Question

 Dear Mitch,

 With only a few days to go before the PSAT exam, I want to tell you how much I appreciate your hints and tricks. I have to admit, I haven't told anyone about it, except if they live in a different town and don't know any of the kids I know, because I'm starting to become a competitive person, at least until after this test. And since my scores on tests aren't usually anything to brag about, I need whatever edge I can grab. But one kid I know in the school is always printing out your SAT hints, BUT he only does it when he thinks no one is watching! Then he quickly changes the screen to another site and logs off. So there are probably others who do it at home who don't tell anyone either.

 Anyway, I just want to say that I appreciate it so much that I decided as soon as I get the last of my scores and send them off to colleges, I'm going to tell everyone about your site. Until then, though, I don't even wear my adler-n-subtract.com tee shirt unless I'm alone in the house (or with just my family, because I told them not to tell anyone in town and they've been pretty respectful.) But guess what? I've seen both my parents reading your math and verbal tricks on their own, so I guess they must like it too!

Anyway, so could you do another and another and another until the test? Please?

Sincerely,

A Kid Who Suddenly Can't Remember His Name...

Some town that has trees in it, U.S.A.

 

Answer

Dear A.K.W.S.C.R.H.N.,

As I'm sure you can imagine, it would be terrific for me if you did tell everybody you know, BUT I totally respect your approach. The best part of your letter, for me, anyway, is that you're finding it helpful. (Oh, and thank you for buying one of our tee shirts; they've certainly surprised us by becoming popular the way they have, and when people email me directing me to see someone's pictures on MySpace.com, and the screen pops up with someone wearing an a-n-s shirt or a-n-s tank top, I am astounded! One more thing before we get to answering your question: There is an eleventh grader in Florida who is one of those 'SUPERKIDS' (brains, athletic talent, appropriate and mature around adults, a true teen when with other teens – in the best sense – and he possesses the wisdom to be humble when self-assessing. He also happens to be a 'ranked' tennis player who has to juggle his intense academic workload with many hours and days and weekends out of town winning tennis matches. Recently, he played a match wearing an adler-n-subtract.com tee shirt. From what I understand, it was to be a tough match. He won. Now, guess what?

He thinks the tee shirt brings good luck. And here's the weird part: He is right. The thing I don't understand is how he figured it out? (available in a variety of colors)

Sure, here's something that can help you get many questions right on the SAT that students often get wrong: It can be very helpful to keep in mind that algebra and geometry are woven together, and sometimes if an answer is not coming to you in one of those areas, try thinking about it the other way.

Here are two easy examples that make the point:

EXAMPLE # 1:

Thomas has a container of square tiles, each the same size. If he reaches into the container and pulls out 24, will he be able to arrange those 24 into one big square with no extras or unfilled spaces inside the new shape's borders?

A) YES, because 24 is an even number and is divisible by 4, which is the # of sides of a square

B) YES, because all the pieces he has to use are squares so they can be lined up in perfect rows that will fit together to form a perfect square

C) NO, he will not

D) NOT ENOUGH INFORMATION PROVIDED

E) Can I go home now?

To be answered in a moment...)

EXAMPLE # 2:

On another day, Thomas from the problem above reaches into the same container and pulls out 39 squares. If he finds it too hard to form a square with no gaps or extras, how many is the least amount of additional square tiles he would have to remove from the container to add to the pile on the table to do the task correctly?

A) 7

B) 8

C) 9

D) 10

E) 11

The answer to the first one is C, "No, he will not".

The answer to the second one is................ Drum roll .................

....................................................................

Choice D, 10

Why?

Think of the word "square" in algebra. A square number is a number that has a factor that can be multiplied by itself to get the square number. 4 is a square number because 2 x 2 = 4, but 5 is not because there is no number that can be multiplied by itself to get 5. And with Thomas' little squares, he needs a square number of tiles, so that he can have a certain number of rows that each have the same number in that row, so that when they are all slid together neatly, the number of rows will equal the number of columns.

Thomas would need one more in the first example, giving him 25 tiles. 5 rows of five each will give the shape the dimensions of 5 by five.

In example two, 39 is not a square number, and the next square number up is 49, because 7 x 7 = 49. The next square down, by the way would require 36 tiles, because 6 x 6 = 36.

So, since he has 39, he needs 10 more to bring him up to 49.

Hope that helps,

Mitch