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In the process of finalizing my notes for my younger sister's school, I spent some time reading the latest offerings that are available in bookstores.

I started with the juggernaut: Princeton Review. In the past, I have liked their SAT books sufficiently to recommend buying them. I do, however, recommend to buy as many books as you can afford, check them out, and use the strategies that works for your individual situation.

Having read the 2005 version for the PSAT/NMSQT, my verdict is that the acronym should stand for Never Mind the Sub-par Quality of our Textbook! Seeing such books being published helps me understand why so many students do NOT do well on the PSAT. In many circles, the PSAT is viewed solely as a test run for the SAT, schools do not encourage the students to prepare for it -unless the student tries to score the the NM level. In a typical scenario, the vast majority of juniors will take the test after GLANCING at the flyers distributed at school. A great number of students will also face a parental gift: a book like the PR in question that was picked up at the local bookstore by the concerned parents. After all, doesn't the cover spell out "EVERYTHING YOU NEED FOR THE NEW PSAT"?

So, what does the typical junior do? He (or she) will roll his eyes, take the book to his room, read the first 10-15 pages, glance at the strategies, and jump to the practice tests to see what he knows.

What will he learn? He'll read that the PSAT is NOT that important and that strategies do work very well. He'll be introduced to the famous Process of Elimination (POE) but also told to guess AGGRESSIVELY. While this advice is not bad, it could have ... devastating repercussions. The student is really told that he does NOT need to know the answers and that guessing on all questions is beneficial, as long as he can eliminate one of the 5 choices. Armed with this knowledge, the common student takes a practice test and burns down in flames. What was missing in the advice? The fact that most students have the necessary education and are able to answer ALL the questions correcty. Yet, the theory is that tricks and strategies will yield a higher score. What is also missing? The fact that it takes a LOT of work to excel at the test.

Well, enough blah-blah! Let's check a few examples.

Question: If n is an integer larger or equal to 1 but smaller or equal to 20, what is the sum of the unit digits of all possible values of b when b = 2ⁿ. (Note: This could be expressed as b=2^n)

A. 40
B. 60
C. 64
D. 80
E. 100

Here is the answer from PR: This question wants us to work with the exponential vaues of 21 through 220. So work these out and keep your eye on the unit digit 2, 4, 8, 16, 32, 64, 128, 256 ... There is a repeating pattern of 2, 4, 8, 6. Their sum is 20, and this pattern will repeat five times between 20 and 220. So that's 50 x 20 = 100.

Isn't that great? Except for a small detail: where in the world does 21 or 220 come from? Will an unsuspecting student looking to LEARN from the answer see that they MEANT to write 2^1 and 2^20?

This case is sufficient to throw any student in a tailspin of self-doubt. In addition, I have no idea why PR believes that such a question COULD show up on a SAT. I'll spare you the details but ETS will never expect a student to write out 2 to the 20th power. Even if the pattern could be verified after a handful of calculations, this is a BAD question that shows why companies like PR are NOT able to produce decent emulations of the real tests. Not only do they fail to develop the question properly, but they also display a total lack of care in verifying the proposed answers. The first part is understandable, the second part represents a cynical lack of concern for their customers.

The book published by PR has not been edited very well and has been put together with little care or attention. They recycled old material, deleted the analogies and QC, and finally added the new questions in their two tests without doing much effort to provide an adequate guidance for the new material. The wannabe tests produced by PR and others have always been dubious, this new version is simply abysmal. I am dumbfounded to see a company with vast resources producing such poorly written and researched material.

Now, let's look at what has not been updated from the 2003 version.

In the very beginning of the book, we get this strategy:

To follow the example, you need to visualize a square ABCD, and inscribed inside the square a half circle CFD. The half circle diameter is also CD. In this case, the side is 8. This is a very common SAT problem and PR asks the student to identify the area represented by the square MINUS the half circle.

The 5 proposed answers are:

A. 16 - 8 Pi (Pi for p)
B. 16 - 16 Pi
C. 64 - 8 Pi
D. 64 - 16 Pi
E. 64

This is what PR proposes: We know that the value of PI is a little more than 3. Let's replace Pi with 3 in the proposed answers. Choice A and B are negative numbers. From here, you could guess C, D, or E and it is a guess we SHOULD take. However, we can also eliminate E because 8*8 is 64 and represents the whole square. What do we end up with? A one-in-two shot of getting this problem right. Neat, huh!

Well, not quite!

Let's look at the problem. How fast can we solve it?

1. Area of square? 8*8 = 64 .... 5 seconds
2. Area of half circle? Any student sitting for the PSAT or SAT should be able to play with the areas of circles, squares, and triangles. In this case, the 1/2 circle has a diameter of 8, hence the area of the 1/2 circle should be radius^2 * Pi * 1/2. The answer is 16 Pi/2 or 8 Pi. Time to compute this ... 15 seconds
3. Guess what? The answer to the question is 64 - 8 Pi. Check answer C after about 25 seconds?

What is bad about the PR method? First, if forces the student to write down FIVE calculations. Despite being trivial, it introduces potential errors. Most students make careless mistakes and calculating 16 times 3 easily falls in that category. Assuming the student does not make any error and gets it done rather quickly ... now, he still has TWO choices or a 50/50 chance. It could mean a plus 1 or a ...MINUS 0.25 in his tally, a swing of 1.25!

Why is the particular message wrong? It tells the student to forego attempting to solve a problem that most 7th graders can solve FAST and CORRECTLY. It also reinforces the idea that the test is all about gimmicks and tricks.

While the POE taught by PR is a GOOD technique, I do not quite understand why they selected this problem to illustrate their method.

The next one involves a perennial favorite problem on the SAT: the average rate of speed

A girl rides her bicycle to school at an average speed of 8 mph. She returns to her house using the same route at an average speed of 12 mph. If the round trip took 1 hour, how many miles is the round trip.

A. 8
B. 9 3/5
C. 10
D. 11 1/5
E. 12

PR proceeds with this solution: First the problem is a hard problem (level 5). TCB assumes that the common student will not attempt to solve the problem and pick the trick answer of 10 since it represents the average of 8 and 12. The common student second choice will be to pick a value that is stated in the problem: 8 or 12. PR provides the strategy to eliminate those Joe Blogg answers. Again, the conclusion of PR is to end up with two choices and pick between B and D. In their words, the student will be in great shape!

What's my beef with this? In my eyes, a 50-50 chance is really not good enough. When you consider how this problem can be solved, the recommendation to guess becomes highly dubious.

What could a student have done. Know the formulas for related rates -an opportunity that PR strangely forgets to mention. Is this formula really complicated? Here it is:

(2*Speed1*Speed2)/(speed1 + Speed2) or in this case:
2* 8 * 12 / 8 + 12.

Most everyone will notice that the answer is 2*96/20 or simply 96/10. This yields 9.6 or 9 3/5. The total time to do this, probably 20-45 seconds. Not a bad method to know!

It could even get better. How would I solve it?

1. Check the problem to make sure we have a ONE hour unit. Most often, TCB will use a one hour limit and not a different number of hours.

2. As soon as I verify that the unit is 1 hour, I will check B because I know that the answer is ALWAYS a number slighly BELOW the straight average. It takes only a few problems OF THAT TYPE to realize that it ALWAYS works.

3. My total time including reading the problem: about 10 seconds!

Here you have it: two methods that are faster and are bound to yield the correct answer and a healthy dosis of self-confidence!

By Jaredthegreat (Jaredthegreat) on Thursday, August 12, 2004 - 05:49 pm: Edit

Here's how I would do that last one.

d=rt; t=d/r

d/8+d/12=1
(12d+8d)/96=1
20d=96
d=4.8

but it asks for round trip, so 2d=2*4.8=9.6

That would be the straightforward, no tricks, no special equation, method, right?

I agree. I don't like their guessing tricks, etc. Though it is useful to say it won't be the average of the two.

Do they have any similar tricks (good, bad, or stupid) for the age questions (ie. twelve years ago, Joe was three times as old as Jessica. In three years he will be twice as old as she was three years ago. How old will Jessica be in eight years? (A)3 (B)12 (C)15 (D)18 (E)24 )

By Thunder77 (Thunder77) on Thursday, August 12, 2004 - 06:27 pm: Edit

You are correct Xiggi

I never really liked PR becuase they teach you useless tricks to try to get at the answer. They try to make everything too simple, which often is not helpful at all. I would prefer that they give us real strategies to actually approach the question as quickly as possible instead of wasting time and trying to get to the answer indirectly with the least bit of knowledge required.

However, I still bought the book not for the explanations but for the practice. Do you think it is good enough for just practice?

By Legendofmax (Legendofmax) on Thursday, August 12, 2004 - 06:28 pm: Edit

2. As soon as I verify that the unit is 1 hour, I will check B because I know that the answer is ALWAYS a number slighly BELOW the straight average. It takes only a few problems OF THAT TYPE to realize that it ALWAYS works.


This is what I do. It always works =) Average it the "wrong" way and take the answer that is a little less.

By Xiggi (Xiggi) on Thursday, August 12, 2004 - 06:59 pm: Edit

Here's how I would do that last one.

d=rt; t=d/r

d/8+d/12=1
(12d+8d)/96=1
20d=96
d=4.8

but it asks for round trip, so 2d=2*4.8=9.6

That is exactly what the formula (2*Speed1*Speed2)/(speed1 + Speed2) does!

Look below:
2* 8 * 12 / 8 + 12.
2 for Round Trip, 8*12 = 96 and 8+12=20.

By Xiggi (Xiggi) on Thursday, August 12, 2004 - 07:15 pm: Edit

(ie. twelve years ago, Joe was three times as old as Jessica. In three years he will be twice as old as she was three years ago. How old will Jessica be in eight years? (A)3 (B)12 (C)15 (D)18 (E)24 )

Good one!

By Jaredthegreat (Jaredthegreat) on Friday, August 13, 2004 - 03:59 pm: Edit

"twelve years ago, Joe was three times as old as Jessica. In three years he will be twice as old as she was three years ago. How old will Jessica be in eight years? (A)3 (B)12 (C)15 (D)18 (E)24 ) "

OOPS!!!

I meant to write "how old will Jessica be in THREE years?"
(A) 3
(B) 12
(C) 15
(D) 18
(E) 24

By Vtran31 (Vtran31) on Friday, August 13, 2004 - 05:05 pm: Edit

so do u know of any good prep for the new PSAT?

By Thunder77 (Thunder77) on Friday, August 13, 2004 - 06:35 pm: Edit

So what is the final word Xiggi?

Is this book good for practice? Are he questions too hard/too easy or just accurate? I bought the book solely for practice(not the explanations) and I hope that it will be useful.

By Xiggi (Xiggi) on Friday, August 13, 2004 - 07:50 pm: Edit

---

Quote:

"twelve years ago, Joe was three times as old as Jessica. In three years he will be twice as old as she was three years ago. How old will Jessica be in eight years? (A)3 (B)12 (C)15 (D)18 (E)24 ) "

OOPS!!!

I meant to write "how old will Jessica be in THREE years?"
(A) 3
(B) 12
(C) 15
(D) 18
(E) 24

---

By Xiggi (Xiggi) on Friday, August 13, 2004 - 07:56 pm: Edit

Best prep/test books?

The old list of recommended SAT books + SAT-II Math and Writing.

For practice, since there are no new official tests in existence, you can use the current crop of wannabe tests. I would, however, toss them out as soon as the Official Real Test book comes out in the fall of 2004.

By Jaredthegreat (Jaredthegreat) on Saturday, August 14, 2004 - 01:30 pm: Edit

Okay. In order to solve my problem, I started out from the beginning: Joe=3Jes, but I called Joe J, and Jessica X.

12 years ago:
J=3x.
in three years he will be twice as old as she was three years ago.
J+12+3=2(x+9)
but J=3x, so
3x+15=2x+18
x=3
that was twelve years ago, so now would be x+12=15. And in three years would be 15+3=18.

The only obvious "shortcut" I had found was that 3 and 12 were less than the fifteen years that would have to pass. I was just wondering if PR (or anyone else) had dumb guessing strategies for this type of problem, as it is one of the most difficult types of problems (or at least time-consuming) on the test.

By Xiggi (Xiggi) on Saturday, August 14, 2004 - 07:33 pm: Edit

Jared~

The shorcut in this case is to "backsolve" by plugging in one of the answers. In this case, you only have two potential answers (15 does not work either because Jess would have been ZERO years old at the start of the puzzle).

Your method works but the backsolving (after drawing a diagram) is surprisingly fast. I think less than a minute. The good news was that in this case you would only backsolve ONCE. If we would have picked 24 to start and it did not work out, the answer HAD to be to 18. There would no need to verify the answer.

An additional good news is that this type of problem should be at the end of the section, and if you worked rapidly enough, you should have a couple of minutes to waste on a word problem.

By Sonar (Sonar) on Monday, August 16, 2004 - 01:16 pm: Edit

I just want to add my two cents regarding PR's practice tests in its New PSAT book.

First of all, I can't give a real review of the strategies as I glanced through them, only to see that they were the same ones given in PR's old SAT book. There may be new ideas and strategies, but I didn't notice anything significant.

However, I took the first practice test yesterday, and I have to agree with Xiggi, it reeks of a rushed print. After taking the test, I have reasonable doubt that PR had a run through of the test, as some questions are unanswerable and the answer sheet was flawed.

Flawed Questions:

Section 2

7. If (2^a)^b, then ab =

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

PR clearly forgot to put in what (2^a)^b equaled (it's supposed to be 64).

Section 4

23. What is the y-intercept of the line with equation?

(A) 4
(B) 3
(C) 2
(D) 1/4
(E) -2/3

Here, PR forgot to give the equation.

27. The positive difference between -5 and p is the same as the positive difference between and 2.5. Which of the following could be the value of p ?

(A) -8.5
(B) -6.5
(C) -2.5
(D) 6.5
(E) 8.5

PR fails to mention what 2.5 is being compared to (it's supposed to be -1).

The flaw on the answer sheet is in section 3. The numbering skips 28.

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26 ***
27 ***
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29
30
31
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Also, I'm a bit skeptical of its difficulty, as I scored a 239 on my first time.

Oh, as for the question xiggi refers to as being flawed, it is presented differently in the text I am looking at; unless, xiggi is refering to a similar question that is in the review.

Section 4

28. If n is an integer, and 1 <= n <= 20what is the sum of the units digits of all possible values of b when b = 2^n?