<p>Can someone help me with this question: <a href=“IMAG0350 | futoru1 | Flickr”>https://www.■■■■■■■■■■/photos/99755623@N07/14383458778/</a></p>
<p>The picture of the question is in the link.</p>
<p>Thanks,</p>
<p>@7alman
is the answer C? (checking before I try to explain)</p>
<p>No.</p>
<p>That’s what I guessed.</p>
<p>@7alman
Oh duh sorry I must have gotten stupider since I last took the SAT. Is the answer B?</p>
<p>Nope.</p>
<p>Maybe after 3 more guesses ;)</p>
<p>@7alman
It is B, 30 because all radii of a circle are equal lengths. You are told that AB is the same as AO, and BO is also a radii, so the triangle is a 60-60-60 triangle. Since AC is a straight line and BOA is 60, then BOC is 120. For triangle BOC, 180-120 is 60 (which is angle B plus C). BO is also equal to OC, so the angles are equal. 60/2=30.</p>
<p>XD yah stupid mistake</p>
<p>Appreciate the help skittle bug.</p>
<p>Thanks for the explanation.</p>
<p>@7alman
I knew I had a brain up there…somewhere…</p>
<p>Haha </p>
<p>Knowing properties of angles and hexagons inscribed in a circle : solve last problem in 5 seconds! </p>
<p>New Question:
When 7x+3 is divided by 6, the remainder is 2. if x is an integer then x could be
A 4
B 5
C 6
D 7
E 8</p>
<p>If 7x+3 leaves a remainder of 2 when divided by 6, then 7x leaves a remainder of 5 when divided by 6. But 7x=x+6x and 6x leaves a remainder of 0 when divided by 6 if x is an integer. x then leaves the remainder of 5 when divided by 6. Plugging in, we verify that that B) 5 works (7<em>5+3=38=6</em>6+2).</p>
<p>we can just plugin then numbers. The only option that works is B) 5.</p>
<p>Yes you can; I just tend to avoid plugging in answer choices if there is a way to directly solve.</p>
<p>Most students will want to plug in as suggested by egg yolk. Just to see the details, let’s plug in choice (B). If x=5, then 7x+3=7(5)+3=35+3=38. Now 6 goes into 36 evenly. So when we divide 38 by 6 the remainder is 2. That’s correct. So (B) is the answer.</p>
<p>The most common mistake made here would be to divide 38 by 6 in your calculator and get 6.3333… and then say the remainder is 3. Division in a calculator does not give a remainder. To get a remainder you must do the division by hand, or use a calculator algorithm that simulates long division.</p>
<p>Random’s solution is very good, but much too sophisticated for most students. It is definitely worth taking some time to try to understand this solution, but if you don’t get it, don’t worry. You will never have to do something so advanced on the SAT.</p>
<p>@DrSteve I don’t think it’s too sophisticated for most students. Rather, working with remainders is very rarely taught well (at least where I went to school) so many students struggle with these problems.</p>
<p>And why doesn’t the calculator method work? 38/6=6.33…=6+1/3=6+2/6, so the remainder is 2.</p>
<p>In general, to find a remainder by a calculator in the division of positive integers a/b, on can find a/b by calculator, drop the integer part (so the new result is between 0 (inclusive) and 1 (not inclusive)), then multiply by b. </p>
<p>
</p>
<p>We have indeed a solution based on plugging, but the better question might be about where to start with the plugging! Is there a more direct solution or one that happens to be an elegant hybrid. After all, there are guesses of all kind: wild and smart. </p>
<p>Here is the problem in all its glory</p>
<p>When 7x+3 is divided by 6, the remainder is 2. if x is an integer then x could be
A 4
B 5
C 6
D 7
E 8</p>
<p>Are there choices we could eliminate? How about realizing that eliminating the remainder yields a simpler proposal, namely that 7x + 1 is divisible by 6. That means that x has to be odd. Bam, here go 3 choices and we now get into the JoeSixPack tgheory that PR adores. Two choices and we can guess! Of course, that strategy is usually for dummies, and it should not in the arsenal of CCers. So we go to the plugging an adopt one of of DrSteve’s suggestions. As luck would have it, starting with 5 gives the right plug. </p>
<p>Is there a better way? I would say yes, but since this problem is so easy, the time savings are NOT that great. What is the saving tip? None other than one that realizes that 7x + 1 is 50 when using the value of 7. For some, that might (and should jump) of the page. </p>
<p>Is there a lesson here. Yes, one could solve this in various ways, and that includes plugins. Yet, resist the tentation to try all FIVE proposed solutions (no need as only one is correct) and try to add some smarts in choosing your tested values. Chances are that you can eliminate 2 or 3 by simple reasoning. </p>
<p>PS Fwiw, there might be an intuitive way to look at this as well. But it is a tad harder to “explain” but here we go. If I look at 7x +1 being divisible by 6, I think that “completing the remainder” to make 8x divisible by 6 requires to add … 5. And 5 happens to be the correct value. :)</p>
<p>@RandomHS Perhaps the average student on college confidential can handle that solution, but most students with a current math score of about 500 (or lower) cannot without a lot of practice first. I would generally not teach this type of solution with a student below a 600. </p>
<p>And by the way I do like your solution, and do think it’s worth going over this with more advanced students.</p>
<p>The calculator method you gave is perfectly fine, and I do encourage using this kind of algorithm. I didn’t say you can’t use your calculator to solve a remainder problem - I said that performing a single division in your calculator does not produce a remainder. </p>
<p>Xiggi’s explanations are all very good too, and again I would usually go over these with stronger students, but I would encourage them to solve it strictly by plugging in first.</p>