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=20140510&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.)
Reading this blog is 10% about learning how to answer today’s questions and 90% learning how to apply strategies and analyze questions you may see on test day.
The answer is D. What’s weird about today’s question is the format. In algebra class, you would normally see this problem stated as: a – b = 6 and b – 3 = 6 and be asked for the value of a. Then you would see that it is easy to solve for b using the second equation: b = 9. The next step would be to substitute 9 for b in the first equation: a – b = 6 becomes a – 9 = 6 and a = 15. All done.
Notice all we did was use Pillar II: Restate the Given Information. We simply changed the way they presented the equations into a format that looked more familiar to us.
There’s another way to do this question. Whenever the question asks, “what is the value of …?,” one of the answers must be its value. So, we know that a has to be equal to one of the answers. Always start with the middle answer, Answer C. Plugging in 9 for the first equation, a = 9, then the second equation 9 – b = 6 would make b = 3. However, if b = 3, the second equation doesn’t work because b – 3 = 3 would become 3 – 3 = 6 and that isn’t true. We need a larger value for a. Plugging in Answer D, 15, for a we get 15 – b = 6; so, b has to be 9. Trying 9 in the second equation, we get 9 – 3 = 6. Yep, that works. All done.
Of course, this approach leads to even a third way to do the problem. “What did they tell me and what do I know because they told me that?” There are two even numbers that add up to 34. Then we are asked for the largest possible product of the two numbers. So, start working. 0 and 34 are even (Yes, 0 is even.) and add up to 34 with a product of 0. 2 and 32 are next with a product of 64. 4 and 30 are next with a product of 120. Now you can see that every time you increase the smaller of the two numbers the pattern is the product gets larger and you know how I like to say, “The world of math is a world of patterns!” Just ask yourself, “What is the largest smaller number I could have?” It’s 16. That makes the two integers 16 and 18 with a product of 288.
Remember the old adage, “There’s more than one way to skin a cat?” Well, there’s more than one way to skin an ACT or SAT math question! Practicing will help you decide what approaches work best for you. Keep it up.
Let’s see what the ACT folks have for us today.
ACT Question of the Day: Use your “back” button to return to my website after reading the ACT Question of the Day.
Well, cool, the ACT folks have a math question and we can use it to see if what I said about there’s more than one way to skin an ACT math question is true.
Are you a math genius? Then you would do this question the way the ACT folks explain it. But it would still take a lot of time. Go ahead and read their explanation but don’t get too bedazzled.
I did it with a little reasoning and without a calculator in less than 5 seconds. Before you read my explanation, think for a few seconds using my mantra of “What did they tell me and what do I know because they told me that?”
If two integers have a sum of 34, their average (mean) is 17. The “largest possible product for 2 even integers” would have to be the two even integers that are closest to 17: 16 and 18. Using the units (ones) digits, I know their product has to end in an 8 (6 times 8 is 48). That’s Answer K, 288. (I know it can’t be Answer G, 68, because 10 times 18 would be 180; so, 16 times 18 has to be a lot more than 68!)
If you didn’t know that the two integers had to be the closest ones to 17 (16 and 18), then you could have done a quick check by seeing what you would get if you multiplied the two even integers that are the extremes from 17: 2 and 32. That would get you 64. Check the product of next closest pair of even integers, 4 and 30, which would get you 120. Now, my mantra of “The world of math is a world of patterns” kicks in. You can see that each time you pick the pair of even integers that has a mean of 17 that is getting closer to 17, you end up with a larger product for those integers. That means you need the closest pair: 16 and 18. Shazaam!
By the way, I don’t have any problem with you doing this question the “math teacher” way or using the test writer’s way. I just think you need to figure out (through practice) what the best way is for you to approach questions. Many times it is easier and much faster to think your way to the answer than it is to do all that math. Just remember that you aren’t trying to dazzle somebody with your math skills; you are trying to get the correct answer as quickly as possible! Nobody is going to check to see how you did the problem.
QotD Words of “Wiz-dom”:
Take a study break now and then. Final exams are coming. SAT and ACT tests are coming for many of you. Final papers are about due. Like your phone batteries, your brain needs to be recharged too. You need to relax between intense study sessions. Do something nice for yourself. Get your mind off schoolwork for a while. Then go back to work refreshed. You’ll perform better. Caution: It is wise to set a time to resume studying if you want to maximize your performance. Don’t let relaxation get you away from meeting your goal.
Have a great and productive weekend.
Bob Alexander, the “SAT and ACT Wizard”