http://sat.collegeboard.org/practice/sat-question-of-the-day?src=R&questionId=20130114 (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. However in my first few blogs, I didn’t use a date in my link and you won’t get the proper question. Sorry.)
The answer is D. As usual, let’s focus on the topic and make a prediction based on key words and phrases. Doing so leads us to realizing that the word “unfair” signals a change in the meanings of the words that fit in the blanks. That is, they are opposite of one another.
Many students are going to struggle with some of the vocabulary with this question and I can see that because less than 40% of the students are getting it right. So, what do you do? Realize if you can eliminate one answer, you should guess at the rest. What answers could you eliminate because they aren’t opposites of one another? Eliminate those and guess at the rest. On the other hand, the right answer has two words that aren’t too difficult; if you recognize them as opposites, you are all set. Pick Answer D and move on.
Let’s see what the ACT folks have in store for us today.
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 J. I’m convinced that if there is a way to make their explanation more difficult than the question, the ACT and SAT folks will do it!! Forget the whole first paragraph of their explanation. I teach a simple technique I refer to as “change the abstract to the concrete.” I sometimes describe it as “change the algebra to arithmetic.” Always use it when the SAT and ACT folks only give you variables and some rules about those variables; simply substitute real numbers that follow the rules they give you in the question. For example, they tell us a is between 0 and 1 (a is a positive fraction) and b is greater than 1. Pick real numbers for each that follow the rules or parameters they give you. Then turn the math crank.
In this case, the ACT folks finally get around to doing that in the final paragraph of their explanation. 1/2 or any other positive fraction works fine for a and 2 or any number greater than 1 works fine for b. So, just multiply them. You can see that ab or 1/2 times 2 is equal to 1. (Of course, you could have used 1/4 and 15 but the math would have been harder to do in your head.) In either and all other cases, ab would be between a and b on the number line.
This question is a fine example of one of the most important principles you can learn: the world of math is a world of patterns. You can use it frequently on the test. In this case, you see that the pattern is that whenever you multiply a positive fraction and a number greater than 1, the product is going to be in between the two numbers. There are other patterns that are valuable when multiplying. For example, when you multiply two positive fractions, the product will always be a positive fraction that is less than both initial fractions. Go ahead and prove it to yourself. What happens when you raise a fraction to larger and larger powers? Try it with 1/2. Now try it with -1/2. Enjoy you week.
I hope my SAT and ACT Question of the Day strategies and explanations are helpful and, if so, spread the word. Tell your friends at school and social media friends.
If you are taking the January SAT, time is running short. I recommend you watch my online Tips and Tricks videos to help you prepare. It only costs $3 to watch an hour of my best test-taking techniques for taking the SAT and ACT tests.
A special reminder to my Osceola County students: Be sure to remind your friends about our upcoming class on this Saturday. Do your assignment and email me so I know you’ll be attending.