http://sat.collegeboard.org/practice/sat-question-of-the-day?src=R&questionId=20130219 (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. To begin, always determine the topic of the sentence. The topic of the sentence is about how Allison had only “glanced at a summary” which would result in her having little knowledge of the legislation. A glance or quick look, would limit her understanding and on top of that it was only a short version or a “summary,” so, she didn’t have the whole legislation in addition to her glance. At this point, I’ll predict she has **“limited** knowledge” for the first blank and “not **inspected** the details” for the second blank.

After making my predictions, I’ll now look at the answers for the first time. After all, most of them are only there to distract me and looking at them sooner can cause silly mistakes. Having two predictions, let’ use one at a time. I like both of them so it doesn’t matter which one I use first. I’ll go with “limited.” Checking out the first column of answers, I can eliminate B, *subjective* since it isn’t related to “limited”. D is a weak answer sense her knowledge could be “questionable” even if it were complete; I’ll now discard it but I’m sure suspicious. Now I’m going to look at the second column. Only A, “examined” and B “studied” are synonym for my prediction: “inspected.” That throws out all the other answers. C-E don’t mean “inspected” and and answer B was thrown out due to the first word. All done and time to move on.

Let’s take a look at the ACT question.

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 G. The ACT explanation of the math is quick and to the point. No quibble there. However, this question raises a point: you have to be very careful when you read ratio questions that are expressed in a way that look like fractions. On the SAT, a fraction is expressed with a hash, 1/40; so, it is not confused with a ratio. If the SAT expresses a ratio so that it looks like a fraction they always use a horizontal bar like you see in this ACT question; that eliminates confusion. (I haven’t figured out how to make a fraction with a horizontal bar like you see in this ACT question and am hoping you see what I mean when you look at their test item.) Obviously the ACT folks don’t necessarily distinguish between fractions and ratios with the two different bars and it can cause simple mistakes so be careful. They are lazy and show both ratios and fractions with horizontal bars. If you see a slash on the ACT, you’ll know it is a fraction but if you see a horizontal bar, it may be a fraction or a ratio. Just be careful.

Back to the question, the ACT **fraction** says that 1 out of 40 bulbs is defective. That means in the numerator is one defective bulb and the denominator 1 is defective bulb plus 39 bulbs that work fine. So the ratio in the denominator is 1:39. That shorthand using a colon can also be expressed as 1/39 using a **horizontal** bar like they’ve done in answer B (and which I don’t know how to draw). So the question is asking you to find the ratio in the denominator and express it a fraction using a horizontal bar, answer G.

Need to make an educated guess using my “common elements” strategy? Throw out A since “25” doesn’t appear in any other answer. Three of the answers have 1 in the numerator and only two don’t; get rid of J and K. Guess between G and H. You know that the ratio they want doesn’t look like the fraction, get rid of H which leave G, the right answer! I hope you could do the math since it is a sure thing for getting the answer. If you couldn’t, don’t despair, there’s no penalty for guessing on the ACT–don’t leave a blank. This strategy will greatly improve your odds of guessing correctly. Don’t forget “common elements.”

Go back and see how the same concept applies the SAT Q of the D this morning. Eliminate non-synonyms in the first (B and D) and second columns (C, D, and E) within the first and second columns respectively. That leaves you with the right answer! Just to make sure I’m clear. I want you to try the proper way first. However, this is a reasoning test and doing some thinking is way better than random guessing when you are stuck. My line of reasoning will raise your score.

BACK TO RATIOS: If you see a ratio question on either test, the key is always to figure out the size of the group and then you may have to determine the population. Let’s apply that strategy to the facts in this question. More typically the question would say the ratio of bad to good bulbs is 1:39. At that point, you would add the parts and get a sum of 40 for the size of a *group* in which there is one bad and 39 good bulbs (the denominator in the ACT question’s original fraction). The key issue is that the total population of bulbs must be a multiple of the group size, in this case 1000. For example, there could not be a total number of bulbs equal to 100. That would require 2.5 groups (100/40=2.5). Half of a group would need to be 40/2 = 20 bulbs or 1/2 of a bad bulb and 19.5 good bulbs. You can’t have half of a bulb! There’s more practice on this issue on DVD #5 and in my online course. If you need more help with this, take a look at those resources.

The Wizard