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=20130329 (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 a pretty common rate question to which the SAT folks have added some algebra. There are a couple of ways to do it. First, you could do it the “math teacher” way. In one hour the two machines can produce x+(x+6) bolts which is 2x+6. Then you have to multiply that amount by the 4 hours: 4(2x+6)=8x+24. That’s not so hard.
Second, if you are concerned about the algebra, you will find it much easier to use the Wizard’s strategy of “changing the abstract to the concrete.” Just start by changing x to a real number. Any number works; so, pick an easy one. How about 3? The first machine makes 3 bolts per hour and the second one produces 3+6 or 9 per hour. Together they produce 3+9 which is 12. In four hours they would produce 4×12=48 bolts. Now just plug in 3 for the x in each answer. Only Answer D gives you 48 when you change the abstract to the concrete.
It doesn’t matter what way you do the problems on the SAT or ACT. Just practice so that you aren’t surprised by what you see on the test. Keep reading my blog because I’ll keep writing about the different strategies you can use to do the problems. One is going to work well for you.
Let’s pop down and see what the ACT folks are up to this morning.
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 H. The challenge for the ACT Science Test is speed. How fast can you read the graph in the question and match it up to the table? I see two quick ways to do it. First, you could see that the graph shows you that the concentration goes up and then back down as you get deeper. Looking at the ions and gases and you’ll see that only carbon dioxide (CO2) does that: Answer H. All the other ions and gases either consistently go up or consistently go down.
One of my strategies is “check the trends.” Don’t worry about the specific amounts; that takes too much time. Just seeing what the direction of the data entries is will often be enough.
Second, you can pick a point on the graph and match it to the table. That is usually much faster. For example, looking at the graph you see at a depth of 0, the concentration is 1. Matching that data with the table, you only find carbon dioxide has a concentration of 1 at a depth of 0. All done. If you had chosen a point that matched up with two cells on the table, you simply would pick a second point on the graph and compared only those two gases or ions on the table. Fortunately, you didn’t have to do that for this question. Hurry on to the next question.
Have a great day and tune in tomorrow for more Wizardly strategies.