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Question

Dear Mitch,

My friends and I really appreciated what you did last week when someone wrote in requesting the free collection of SAT tricks your company had on its wrapping paper that his neighbor received with the adler-n-subtract.com tee shirts he ordered.

Last week you only gave away a few tricks (remember it was 7 in all because you wanted it to be a prime number, and after 7 the next prime number is 11, and I guess that would've meant you'd have to spend a lot more time answering just that one letter!) . We really thought those ideas were very good, like we knew as soon as we read them that they really would work for all of us, and so we were wondering if you'd be willing to spare a few more this week. (We have to take the PSAT really soon, and even though no one is saying it, you can just tell that some people are secretly starting to freak out. (Some kids get nervous.)

So if you wouldn't mind...

But before I forget, we did order tee shirts anyway, and since you now know my name you can even check, because I'm not just saying it.

Anyway, I hope you do give away a few more hints, but even if you don't, we still think this is a pretty cool website and we're going to keep checking it out every time we're at his computer. (My laptop is kind of broken and every time I'm in the mood to really concentrate, it starts showing a bunch of movies, and some of the movies are really disgusting.(not all, but the fourth one and even the sixth one, well THEY are REALLY disgusting, and I'm not kidding.))

So please, if you feel like it, more tricks.

Thank you.

Math Kid to Math MAN,

Jeremy B

Answer

Dear Jeremy,

It is always my pleasure to share helpful information with someone who is interested, like you. So, to work up to the next prime number, as you correctly calculated, here are four more TIPS for the SAT, and that will bring the list to 11.

1.Starting with a hint for the verbal section of the test, there will be several reading comprehension passages each followed by a series of questions, and the questions come in FOUR categories. (We won't bother to go through each type, but one of these categories is usually referred to as the 'inference' question. This simply means that the reader is asked to draw a conclusion from two or more facts or ideas presented in the passage, and the answer choice which gives the most logical such conclusion is the correct answer. Inference questions are usually very easy to spot because they include words that make it clear one can only make a logical guess about them and you do not have enough information to be 100% sure. So, an inference question will use words like"most likely", "least likely", or "the author seems to be implying that..." or "from the last two lines of paragraph two (or wherever) we can INFER that..."

(A typical example of the section of a reading passage from which such a question might come looks like this: "Many of the soldiers were too young to understand the politics of the war, and most lacked training and had been involved with activities as far removed from fighting as one can imagine. Furthermore, there were whole groups of the soldiers who had already been in such poor health before entering dangerous territory that it is now impossible to say how different the result would have been if the early circumstances were different."

QUESTION: From the above paragraph we can infer:

A) The nation being discussed had very few soldiers over the age of forty;

B) It was one of the bloodiest battles in that nation's history;

C) It is never in a nation's interest to go to battle;

D) Many soldiers had no training;

E) The nation described had not anticipated the crisis to arise when it did or had not expected its magnitude to reach the level it attained.

 

Okay, now...

There are many, many hints to be plucked from this one example, each of which would serve as a helpful principle on a lot of tests, but, for the sake of brevity, I will list just two.

FIRST, an answer choice that is worded the way choice C is -- is ALMOST ALWAYS THE WRONG ANSWER. Why? It is too extreme. It leaves no room for exceptions. When a nation is attacked in a serious way by a nation which is only interested in obtaining land and its collection of natural resources, the nation under attack has an interest in 'going to battle'. It needs to protect itself and its people.

And SECOND, ... (And this is the one that intrigues me enough to write a pile of words this big) is this: One of the choices up there is a very dirty trick. I don't like it, I think it is mean-spirited, and I think it does not belong on the exam. However, from time to time, one encounters it right there, printed proudly on the surface of the test. I am referring to choice D.

This choice, D, is considered the WRONG choice, and a student who fills in the bubble for it with his number two pencil will not receive credit. In fact, he or she will have one-fourth of a point subtracted from his score. It seems odd, at first, because a reasonable person taking the test might check it, nod in agreement, and move along. (After all, the passage did say that many soldiers had no training). And that is the problem! Oh yes, that is the problem: it is clearly stated, so the reader does not have to INFER it. It is not necessary to draw any logical conclusions.

Nice, eh?

The answer, which the writers of the test would consider the correct one is choice E.

Why? A combination of the lack or preparation and knowledge of the soldiers leads one to conclude that this was not something the nation had time to consider and plan for.

 

Moving along to SAT HINT # 3:

When plugging in numbers for a question on which you have to come up with your own guesses to see which answer seems to work out most reasonably, DO NOT BE CONFUSED ABOUT YOUR ROLE. AS SOMEONE TAKING A TIMED TEST, YOU ARE NOT TO think of yourself as CHARLES DICKENS OR EARNEST HEMINGWAY. No, realism is not only a waste of energy, but it can do damage by making the question harder than necessary.

Example: One summer, Jonny B. Jonny-Jonnson started eating more than he ever had before. And by September he actually grew 10 % taller....

Do NOT waste mental energy saying to yourself, well, if he started off the summer at four-feet-eleven-inches tall.....

NO!

The question is asked in percent. This simply means that it is a portion of 100. So, TELL YOURSELF: Jonny B Jonny-Jonnson began the summer at a height of 100 inches. . .

This way, you will not even have to pick up your pencil to determine that his new height is 110 inches tall. Oh, is that a realistic height? No, he'd be working in a carnival showing each and every visitor that there were no stilts involved. No, it is not realistic.

But when you consider the question and look at the answers, you might discover the advantage to selecting numbers that are friendly to the question.

FOURTH (and final) SAT tip for today:

Almost all parents mean well, but when they advise you that the probability is 'on your side' to venture a guess if you can eliminate even one of the choices as wrong...

They have no idea what they are talking about. Parental advice on this point should be met with a polite nod, an appreciative smile, and a quick expulsion from the listener's mind.

Why?

Because: There is something very important about the way the test is designed that most parents either seem not to know or dismiss as unimportant. It's this: It is true that on a question with five choices a correct answer is counted as one point, an incorrect answer is counted a -1/4 of a point, and no response is counted as a neutral, which of course is zero. This mathematical arrangement is based on the idea that if a person is from another planet and is not familiar with the language of the test, using a strict formula of probability he or she will check the correct answer about one-fifth of the guesses. So, he will get the other four out of the collection of five wrong, and combine to make one full point to 'neutralize' the one-out-of-five lucky guesses. The idea is that a student should not be able to increase or decrease his score substantially by closing his eyes and guessing his favorite letter for each choice. And that is what would happen if the student happened to be a blind monkey. Non-seeing monkeys do not get distracted by over-thinking or having their thoughts fractured by visual stimuli.

But a student who is fairly alert (at least as astute as a blind monkey) does not have the level playing field for guessing that a 'blind monkey' does. In other words, even if the student were to successfully manage to cross off one of the answer choices as WRONG, and they did so correctly, they then have the choice of the four remaining ones, but, unlike the visually impaired primate, the student is enticed by little shinny decorations on one or two of the remaining choices. In other words, the test-writers are crafty at developing correct-looking wrong answers.

For example, if the question is all in variables, each to the third power, then an answer choice with an exponent of 9, perhaps, or twenty-seven, might pull one's pencil toward it with the hope that, well... it sort of looks like it might have a common ancestor. The chimp? He doesn't take the bait.

So, it depends on the student; some are more skillful at it or just lucky guessers, but most aren't.

As it happens, I worked with a student just two years ago who was one of the most committed and skillful mathematicians I have ever met. Yet, repeatedly, on the one (or, on an off-day, two) questions of the entire exam for which he was not sure, he would ALWAYS guess a worng answer. I was finally able to encourage him to put the pencil down at that point and leave one blank. The following day, he took the exam and left no blanks. That time, luck was on his side.

Secret: As he was leaving my home the night before the exam, he presented me with a piece of candy. "I think you said it's your favorite kind," he said, "and I wanted to give you a present. So here." Awkwardly, he shoved it into my hand. It was unwrapped, coated in nervous sweat, but -- and this is the part that really got to me -- it was only HALF of the candy bar I liked.

"Where's the rest?" I asked.

"Oh, I wanted to try it, so, you know, I figured we'd share."

"And?"

"Yeah, it's not bad."

"Well, guess what?" I said, "You are never going to believe this!"

"What?"

"I bought you one. The same exact kind."

"Really??"

"Yup. Give me a second. I'll run into my office, get it, and put the one you gave me in the fridge for later."

"Awesome."

I returned with his.

"Where's the rest?" he asked.

"Oh, I didn't think you'd mind if I tasted it, you know, to share."

He nodded, pushed it into his mouth, and never questioned the miraculous coincidence.

That boy was a genius. He knew better than to question candy.

 

Hope these tips help,

Mitch