 = 32768
2 ^ 16 = xxxxx6</p>
<p>2 ^ 17 = xxxxx2 --------- see the pattern 2,4,8,6
2 ^ 18 = xxxxx4
2 ^ 19 = xxxxx8
2 ^ 20 = xxxxx6</p>
<p>2 ^ 21 = xxxxx2 --------- see the pattern 2,4,8,6
2 ^ 22 = xxxxx4
2 ^ 23 = xxxxx8
2 ^ 24 = xxxxx6</p>
<p>2 ^ 25 = xxxxx2 --------- see the pattern 2,4,8,6
2 ^ 26 = xxxxx4
2 ^ 27 = xxxxx8
2 ^ 28 = xxxxx6</p>
<p>2 ^ 29 = xxxxx2 --------- see the pattern 2,4,8,6
2 ^ 30 = xxxxx4
2 ^ 31 = xxxxx8
2 ^ 32 = xxxxx6</p>
<p>2 ^ 33 = xxxxx2 --------- see the pattern 2,4,8,6
2 ^ 34 = xxxxx4
2 ^ 35 = xxxxx8
2 ^ 36 = xxxxx6</p>
<p>
[quote]
In this case, z WAS needed.
[/quote]
</p>
<p>I have always mantained that z is needed!
As a matter of fact, I desperately need quite a number of them right now.</p>
<p>PS. And how would we say "xiggi" if we did not have z on our tounges?
:p</p>
<p>The Ex-iggi :)</p>
<p>The units digit of 2 to the 33rd is how much less than the hundredths digit of 567/1000</p>
<p>a 1
b 2
c 3
d 4
e 5</p>
<p>er.. correct me if I'm wrong, the unit digit of 2^33 is 2 as shown above, the hundredth digit of 567/1000 is 6, therefore 6-2 =4 which is D not B right?</p>
<p>that is a tricky pattern! </p>
<p>and with that wrong answer problem, there is even an explanation on how to find that answer.....</p>
<p>thanks for all the help!</p>
<p>Sorry, sorry, sorry. I was slack on that.</p>
<p>Thank you for correcting me.</p>
<p><em>Slaps self</em></p>