Feb 6 ACT & SAT Question of the Day

http://sat.collegeboard.org/practice/sat-question-of-the-day?src=R&questionId=20130206 (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 classic SAT question.  They love right triangle questions.  Let’s review my mantra: 1) What did they tell me?  and 2) What do I know because they told me that?  First, I am told that DEF is congruent to ABC; so, it is exactly the same shape as ABC with different labels at each corner–know big deal.  I just can’t assume where D, E, and F are.  For example, D may or may not be in the same position as A.  (It’s very important to never make any assumptions on the SAT or ACT.)

Second, we are told it is a 30:60:90 right triangle.  Your immediate reflex should be to go to the “cheat sheet” at the beginning of the math section and take a look at the 30:60:90 triangle that is there.  Of course, if you’ve memorized the ratio of the sides for a 30:60:90, you can skip this step.  (Be sure to memorize it anyway for the ACT since there’s no “cheat sheet.”)  Anyway, you’ll notice that the long side (not the hypotenuse) is always some value times the square root of three.  That value is always half the hypotenuse.  So on DEF there has to be a side that is half of 12 or 6 roots of three.  In the original triangle, ABC, it would be side AC.

It is a good idea to realize that a 30:60:90 is half of an equilateral triangle and all of this makes sense.  If you turn ABC counter-clockwise so that AB is the base, you’ll see that it is the left side of an equilateral triangle.  AC becomes the altitude or height.  Now imagine (or draw) the other side of the triangle.  The angle at C gets doubled to become 60 degrees and the base angle B is reflected to the other base angle so it is also 60 degrees.  Magic!  You have an equilateral.  This little exercise will help you visualize how you get the ratio that you see on the cheat sheet for 30:60:90 triangles.  For example, the short side of the triangle across from the 30 degree angle is always going to be half of the length of the hypotenuse.

Let’s see what the ACT folks have in store for us 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 D.  First, and foremost, this is a reminder to completely disregard the ACT “directions” that tell you to read the whole passage before doing the related questions.  What a terrible waste of time.  You can do the questions without doing that.  For example, you can go right to 9 on this question and just use that sentence in isolation and get the right answer.  Shame on the ACT test writers for giving you such bad advice because their “directions” certainly aren’t that.  I’ll continue to rant about this until they fix this problem!

Now that I’ve vented, let’s consider the question.  When a verb is underlined, your first response should always be to make sure it is consistent with the tense of any other verbs in the sentence that are not underlined.  Shone is past tense; so, you need a past tense verb for the underlined verb will have to.  That makes the answer “could,” D.

If all the verbs in the sentence are the same tense, be sure to check the related noun or pronoun.  Be sure they are both singular or plural since they have to match: singular noun requires a singular verb.

Enjoy your “hump day.”  It’s all down hill from here to Friday!

If you are taking the ACT this Saturday, time is running short. I recommend you watch my online Tips and Tricks videos to help you prepare. In addition to the free ones on the home page, it only costs $3 to watch an hour of my best test-taking techniques for taking the SAT and ACT tests.

The Wizard


About Bob Alexander

Bob has been a professional educator starting with teaching biology, becoming a school administrator, and then working as an education lobbyist in Washington, DC. He got his start in national testing by becoming a consulting test writer, later joining Kaplan as a director, and finally starting his own business in 1995. He has written numerous books, consulted for school districts and colleges, developed his website and been featured on a DVD set. He offers SAT and ACT prep classes and tutors individuals and small groups of students in central Florida.
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