If you are reading this in an email you received from me, do not click the link to sat.collegeboard.org below. Use the link to my website that is farther down on the email. If you are seeing this in my blog, do the SAT Question of the Day by clicking on this link:
http://sat.collegeboard.org/practice/sat-question-of-the-day?src=R&questionId=20130513 (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 D. This is an incredibly important question. It is really a two-step percent question using geometry as the context. In addition, it is a perfect example of how the SAT test writers take an elementary school math topic (area of a rectangle) and combine it with some middle school math (percentage calculation) and make it really hard for high school students! (Right now only 32% of the 25, 149 students who have done the problem have gotten it right! Usually the percentage is between 45 and 60.) Why is it so hard? What Wizardly strategy can we use to make it easier?
Well, you could do it the way the test writers suggest and that certainly works. However, that’s the long way; it takes too much time and you could certainly get lost in the algebra. I suggest you take a look at their explanation just to see if you can follow it. Then read how I teach my students to do these problems that pop up on the test once in a while.
Use the Wizard’s strategy of “changing the abstract to the concrete.” They don’t give you values for the size of the rectangle (abstract) so make up numbers based on the facts they give you (concrete). Because they tell you it is a rectangle and this is a percent question, let’s make it easy on ourselves. We can use 100 as the lengths of the sides. 100 is always a great starting point for percent questions since percents are about 100ths. Rectangles are special cases of squares; so, there’s no reason we can’t just say our initial “rectangle” is 100 by 100 which is an area of 10,000. Then we increase it just like they tell us. One side goes from 100 to 120 (a 20% increase) and the other goes from 100 to 130 (a 30% increase). Doing the multiplication of 120 times 130 gives us 15,600. Divide 15,600 by 10,000 and you get 1.56 or a 56% increase. I think that is a lot easier than the SAT explanation. How about you?
Whenever you see a multi-step percent question, just do a couple of simple things. First, if they don’t give you numbers, make stuff up and start at 100. Second, remember to multiply each step times the answer you got in the previous step. (In today’s question, we multiplied 120 (the first step) times 130 (the second step.)) Finally, compare that answer with the initial value–15,500 divided by 10,000–to get the increase. Shazaam, all done.
What if the question had been to decrease by 20% and 30%? Same process. Decrease sides of 100 to 80 (100-20) and 70 (100-30). The area is 5600. Subtract from 10,000 and you get 4,400. 4,400/10,000 is .44 which is a 44% decrease.
Make it extra confusing by making one an increase (20%) and one a decrease (-30%). Eeks! Don’t panic. Use the same process. Multiply 120 times 70 and get 8400. Subtract 8400 from 10,000 and get a 16% decrease. Of course it is smaller. You shrunk it more (30%) than you expanded it (20%).
These problems always become manageable when you use the Wizard’s strategy of “changing the abstract to the concrete.” Remember it, use it, and beat a common trick used by the test writers which is to not give you numbers!
Let’s see what magic we can do with 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 D. There’s just a little magic needed here. Both the ACT and SAT question writers love to test you on “parallel structures.” In this case, the sentence doesn’t underline “took” and “sailed” which are verbs in the sentence. We have to get all the other verbs “parallel” or consistent with those two verbs–tense and form. They are both simple past tense. We now need to get “should she settle,” consistent with them. Simply change it to the simple past tense, “settled.” All done. Circle D, bubble it in, and move on.
I hope you have a great week. Final exams are coming up for many of you. Start reviewing now so that you don’t get all jammed up. Get out your planner and make “appointments” with yourself for when you are committing to prepare for your tests. Be sure you also schedule “appointments” for relaxing. Then keep to your schedule.
Surprise your mother today and say, “I love you every day, not just on “Mother’s Day!” Don’t forget the hug. Give her a big “thank you” for all she does.