[720 Q49 V40] My Blog: Errors and lessons learned

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by mayonnai5e » Sat Sep 15, 2007 3:12 pm
I've seen the SC problem several times, but have never been able to figure out what's wrong with one particular answer choice. Tonight, while I was doing a timed practice set from the OG SC set, I saw this problem again and finally figured out what the error is.
The peaks of a mountain range, acting like rocks in a streambed, produce ripples in the air flowing over them; the resulting flow pattern, with crests and troughs that remain stationary although the air that forms them is moving rapidly, are known as "standing waves."

(A) crests and troughs that remain stationary although the air that forms them is moving rapidly, are
(B) crests and troughs that remain stationary although they are formed by rapidly moving air, are
(C) crests and troughs that remain stationary although the air that forms them is moving rapidly, is
(D) stationary crests and troughs although the air that forms them is moving rapidly, are
(E) stationary crests and troughs although they are formed by rapidly moving air, is
A, B, and D are clearly wrong because of the "are" at the end. However, the last two choices are similar and both appear to be correct in terms of verb tense and pronoun agreement, but E is wrong and C is the correct answer.

Why is C more correct than E? Because of the word although. Although signals a specific linguistic element - mainly that something occurred even though something that appears contrary to it is evident. For simplicity's sake, let's interchange although for the phrase "even though" because even though is more often used in spoken English:

"Harry Potter is a great wizard even though he is a young boy" (I just watched Harry Potter and the Order of the Phoenix =P).

Notice how the thing that is being contrasted (great wizard) occurs just before the even though in the sentence. Now let's change even though back to although:

"Harry Potter is a great wizard although he is a young boy"

Let's look at choice C:

(C) crests and troughs that remain stationary although the air that forms them is moving rapidly, is

What is being contrasted? The "stationary-ness" of the crests and troughs.

--> Harry Potter is a great wizard although
--> crests and troughs that remain stationary although

Now let's look at E:

(E) stationary crests and troughs although they are formed by rapidly moving air, is

Notice how what is being contrasted is far away from the although. It is actually a little bit unclear what is being contrasted.

Convert this to the Harry Potter analogy:

"The great wizard Harry potter although he is a boy"

Hmmm....this is far from clear. In fact, the use of the although in these last two sentences suggests something is coming up to clarify the contrast:

"stationary crests and troughs although they are formed by rapidly moving air, are slow and dormant"

"The great wizard Harry potter although he is a boy, is very tall."

Lesson: Make sure what is being compared/contrasted by "although" is clear and close to the word although*

*unless although is used at the beginning of the sentence ==> "Although Harry Potter is a young boy, he is a great wizard"

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by mayonnai5e » Mon Sep 17, 2007 4:21 pm
Wow, it turns out that I'm terrible at DS under timed conditions. I just did questions 76-95 of the DS in OG11, which aren't even the hard problems, under timed conditions, and I did terribly! How bad? My hit rate untimed for questions 1-75 was roughly 93% and my hit rate tonight for this set was 75%.

Granted 1) I did this set at 1AM in the morning 2) got a total of 6 hours sleep last night and 3) worked 8 hours 4) studied permutation/combinations/probabilities for 2 hours and 5) these problems are noticeably more "tricky" than the previous 75, I'm still surprised by how many I got wrong. I stopped because it was too demotivating seeing so many errors. I noticed the time pressure forced me to move on without spending the extra seconds needed to ensure I covered all my bases. There were definitely things I simply overlooked and would have clearly seen had it not been for the time pressure.

I'll see how I fare on the next few sets, but this may be another weakness that I need to address (timed DS questions).

By the way, anyone have a similar experience and/or have advice on how to minimize this weakness?

Lesson of the day: don't do DS timed at 1 am in the morning off 6 hours sleep and after 8 hours of work and 2 hours of studying. =\

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by beatthegmat » Mon Sep 17, 2007 5:29 pm
I ran into a similar situation as you did during my GMATPrep--I found that I could go through PS questions much faster than DS questions.

My workaround for this situation was to train myself to go through PS questions under 1 minute, and DS questions under 2 minutes. By keeping this pace, I was able to complete the overall quant section in time.

Otherwise--the key to getting faster in DS is just simple practice. Understand the concepts well and apply them over and over again, and you'll speed up your pace...
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by mayonnai5e » Tue Sep 18, 2007 12:23 am
beatthegmat wrote: Otherwise--the key to getting faster in DS is just simple practice. Understand the concepts well and apply them over and over again, and you'll speed up your pace...
Agreed. I hadn't done any DS questions in over a week and that may have affected my accuracy and speed as well.

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by mayonnai5e » Tue Sep 18, 2007 7:02 am
I've taken a lot of good lessons learned in the past few days and will post some soon...

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by mayonnai5e » Tue Sep 18, 2007 9:38 am
Some important properties of 0:

--> 0 * 0 = 0
when? DS
context? xy = 0; xy >=0; xy <=0
why? unless stem states x, y are non-zero either or both can be 0

--> |0| = 0
when? DS
context? |x| used in anyway (e.g. |x-3| > y, |xy| = c)
why? special case that can be a trap

--> (0)^2 = 0
same as |0|...see above

--> 0 is non-negative
when? PS/DS
context? N is the set of first 15 non-negative integers, x and y are non-negative integers...
why? don't forget to include 0 in sets/ranges/values/etc

--> 0 is non-positive
same as above

--> 0/y = 0
when? DS/some PS
context? x/y >=0
why? 0 divided by anything is 0 so any division that does not exclude 0 as a possible value for the numerator can have 0 as the numerator

--> sq. root(0) = 0 since 0^2 = 0
when? DS
context? if sq root(x) = y, what is y?
why? may forget to leave out a possible value for x

There may be others that I've forgotten to include.

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by mayonnai5e » Tue Sep 18, 2007 9:59 am
Dealing with divisors, factors and multiples:

Remember they are all different sides of the same coin (if a coin had 3 sides). What do I mean?

If X is a divsor of Y, then X is a factor of Y
4 is a divisor of 8, 4 is also a factor of 8

If X is a multiple of Y, then X is divisible by Y
4 is a multiple of 2, 4 is divisible by 2

If X is a factor of Y, then Y is divisible by X and Y is a multiple of X
4 is a factor of 8, 8 is divisible by 4, 8 is a multiple of 4

If X is divisible by Y, then X is a multiple of Y and Y is a factor of X
4 is divisible by 2, 4 is a multiple of 2 and 2 is a factor of 4

If X is a multiple of Y, then X is divisible by Y, Y is a divisor of X, and Y is a factor of X
4 is a multiple of 2, 4 is divisible by 2, 2 is a divisor of 4 and 2 is a factor of 4

If the above seems confusing, pick a few numbers and write out their prime factorizations in a tree format and stare at them for awhile. Verify the things I've said above and see how the tree describes the relationship between the three.

Remember: Multiples are at the root (top of the tree), divisors and factors are on the bottom of the tree.

Post reply or PM if this needs further explanation.

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by mayonnai5e » Tue Sep 18, 2007 3:41 pm
DS. Sucks.

I finished the rest of the DS problems in the OG book and found my hit rate plummeted with the harder questions and under timed conditions. (57.5% on the last 40 questions timed). I've made a post in the MATH DS forums for suggestions/ideas on how to specifically improve this area of Q. Please reply on that thread if you have any suggestions.

https://www.beatthegmat.com/viewtopic.php?p=20991#20991

On the bright side, I actually noticed some lessons learned while doing the test. I found faster ways of doing specific problems. Hopefully the solutions will be very good and help a lot.

People on this forum have mentioned that the OG math questions are not that difficult (600-700) range so it's kind of demoralizing to see that my hit rate so low. I guess I'll just have to offset that by getting 100% of the PS questions correct. =P.

On bright side: 57.5% means huge room for improvement.

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by mayonnai5e » Thu Sep 20, 2007 11:55 pm
Anonymous wrote:Hang in there man! You have a great approach to your studies, I'm sure you'll be improving your DS.
Thanks for the support. I'm trying!

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by mayonnai5e » Fri Sep 21, 2007 1:07 am
I haven't done any practice problems in the past two days. I finished up the DS section on Tuesday (last 60 problems) and did poorly on them so I've shifted my focus from completing the OG to focusing on lessons learned from the DS section. To that end, I've been slowly and methodically going over every solution. My approach:

1) Before looking at the solution, go through the problem again mentally and look at my practice work to see how I did the problem
2) Note any approaches that seem overly computational or require a lot of plugging in/picking numbers
3) Read official explanation.
4) Note any shortcuts or insights provided by the explanation that I overlooked or did not see.
5) Write down lesson learned on how I can see that shortcut or insight next time I see a problem with similar characteristics.

At the rate that I've been going, I can only cover 20 problems in 2 hours, which is 6 minutes per question on average.

As mentioned in this blog before, quality over quantity. Quality is where you learn the most.

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by mayonnai5e » Fri Sep 21, 2007 6:02 am
I had an old blog that I was running on blogspot, but I took it down to track all my progress on this site instead.

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by mayonnai5e » Fri Sep 21, 2007 3:34 pm
Investigation of N = Dq + r:

So one day while I was sitting at a cafe in Paris, I decided to study this equation. This equation can be used to describe any number. On the GMAT, you'll likely see this equation in the format:

Y = Xq + r, where 0 <= r < X

But I'll represent it with different variables to make it more clear what the variables represent:

N = Dq + r

where
N = any Number
D = any Divisor
q = quotient of N/D
r = remainder of N/D

The most basic form of this equation you'll see is:

N = 2q ----------> EVEN
N = 2q + 1 -----> ODD

Why are these true? N = 2q is the same as N = 2q + 0 where 0 is the remainer when N is divided by 2. So N is divisible by 2 and N must be even. For the other, the remainder is 1 when N is divided by two so it must be odd.

# 147 OG11: If n is a positive integer, is n^3 - n divisible by 4?
(1) n = 2k + 1, where k is an integer

You can see that n is odd from stmt 1.

Now, here's the most complex stuff...

This equation can also be represented as N = q (r/D). This is not supposed to be multiplication; think 7.5 as 7 and one half.

For example, N = 8, D = 3:
8 = 2 (2/3)

N = 8, D = 5:
8 = 1 (3/5)

* Note the (r/D) portion implies that r is not divisible by D. If r were divisible by D, then there would be no remainder. In addition, the (r/D) portion also represents the decimal portion of the number. To illustrate this look at 7(1/2). This is 7.5 where the .5 comes from the (1/2)

* Note given D, we can sometimes determine whether a number can be represented as a terminating decimal:

#107 OG11: Is r/s a terminating decimal?
(2) s = 4

--> Recognize that r/s can be represented as r = sQ + R, where s is the divisor, Q is the quotient and R is the remainder. We know that 0 <= R < s (stated above), so given s = 4, we know the possible values for R: 0, 1, 2, 3. The decimal portion of the number is (R/s) so the possible decimal values are 0/4, 1/4, 2/4, 3/4, which is .0, .25, .5, .75.

Let's look at another example:

#148 OG11: What is the tens digit of positive integer x?
(1) x divided by 100 has a remainder of 30

--> Convert to the equation: x = 100q + 30. Choose values for q:

q = 1: x = 100 + 30 = 130
q = 2: x = 200 + 30 = 230
q = 3: x = 300 + 30 = 330
Sufficient.

(2) x divided by 110 has a remainder of 30

--> Convert to the equation: x = 110q + 30. Choose values for q:

q = 1: x = 110 + 30 = 140
q = 2: x = 220 + 30 = 250
q = 3: x = 330 + 30 = 360
Not sufficient.

Now back to N = Dq + r.

We know from this equation that N is not divisible by D because of the remainder r.

# 12 Paper Test 14, Section 7:

If x is an integer and y = 3x + 2, which of the following CANNOT be a divisor of y?

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

--> y cannot be divided by 3 because of the remainder 2. Which of the answer choices are dependent on division by 3? Only 6 so that is the correct answer.

So as you can see, this equation can be used to give you extra insights into certain classes of problems (namely number properties, but it may also appear in something like probability). For an example of a probability question, take a look at this little twist to the last problem above:

If x is an integer and y = 3x + 2, what is the probability that y is NOT divisible by a number chosen randomly from a set of the first 10 integers greater than 0? (I just made this question up on the spot)

Answer:
* Set of first 10 integers greater than 0: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
* y NOT divisible by 3, 6, or 9
* 3 choices/10 total numbers = 30%

How do you recognize when to use this equation?
1) Number property problem or probability problem that contains a variation of this equation.
2) Questions that involve remainders

So that's all. If anyone finds anymore interesting applications of this equation, please let me know.

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by mayonnai5e » Sat Sep 22, 2007 8:51 am
Took my first MGMAT CAT and man was it brutal. The math was just ridiculous! The last few CATs I've taken were PR and PowerPrep and the math pales in comparison. The questions were just layered with complexity and often were time-consuming. About halfway through the math, I thought to myself, "make it stop, please make it stop...." =P

After the math, my brain felt fried - it was kind of like taking a midterm or final in college all over again...except that there was another 75 minute portion coming up! Well at least I stuck with it and finished the exam without hitting the pause button.

As far as timing goes, I had to guess from 30 to 37 on Math and 38 to 41 on V. That's about 11 problems guessed, which is an improvement, but still not satisfactory.

Anyways, my score was 650 Q40 and V38, which is right in line with the last few scores I've achieved:

GMAT Paper Test #14 680
GMAT Paper Test #55 660
PR CAT 3 660
MGMAT 1 650

My V score was a bit disappointing because I thought I was doing fairly well and was generally confident on most answer choices.

When will I break the coveted 700 mark?

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by mayonnai5e » Sun Sep 23, 2007 1:37 pm
I did questions 76-116 of the RC set in OG11 under timed conditions. I started off giving myself 3 minutes per passage + 2 minutes per questions, but I found that too be too lenient so I lowered the time to 1.5 minutes per question. I got all of them right except question 116 - that's a 97.5% hit rate. =)

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by mayonnai5e » Mon Sep 24, 2007 5:12 am
I've taken several different CATs thus far in my practice. Here are my thoughts on them:

PowerPrep
- First CAT I took
- Felt the math was not too tough - I didn't see too many problems where I just had no clue how to solve it, but the difficulty progression was slow
- Verbal was difficult to read
- This program does not handle screen resolution well - on my 20 inch widescreen monitor, the program changed my default resolution and made it very hard to read the Verbal portions

GMATPrep
- Undeniably the best CAT out there as it is the official practice CAT
- The math got tough very quickly so I knew I was in the upper bin territory, which really upped my anxiety and nervousness and took me out of my "comfort" zone.
- Verbal was verbal. I hadn't studied verbal at all when I took my first GMATPrep CAT so wasn't expecting anything different from PowerPrep and didn't score any differently

PR
- My scores with these CATs have been in the same range as the GMATPrep and PowerPrep exams, but I think there are significant drawbacks to this CAT
- The difficulty progression is very, very slow. This makes it difficult to reach the more difficult questions because you have to get many correct in a row (I had sequences of 9-13 correct in a row on several CATs). This does not simulate the real CAT, which very quickly pushes you to your limits. On GMATPrep, I found myself out of my "comfort zone" around question 15 whereas on the PR CATs I usually didn't hit that point until question 25.
- There seems to be a huge penalty for getting an answer wrong in the first questions. This combined with the slow difficulty progression means that if you get one or two of the first questions wrong, you'll be digging yourself out of a very large hole. I think PR followed their own advice too much and purposely adjusted their algorithm to penalize takers severely for questions missed at the beginning.
- My opinion: This CAT is flawed in the difficulty progression of the algorithm and the scoring algorithm

MGMAT
- These are the closest CATs I've taken to GMATPrep.
- At around question 10 on the math, I was already seeing questions for which I had no idea how to solve correctly.
- My stress/anxiety levels on this CAT were similar to those I experienced on GMATPrep.
- The Verbal section seem a bit off from the OG11 problems. I feel like the verbal section was designed to match the ideas taught in the MGMAT books instead of matching the OG11 questions.

Overall, GMATPrep is the best with MGMAT following behind. The reason is because I felt the MGMAT CATs pushed me like the GMATPrep did. The questions became difficult very quickly, and I was constantly stressed. If I were taking the real CAT, I imagine I would feel the same level of anxiety as I felt on the MGMAT CAT.

Oh, while I'm on the topic of tests, I've also taken some of the paper tests, but I found them to be unrepresentative because 1) they're non-adaptive 2) they seem to contain more easy to middle difficulty questions 3) a large portion of the old problems are included in the OG guides. As a result, I do not recommend them for gauging your score level; they are better for practice or to practice timing.