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.
http://sat.collegeboard.org/practice/sat-question-of-the-day?questionId=20140404&oq=1 (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 A. There are lots of ways to do this question and the SAT folks provide you with one. It will take a while to do the problem that way but it will eventually get you there.
It is a simple proportion question; so the first thing you need to do is get the units balanced for the two machines. Because the inserting machine can do 120 per minute, that is the same as 2 per second. We are told that the stamping machine can do 3 per second. That is a simple situation where the stamping machine takes 2/3 as much time to do an envelope as the inserting machine takes. So, we need 2/3 as many stamping machines. 2/3 of 18 inserting machines is 12 stamping machines, Answer A.
You could have done it on a per minute basis as well. We are told the inserting machine can do 120 envelopes per minute. The stamping machine can do 3 per second which is the same as 180 per minute. That’s 180/120 or 1.5 times as fast. So, using the answers, Answer C is 20 stamping machines that could do the work of 30 inserting machines. That’s too many inserting machines. Go smaller. Answer B, 16 stamping machines could do the work of 24 inserting machines. Still too big. Answer A, 12 stamping machines could do the work of 18 inserting machines. That’s just right. Let’s move on.
That was fun. I wonder how much faster my techniques were than the SAT approach. What do you think? It makes me think of another question. If the SAT staff”s explanations take an average of 60 seconds and the Wizard’s take 40 seconds, how much extra time do you have for the 54 math questions to check you work? :-)
I wonder if the ACT folks have something interesting for us this morning.
ACT Question of the Day: Use your “back” button to return to my website after reading the ACT Question of the Day.
It sure is interesting. I can’t even figure out their explanation. They left out a lot of steps. Could you understand it?
The answer is C. Again there are a number of ways to attack this question. But let’s begin by playing a little game! If you had no idea how to do the math, you could use a little reasoning. 24 minutes is slightly less than a half hour. So, you could go slightly more than twice 4.8 miles in an hour. That quickly eliminates Answers A, D, and E and leaves us with 10 or 12, Answers B and C. Then go ahead and guess.
Here’s a better way to think your way to the answer. Because you can go 4.8 miles in 24 minutes you could double that or 9.6 miles in 48 minutes and you would have 12 minutes to keep peddling to get you to an hour. 12 is half of 24 which means you could go another half of 4.8 or 2.4 miles. 9.6 plus 2.4 is 12. Bingo! That’s answer C.
Here’s the first way I did this question. 24 is 2/5 of an hour (24/60 = 2/5). Half of that is 1/5 and half of 4.8 is 2.4 miles. This means you can go 2.4 miles in 1/5 of an hour. 5 times 2.4 is 12. All done.
Your math teacher probably did it even another way. 4.8 miles/24 minutes = x/60 minutes. Get out your calculator and start pushing buttons! You’ll eventually get 12 miles per hour if you push all the right buttons in the right order.
My point is pretty simple for these two math Questions of the Day. There are lots of ways to do SAT and ACT math questions. With practice you’ll see that time and time again. You’ll also figure out which one works best for you. Are you better at doing the math teacher thing? Or are you better at just seeing what is going on and thinking your way to the answer? My experience suggests that the answer will vary from question type to question type. For example, you may discover for ratio and proportion questions like we see today, you are faster at getting the answer if you just think your way to it. On the other hand, you may want to use the math teacher approach for algebra questions. You will only figure that out with practice. That’s why I encourage you to grab your books and get to work!
QotD Words of “Wiz-dom:”
Einstein is given credit for having said something like, “Insanity is continuing to do what you’ve always done and expecting different results.” I love this statement because it applies to your situation in so many ways.
The first thing that comes to mind is the student who thinks that taking the test repeatedly will raise his score. It won’t. Research even indicates a large number of students actually go down between their first and second times taking the test. The exception is for students who do something different before taking the test the second time and prepare; however, keep in mind the score increase will vary depending on how you prepare.
The second thing that comes to mind is the student who takes the test “just to see how I’ll do.” Bad plan. Why would you do that? Why pay the money and get up on a Saturday morning for something you can do for free at your house? Just get a free copy of a previous test from your counselor or on the SAT or ACT website. Take it at home following the time limits and score it. All done.
In addition, the “just see how I’ll do” plan can cause you problems. With that attitude, you probably won’t do nearly as well as you could because you are not motivated or focused. Your results will reflect that. You’ll probably get a score that is less than you would get if you were taking it seriously. Now you’ve had a bad experience and you’ll feel more pressure the next time. Not good.
The most important thing that comes to mind is that if you are serious about raising your score you have to considerably change what you’ve been doing (Einstein). Take your preparation seriously and learn how to become a better test taker. Learn how the test writer thinks when he/she is writing questions and coming up with wrong answers (distractors). Focus on developing your reasoning and analytical skills. Guess what? That not only will improve your SAT and ACT scores but also will improve your performance in the classroom. That’s a real bonus. (By the way, students frequently report that my program also improves their AP scores.) The bottom line: change what you have been doing before you go take the test again or you’ll get the same results you got the last time.
Be sure you get the most out of this day. As you go to sleep tonight, you won’t get to change what you’ve done or not done.
Bob Alexander, the “SAT and ACT Wizard”