<p>Okay, I’m back. </p>
<h1>8.</h1>
<p>I did a quick sketch with Teams A, B, C, and D:</p>
<p>AB
AB
AC
AC
AD
AD</p>
<p>BC
BC
BD
BD</p>
<p>CD
CD</p>
<p>That’s 12 games. Right?</p>
<p>Right, but it’s way too time consuming. Got any other strategy?</p>
<p>Well, you could just sketch one match-up for each team and multiply the total number by 2. Really, it only took me 15 seconds or so.</p>
<h1>10.</h1>
<p>1/k = .13_…</p>
<p>Plug in numbers into your calculator that will give a result near 0.13. 1/6 = .166 and 1/8 = .125 so k must be between 6 and 8.</p>
<p>1/7 = .142
1/7.5 = .133…</p>
<p>so k = 7.5</p>
<p>(7.5 - 1)/7.5
6.5/7.5 = .866</p>
<p>The tenths digit is 8.</p>
<h1>11</h1>
<p>ab=5</p>
<p>5, a, b, 5,</p>
<p>ab, a, b, ab, ab^2, ab^3, ab^5, ab^8, ab^13, ab^21</p>
<p>10th term: ab^21
ab= 5</p>
<p>5^21</p>
<p>Awesome first post on the forum, Enquiry, thanks!</p>
<p>Questions left to go -> 6, 8, and 12.</p>
<p>For #6, is the root raised to the nth power or is just a raised to the nth power?</p>
<p>( root of a ) ^ n</p>
<p>All of it, is raised to the nth power.</p>
<p>For #6, I couldn’t use exponent rules to do it algebraically, so I plugged in some numbers, namely:</p>
<p>5 for a and 2 for n
and
25 for a and 1 for n</p>
<p>They both worked in the original equation</p>
<p>Since a^n equaled 25 on both of them, I tried another one (this time 625 for a and .5 for n), and it still worked. Thus, I determined that a^n will always equal 25. After I did this, I divided 1 by 25 and reached the answer of 0.04</p>
<p>12 is a)b=0?</p>
<p>sqrt(a+b) = sqrt(a-b). Square both sides and get a+b = a-b. 2b=0 thus b=0</p>
<p>Not a fan of plugging in numbers in grid-ins, but that seems to be the most advisable approach, thanks!</p>
<p>You are correct, MingFs, I can’t believe it was that easy…lol</p>
<p>Anyway, last question is number 8, can someone provide a more time-friendly approach please?</p>
<p>\ For 8 the way I did was imagined like 4 slots</p>
<p>You have 1 team in the first slot so a 1 goes there, then in the second slot it can play 3 other teams, then I put times 2 because then 2 other teams would be able to play and in the last slot a 1 because 1 team would be able to play so</p>
<p>1<em>3</em>2*1 = 6
*2 because they played 2 games
=12</p>
<p>Also for 10 is the question (k-1)/k or k - (1/k)?</p>
<p>(k-1) / k, Brolex</p>
<p>Btw, nice approach to number 8. All the questions are solved! Thank you CC, I won’t forget this! :-)</p>
<h1>4 doesn’t need any kind of arbitrary plugging in of numbers.</h1>
<p>Just do 1/x = 12.5
1/12.5 = x = 0.08 (use a calculator). Obviously, 12.5 is the biggest number in the answer choices, so it’s right.</p>
<h1>5 can’t have any negative numbers, and must have the smallest possible value in the positive ranges given to get the great resultant value. C. is the smallest of those, and, if tested, satisfies the inequality in all of it’s cases.</h1>
<h1>6 requires squaring the (sqrt(a)^n) = 5 equation. You get a^n = 25. Since (1/a)^n is (1/(a^n)), replace a^n with 25 to get 1/25 (although I’d like it if someone tested this).</h1>
<h1>7 has the factoring factor (lol), but you can also simply make a or b equal to 1, minus 10 from 32 to get 22 and then divide 22 by 10 to get 2.2; 2.2 + 1 = 3.2</h1>
<p>Looking at the “logic” problems (ie #2) made me want to cry. Are these SAT problems made by College Board? I want to think that there is hope for math peons like me…</p>
<p>I think number 1 is actually B) 9, not A) 6.</p>
<p>“the number of students that study both subjects is the **same as the number of students that study exactly one **subject”, meaning Both (B) = either German (G) or Italian (I), NOT G + I. </p>
<p>Therefore, G + I + B = 30 translates to I + 3 + I + either I or I + 3.
To solve this, I plugged in the answer choices. If 9 people studied Italian, then that means 12 people studied German, which is 21 people in total. The remaining number of people is the same as either Italian or German, in other words 9 or 12. 21 + 9 = 30, where 9 is the number of people studying Italian because adding the number of people studying German would yield a 33, which is greater than 30.</p>
<p>I thought #1 is B) 9 too
if number of students taking Italian is 6, then G=9, and B can be either 6 or 9, which adds up to 6+6+9=21 or 6+9+9=24, but if number of students taking Italian is 9, then G=12 and B can either be 9 or 12, which adds up to 9+12+12=33 or 9+9+12=30</p>
<h1>6</h1>
<p>Whether it’s (sqrt(a))^n or sqrt(a^n) doesn’t matter because it ends up being a^(n/2) either way.</p>
<p>So: a^(n/2)=5
Square both sides: a^n=25
Now just plug in 25: 1/25 = 0.04</p>
<p>And you have your answer.</p>
<h1>7</h1>
<p>Just divide the entire equation by 10 and you get a+b=3.2</p>
<h1>10</h1>
<p>k=0.13x where x represents the digits after 3</p>
<p>(k-1)/k is the same as 1-(1/k). So subtracting 0.13 from 1 gives us 0.8x where x represents the digits after 8. So the answer is 8.</p>
<p>If I may ask, where did you get these questions from? These look so much different from sat problems I’ve been doing.</p>
<p>1) 6. Since theres 30 students total, then there must be 15 students studying a single subject and another 15 studying both subjects. We can eliminate E, D, C. Now if 15 students studying a single subject, and the students studying German is 3 more than students studying Italian, then we know that Students studying Italian is less than students studying German. Therefore, the answer is 6.</p>
<p>I’LL REPLY AFTER I SOLVE THE REST.</p>