http://sat.collegeboard.org/practice/sat-question-of-the-day?src=R&questionId=20130221 (This link takes you to today’s question. If you use my archive, you will see the question related to my SAT explanation for that date.)
The answer is E. This SAT question is probably the easiest one I’ve seen since I started my blog. If you don’t know that “profit” is the difference between expenses and sales price, you have a problem. The test writers assume you know that.
The florist makes a profit of 50 cents on each rose that is sold; so, to make $300 the florist needs to sell 600/$0.50. Once you realize the florist is making half a dollar each you could see that the florist needs to sell twice as many roses as dollars that are needed for profit. You could also have started with the answers to see which one works. Beginning with C, you can see that 200 divided by half a dollar would result in only $100 profit which means you need to go bigger. 300 is too small. E works fine.
I’m not sure why students would have trouble with this question. Help me out. If you missed it, please send me an email and tell me what kind of trouble you had. That will help me be a better teacher. Thanks.
Let’s take a look at the ACT question.
http://www.act.org/qotd/ (The ACT staff does not put a date on their questions so if you click on an archived blog, you’ll get today’s question and the old explanation. Sorry. The SAT staff has dated their questions; so, the archive is helpful. The ACT folks simply don’t do that.)
The answer is C. The ACT folks are being easy this Thursday morning as well! If the stick is half as long, then the shadow has to be half as long. I learned about this in Boy Scouts. Let’s use the question to learn an interesting thing.
We are talking about similar triangles! The stick is one side of a right triangle; the shadow is the second side; and the imaginary line from the top of the stick to the end of the shadow is the hypotenuse. (Sorry I can’t draw but go ahead and do that on a piece of paper.) In your triangle, the length of the shadow is however long you want it to be. Let’s say 3 feet. Now draw a second stick that is half way between the first stick and the end of the shadow making sure it is parallel to the first stick. The new, smaller triangle inside the first triangle is in proportion (similar) to the first triangle and all of its measurements are exactly half of the original triangle. In this example, 1.5 feet.
The important thing to learn here is that on both the SAT and ACT there are questions about this issue. My strategy is that anytime you see a line inside a triangle that is parallel to one of the sides of the triangle, you have a question about similar triangles. The little one on the inside of the larger one will always have sides that are in proportion to the larger one. They are similar triangles. Watch out for this “signal” or “flag” on both tests. It shows up quite a bit.
I’m looking forward to seeing my students at Stetson University on Sunday and hope you all enjoy watching DVD #5! The LNHS students said it took them about an hour and 40 minutes to watch it; schedule your lives accordingly!
Enjoy your day.