<p>72 is correct! </p>
<p>Now here is a very nice, challenging probability question:</p>
<p>A store sells surfboards that are made so perfectly that for every 1000 surfboards, 1 is bad. An inspector comes into the store and conducts a “99% accurate” inspection to all 1000 surfboards to see if surfboards are good or bad, based on the inspection. If my surfboard is inspected “bad,” then what is the probability (to the nearest 1%) that my surfboard is actually bad?</p>
<p>@SATManiac98 I got 9% using Bayes’ theorem. I’ll withhold writing a solution to let others think about it.</p>
<p>We’ve gotten a bit far away from SAT math problems with those last two. Here’s a Level 5 Counting problem that COULD actually show up on an SAT:</p>
<p>How many integers between 3000 and 4000 have digits that are all different and that increase from left to right?</p>
<p>3456, 3457, 3458, 3459, 3467, 3468, 3469, 3478, 3479, 3489, 3567, 3568, 3569, 3578, 3579, 3589, 3678, 3679, 3689, 3789 --> 20</p>
<p>^Listing and counting! But for fun, can you find the combinatorical way? A way that works even if the problem had said “between 300,000 and 400,000”? Not that an SAT problem would say that…in fact, I’m wondering if counting problems will stay on the new SAT. </p>
<p>x = 4, 5, 6, 7, 8, 9 (you don’t need 0, 1, 2, or 3, so you have 6 digits you’ll use)
You need 3 digits that increase from left to right from those 6.</p>
<p>6C3 = 20</p>
<p>So if it’s between 300,000 and 400,000 in increasing order…
x = 4, 5, 6, 7, 8, 9
p = 5</p>
<p>6C5 = 6</p>
<p>In triangle ACE above, AD bisects angle FAB, CF bisects angle BCD, and BE bisects angle DEF. If the measure of angle FAB = 50 degrees and the measure of angle BCD = 60 degrees, what is the value of x?</p>
<p>Photo in the link below— </p>
<p><a href=“https://www.■■■■■■■■■■/photos/99755623@N07/13938208591/in/photostream/”>https://www.■■■■■■■■■■/photos/99755623@N07/13938208591/in/photostream/</a></p>
<p>Could you guys show me how to do this question - I keep getting 55 degrees for x, its wrong…</p>
<p>Please explain it thoroughly. </p>
<p>PS. Sorry for my horrible picture taking skills, the photo isn’t correctly positioned (its horizontal). Just download it and rotate it from your computer. </p>
<p>Thanks guys,</p>
<p>DEF has measure 180 - 50 - 60 = 70. BEF has measure 70/2 = 35. FAD has measure 50/2 = 25. BCF has measure 60/2 = 30. AFC has measure 180 - 30 - 50 = 100. CFE has measure 180 - 100 = 80. Finally, x = 180 - 80 - 35 = 65.</p>
<p>@DrSteve can u give the correct answer to and explain your way of doing the “3000 4000” question?</p>
<p>@Sparkkid I generally teach SATManiac’s method of listing for this problem. Simply list the numbers in increasing order. The smallest number is 3456. Then start increasing the rightmost digit by 1: 3457, 3458, 3459. Once you “run out of room” go back and increase the next digit to the right: 3467, 3468, 3469, and so on (see SATManiac’s post above for the complete list).</p>
<p>Now that’s how I teach it. If I were to solve it myself I would use CandyPant’s method above: 6C3 = 20.</p>
<p>Note we are simply choosing 3 digits from the digits 4, 5, 6, 7, 8, and 9. Since we MUST put them in increasing order (we are not allowed to “arrange” them another way) this is a combination and not a permutation. For example, if we choose 5, 8, and 9, we get the number 3589 (only one choice - we can’t write 3598 as this would violate the condition that he digits be increasing).</p>
<p>@DrSteve could you help me with this problem? Or anyone else who knows how to do it.</p>
<p>If
F(a-3) = a^2 -7a +12, what does f(x) equal?</p>
<p>It’s a multiple choice - I don’t have the answer choices on me.</p>
<p>Replace a with x+3.</p>
<p>f(x) = f((x+3) - 3) = (x+3)^2 - 7(x+3) + 12 = x^2 + 6x + 9 - 7x - 21 + 12 = x^2 - x</p>
<p>@MITer94 why do you replace a with (x+3) ? Its not even part of the question. Could you please explain more? </p>
<p>EDIT : Never mind - I just understood. You have to make a = x+3 , so the equation can equal to f(x)</p>
<p>Thanks man,</p>
<p>Level 3 Counting</p>
<ol>
<li>How many integers between 9 and 200 have the tens digit equal to 5, 6, or 7,and the units digit (ones digit) equal to 2 or 3?</li>
</ol>
<p>52, 53, 62, 63, 72, 73, 152, 153 . . . = 12</p>
<p>Between 10 and 100, there are 1x3x2=6 solutions. Moreover, Between 100 and 200, there are 1x3x2=6 solutions.Therefore,there are 12 solutions
(Edit)
OR you can just use 2x3x2… which basically means that u have 2 choices in the hundreds digit, 3 choices in the tens digit, and 2 in the third digit.</p>
<p>^That’s basically my solution, just check that all possibilities work.</p>
<ol>
<li>A typist types the first n pages of a book where n>0 at an average rate of 12 pages per hour, and types the remaining n pages at rate of 20 pages per hour. What was the typist’s average rate in pages per hour for the entire book? </li>
</ol>
<p>Since the first and second section each have n pages, they have the same number of pages. Since the second section includes the remaining pages the two sections comprise the entire book. Half the pages were types at 12 pph and the other half at 20 pph, so the average rate was ((20 + 12) / 2) = 16 pph.</p>
<p>@CHD You made the common mistake of using the arithmetic mean. This is NOT how rates get averaged. Instead you need to use a different kind of average called the harmonic mean (commonly known as Xiggi’s formula on this forum).</p>
<p>Try to solve the problem using one of these two methods:</p>
<p>(1) Xiggi’s formula
(2) By picking a value for n ( a good choice for n is 120 - Why?)</p>