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

mayonnai5e · Posted: Mon Oct 15, 2007 4:32 pm Post subject:

Anyone know how I can change the message next to my name from "Really wants to Beat The GMAT!" to "Already Beat The GMAT!" ?? =P

beatthegmat · Posted: Mon Oct 15, 2007 8:17 pm Post subject:

mayonnai5e · Posted: Mon Oct 15, 2007 10:11 pm Post subject:

abhi75 · Posted: Tue Oct 16, 2007 6:12 am Post subject:

Hi mayonnai5e,

First of all congrats on your terrific GMAT score. I really appreciate your effort in sharing your GMAT strategy and improvements techniques with everyone on this forum.

Your log has been very very useful to me. It seems that you had the exact same weakness that I have right now and I will be referring to your blog now and again to improve my GMAT score.

I appeared for GMAT in Sep 2007 and the GMAT score was 550 (Q 40 V26). I would appreciate any suggestions/advice. But my very basic problem is timing on the Test and nerves. I am familiar with most of the concepts but I need to work to be a smart test taker.

Just like you I have decided to give maximum CATs possible. I was planning to appear for GMAT again in Jan. In a seperate thread I will post my experience so far.

All the very best for your apps.

Abhi.

achandwa · Posted: Tue Oct 16, 2007 11:05 am Post subject:

What I can gather from mayonnai5e's experience is it's best to answer as many questions, especially in the beginning, without random guessing as you possibly can even if it means you will need to randomly guess on some towards the end (to a limit ofcourse). Sure, on some difficult ones, you may need to make an educated guess after eliminating 2-3 choices but try to avoid random guesses. I came across one recommendation that advocated doing your best on first 20 questions even if you had to spent first hour on them and randomly guess on the rest by picking one of the choices, say D, for them all. It was a bit too extreme I thought. But it did highlight the importance of the initial questions.

On the 4 tests I have taken so far, I have always struggled on my timing. If I try to avoid mistakes in the initial questions, I end up guessing randomly on 6-8 problems on both sections. In one test I did manage to answer most questions without random guessing but I gave up far too easily on some difficult ones in the beginning that I knew would suck up too much of my time. In another, I tried to get as many correct in the beginning as I could and randomly guessed 5 on quant and 8 on verbal and ended up scoring my highest so far. The 4 tests I have taken don't have anything in common (they are from different sources); so I cannot read into it too much at this point. But I am trying to understand the importance of initial questions.

Minimizing mistakes in the early part of the test does mean spending more time on initial questions. I am enrolled in Veritas online course and they advocate pacing yourself evenly - 25 minutes each for each of the set of 13-14 questions. The official guide too advises against giving too much importance to the initial questions. But I am not sure that's the best strategy.

I would love to hear public opinion on the importance of initial questions and on pacing.
Thanks, Ashish

abhi75 · Posted: Tue Oct 16, 2007 11:11 am Post subject:

I have been following the method of uniform time distribution and it has not worked in my way. As you said I end up giving easily on the problems. This is what I did on my last test. As pointed out by others, if we limit our guesses to 3 to 5 max per section, we might be better off.

But again its worth experimenting with what you have mentioned.

mayonnai5e · Posted: Tue Oct 16, 2007 11:30 am Post subject:

Here is my take and my experience on the topic. I struggled throughout my entire prep on timing. Even after 10 practice CATs I still could not consistently complete either section. However, I noticed that when I tried to force myself to move ahead, I had too much pressure to give up on a question and move on to the next question and hope that it would be significantly easier than the last. In addition, I made more careless mistakes than necessary because of the little voice in my head screaming, "You're taking too long! You're taking too long!!"

But on practice sets, I noticed that I could move calmly through the questions and usually finish with just 1 or 2 left over. And, in addition, I would spend more time focusing on how to do a problem instead of "should I skip this problem? oh no i'm spending too much time on this...i need to start doing some grunt work start writing stuff down" In the end, MY experience told me that when I put TOO much pressure on myself, I would: 1) make more careless mistakes than usual and 2) give up on questions that I actually KNEW HOW TO SOLVE. This was very evident to me on my last GMATPrep because a majority of the questions I missed were ones that I solved very easily when I sat down and looked at it calmly after the test (by this I mean I was able to finish them under 2 minutes without any problems at all).

In light of my findings on how I performed under pressure on Quant, I made a conscience decision to NOT force myself to move too fast and to give myself ample time to evaluate a question and make a clear decision on whether I knew how to solve this problem. AND I knew I wasn't going to finish the exam. If I could not finish the other 12 exams, I wasn't going to finish this one.

With that decision made, two nights before my actual exam, I practiced by doing a set of the last 10 problems in the OG Q book. I gave myself ample time to read the problem, understand the problem, and evaluate the problem. If, after that initial evaluation, I found that I still had no clue how to solve it then it was time to guess and move on.

The important thing to take away is that this was MY experience and mine only. I noticed my accuracy was suffering severely yet I was not making any gains on speed and number of questions answered. So I decided to go for accuracy. My recommendation is not to follow my path blindly, but to practice a few CATs using different strategies and determine which method works best for you and what YOU feel most comfortable with.

BUT what I recommend everyone do is to practice all problems timed after you have completed the initial ramp up phase (i.e. learning the question types, reviewing math basics, etc etc. -- do not start from the very beginning timing yourself!)

mayonnai5e · Posted: Tue Oct 16, 2007 12:02 pm Post subject:

My Greatest Preparation Mistake.

In this post, I will discuss what I feel was the most significant mistake I made in my preparation.

You will recall that in the very first post of this blog, I stated that I did not like the error log concept because it became unwieldy with lots of problems ranging from SC to PS to DS. In light of that, I moved to lessons learned logs where I could just track my mistakes and the lessons I have derived from those mistakes.

However, I failed to consider how that method affects the context of the lesson itself. In Verbal, my lessons learned logs were very, very good. However, for Quant, I believe lessons learned logs are not enough. Why? Because my logs did not capture the context of the lesson. For example, I have one lesson that simply contains this:

|x| = -|x| and |x| >= 0
so
|x| = -|x| implies that X = negative * positive and x MUST be < 0 or = 0

Hmmm.....

What I found was that simply writing out specific lessons and notes did not work well for Quant whereas it can work very well for verbal because a verbal lesson usually applies in a general way. In Q, the lesson usually matters in a certain context and in a certain question asked in a certain way. In other words, when given a particular lesson, I found myself wondering why that lesson was important. Where did I get this lesson from? Why was this fact important? Was this a PS question? Was this a DS question? With my original lessons learned on Q, I LOST all that information.

Once I realized this HUGE mistake, which was ONE WEEK before my exam, I quickly went through all my missed problems in OG11 and all the most recent CATs (I left out the first 4 or 5 CATs because the material was simply too old to really reflect my current capabilities). For each problem, I copied down the problem. I solved the problem in the fastest way that I understood. This point is important. Some official solutions were too confusing to me, but I knew how to solve the problem in another manner so I wrote down MY WAY. NOT the confusing official way. What matters is what you know and what you can understand, not what the author of test question believes is the correct way to solve the problem. I wrote this all in BLACK INK. Next, I looked over the problem again, and at the end of the page, in BLUE INK, I wrote:

"Lessons:
1)...blah blah blah
2)...yada yada yada..
etc"

This last point is also key: each problem you miss should contain at least one lesson learned.

I employed this last method for each problem I missed in OG11 and OG V. In addition, I printed out all the missed Q problems from MGMAT 1, 2, 3 and GMATPREP 1 and 2. Print outs are nice because you don't have to hand copy the problem (laziness factor wins out any day). This idea essentially combines my idea of lessons learned with tried and true method of an error log. The important point is not to simply write out how to solve something because you risk the danger of simply memorizing that solution, but instead, to actively learn a lesson so that you can reapply that lesson on a problem that you've never ever seen before.

How successful was this? My highest Q was 45 on GMATPrep 1, which I took in May, and 45 on MGMAT 3, which I took about 3 weeks ago. Last week on GMATPrep 2, I scored 42 on Q. Immediately after that, I created my Quant error + lessons logged. I posted on this forum and other forums about ideas on how to boost my Q from low 40s to high 40s in one week. Most people who responded said it couldn't be done. IT CAN BE DONE. I scored 49 on Q.

Stacey Koprince · Posted: Tue Oct 16, 2007 7:18 pm Post subject:

I just want to echo something mayonnai5e said about the timing. The decision to just stay calm and not work under too much pressure worked specifically for mayonnai5e's situation. But most people should not follow that method unless they have really tried to crack the timing issue and they just can't make it work (as was the case for mayonnai5e).

The test does not count earlier questions any more heavily than later questions. OG says this and they are telling you the truth. Your score can absolutely tank if you have too many questions wrong at the end.

A lot of the companies out there bought into the myth that the earlier questions are worth more, so they built their practice tests to follow that principle - and then when people take tests and see this effect, it reinforces the myth. Be very wary - if the test is not a GMATPrep test or a test built specifically on the SAME algorithmic theory as the official test (as GMATPrep is, as our tests are), then studying how the scoring works on the test is not going to help and may do significant harm.

Let me tell you two important things to demonstrate what I've said above.

First, this is how the myth started (that we should spend more time on earlier questions). A theoretical study was done to see what would happen if someone answered the first 7 questions in a row correctly.
- if the tester's true ability was in the 200-500 range, the tester's score would go up by 60 points
- if the tester's true ability was in the 500-800 range, the tester's score would go up by 23 points

Great! We should all want to do this, right? Keep reading. We have to read the methodology of the study (that is, what assumptions it made).

The study assumed that the tester would get those first seven questions right without having to spend extra time on them. Somehow that got overlooked by a lot of people in trying to interpret this. So if you can get the first seven questions right without spending extra time, great. Go for it! (Yeah, that's not so useful as a piece of advice, is it? That wouldn't sell so well in test prep marketing...)

And it gets worse: the study's authors also calculated what would happen if the tester DID spend more time on those early questions. If you have to guess on only 4 questions at the end of the test b/c you spent extra time on the first 7 questions, the 200-500 tester's score increase disappears, and the 500-800 tester's increase actually turns into a DECREASE.

And, by the way, think about the likelihood that a tester with a true ability of 200-500 will get 7 questions right in a row, given that we know questions get harder as we get them right. Think this sounds feasible?

This study really does have some theoretical usefulness. But the study DOES NOT conclude that spending more time to get questions right will help to increase your score.

Second, I tested the above to an extreme a few years ago on the official test. I did only 2/3 of the math questions; then I let the time run out with all of the remaining questions left blank. When I take a test normally, I score in the 99th percentile. My math percentile on that test was in the 50s. That is obviously an extreme test - but if the myths were true that the first 10 or even 20 questions really counted for the vast majority of my score, then I should have gotten a score at least in the 90s, if not the high 90s. But I scored in the 50s.

I will say it once again: OG is telling you the truth when it says the earlier questions are not worth any more than the later questions. If you have too many questions wrong in a row at the end, you will not be able to maximize your score on the test.

(Really - I wish I could have worked with mayonnai5e to beat the timing thing because his / her score would have been even higher if that weakness hadn't existed. Essentially, mayonnai5e was probably at a 51, and then lost ground at the end through having to guess on the last 6-7 questions. And even then, s/he probably got lucky and guessed right on at least a couple of those, since the score "only" came down to a 49. It would have been lower if s/he had gotten all of those wrong.)

beatthegmat · Posted: Tue Oct 16, 2007 7:28 pm Post subject:

Wow Stacey--this is an amazing post. And it addresses such a common myth among test takers!

I'm adding this one to the resource wiki, thanks!

mayonnai5e · Posted: Wed Oct 17, 2007 2:24 am Post subject:

Stacy makes a good point that I want to reiterate. I tried very, very hard to fix my timing issues. If you read through my blogs, I mentioned timing in many posts, and I described the many ways I attempted to address the issue. However, I was not successful in completely overcoming my problem, but I was able to improve my timing on the hardest problems, which is still an improvement. My decision to focus on accuracy did not preclude a focus on timing.

During my GMAT CAT I still kept timing on my mind at all times, but instead of letting it be the deciding factor on every decision I made, I used my best judgement on each individual question. If I truly felt I could find the answer within the next 30 seconds with 90% confidence in my answer choice then I would use those 30 seconds; otherwise, I would just move on.

Throughout my prep, timing was the MAJOR focus. It was only after 10 weeks of study with a timing focus, and 3 days before my actual CAT, that I sat down and formulated a timing strategy for my CAT. Ultimately, I chose accuracy over timing, but that does not mean I didn't keep timing in mind. If you have a timing problem, I strongly advise working hard to overcome that problem instead of avoiding it. Even if you cannot finish all 37 problems, a focus on timing will help you think faster on the hardest problems so that instead of taking 5 minutes to solve it only takes 2.5 minutes. There were some problems on my GMAT that I definitely would not have been able to solve quickly had I stuck to my old ways of doing grunt work math.

Improvements in timing may not even be apparent when you are in fact improving. Say, for example, that before I started my timing focus I came across a very hard number properties question that involves picking numbers etc. And let's just assume this problem would have taken me 5 minutes to solve, but only 2.5 minutes after I've studied with a timing focus. That leaves me with 2.5 minutes gained from that very difficult math problem. Now, let's assume, I get another very hard math question and that one also takes me 5 minutes before timing focus, but 2.5 minutes after timing practice. That's a 5 minute difference. Now let's say that these two problems were questions 28 and 29 and the old me has 3 minutes left for the last 8 problems while the new me has 8 minutes. The faster me can spend an additional 5 minutes on solving two more very hard quant questions near the end of the exam, which solidifies/reinforces my score position, and guess on the last 6 while the old me could possibly finish 1 more question with limited confidence then guess on the last 7. Notice that in this scenario both versions of me would have to guess on the last 6 or 7, but the faster me answered 2 more very hard questions with a fairly good degree of confidence at the end of the exam, which helped to verify to the CAT algorithm that I really was a scorer in that range. Yet in both cases, I had to guess on the last 6 or 7!

Stacy put it very well when she suggested that my score perhaps could have been as high as 51 had I gotten to the last 6 or 7 problems. Which would you prefer? 49 or 51?

achandwa · Posted: Wed Oct 17, 2007 6:42 am Post subject:

Thanks Stacy for your invaluable insight!
-Ashish

mayonnai5e · Posted: Wed Oct 17, 2007 2:16 pm Post subject:

Anyways, I'm trying to get as many of my lessons learned onto this blog as possible before I forget now that I no longer have to study for the GMAT.

Today's topic: Picking Numbers in Quant

Picking numbers in quant has been a thorny subject for me. At first, I thought of it as a cheap way of doing problems so I tried to avoid it and instead focused on figuring out answers using critical thinking + math knowledge. In addition, I found picking numbers to be very, very time consuming. However, for the hardest quant problems, I found avoiding this strategy to be detrimental since such a large class of problems can be solved partially or entirely using the Picking Numbers strategy.

Once I realized how many problems could be worked out quickly with this strategy, I made a conscious effort to determine the most consistent way of picking numbers quickly - numbers that are relevant to the question at hand. Now, I concede that picking numbers can be a time waster - a very large time waster - but with practice it is very easy to narrow down the choices for number picking to a small subset of real numbers.

In particular, here are some general numbers to used based on the "description" given in the problem:

* x is a number or no info given on x: -2, -1/2, 0, 1/2, 2
* x is positive (not positive integer): 0, 1/2, 2
* x is an integer: -2, -1, 0, 1, 2
* x is a positive integer: 1, 2, 3, 4
* x is a non-negative interger: 0, 1, 2, 3, 4
* x is a non-positive integer: 0, -1, -2, -3

Note the difference among the last three - 0 is included in the last two because 0 is non-negative and non-positive. Also, you can just as easily substitute -1 and 1 for -2 and 2. Either set works, but it just depends on the problem. For example, with a square or square root problem, -1 and 1 are easier, but if the question deals with primes and/or evens then -2 and 2 are probably better.

If you do not wish to memorize the list above, you can memorize just the first one and reduce the range of valid values depending on the description. For example, if the question states that x is positive, you can start out with -2, -1/2, 0, 1/2, 2 then remove the first two numbers because they are negative. Or, if the question states that the number must be an integer, you can start with the above set and remove -1/2 and 1/2. This method is easier to remember and in some ways safer because you start with a baseline set and remove as necessary but since you start with the baseline set you'll still have all the ranges covered. In the last example, if you just tried to pick numbers ad hoc you may have missed the negative integers, but since you started with the baseline set, -2 was already included.

The big time waster in picking numbers is attempting to use this method without an organized attack plan (i.e. picking numbers randomly just to test a lot of numbers). So the lesson in this post is how I organized my number picking strategy to minimize the amount of time wasted. Now, to speed up calculations, you should pay particular attention to the constraints given by two things: 1) the question stem and 2) the given statements (on DS). First look at the question stem and determine how the constraints can affect the problem. Next, look at statements (1) and (2) on DS questions and use the information provided to further reduce the range of valid numbers. REMEMBER that any picked number must satisfy any and all constraints given by the question stem and DS statements.

In my preparation, I learned that the easiest way for me to organize the information was to build a table. The table consists of arithmetic expressions in the columns and picked numbers in the rows.

Here's an example

#154 OG11 DS:

Is x negative?
(1) (x^3) * (1 - x^2) < 0
(2) x^2 - 1 < 0

Do you remember this problem? Do you remember the crazy explanation given by the test writers where they concede, "The reasoning behind this conclusion can seem a bit complex." Well, I read this explanation and thought, "There's no damn way I'm going to be able to reason this out on the GMAT; I need another method." So I came up with MY own solution. This falls in line with my advice the other day about coming up with solutions that YOU can understand - not what the test writers say is the "correct" solution.

Okay, now the fun...

(1) (x^3) * (1 - x^2) < 0

My thinking process: Hmm. This is a bit complex. I know I can add/subtract numbers on either side of inequalities and there's definitely a subtraction there. Let's see what happens if I multiply the x cubed term:

x^3 - x^5 < 0

Oh wait, now I can move it over to the other side:

x^3 < x ^ 5

Hmm. What do I know about exponents? When can a base to an exponent of 3 be lower than a base with exponent 5? I think it has to be a fraction. What do I know about bases raised to odd exponents? Oh wait, the base must be negative if the expression is negative (e.g. x must be negative if x^3 is negative). But how do I combine that info? Well let's just pick numbers and see.

Hmmm what numbers should I use? The question stem says, "Is x negative?" and that tells me nothing because there are no restrictions on the value ranges so let's try my basic test cases: -2, -1/2, 0, 1/2, 2.

Okay time to build my table. What expressions do I need to test? x^3 and x^5.

_x____x^3__x^5
-2 ____-8____-32 (hey wait, let's fill out 2 also since it's almost the same)
-1/2
0
1/2
2_____ 8____32

Now, time to do a quick check. Okay, if x = -2, -8 > -32 and if x = 2, 8 < 32. But wait, the statement says x^3 < x^5 so x cannot be -2. Okay, cross out that row and continue:

_x____x^3___x^5
-------------------- (imagine the row crossed out)
-1/2__-1/8___-1/32 (hey, let's fill out x = 1/2 also!)
0
1/2___1/8____1/32
2_____ 8_____32

Okay, time to check. If x = -1/2, x^3 = -1/8, and x^5 = -1/32. Is -1/8 < -1/32? Yes (verify on the number line because this is tricky and someone not paying attention can say no if not careful). Now, I have two rows where x^3 < x^5, I can go back and check the value of x. If x = -1/2, it's negative, but if x = 2, it's positive. INSUFFICIENT. (All this took less than 1 minute since I'm very used to building these tables and comparing now). Notice I did not check 0 because I have no need to - I already know (1) is INSUFFICIENT.

(2) x^2 - 1 < 0

Add 1 to both sides and x^2 < 1. So build another table. Again, I do not know anything about x so start with the default values:

_X____X^2
-2_____4 (fill in x =2 now)
-1/2
0
1/2
2______4

Quick check: Is 4 < 1? No. Cross out both rows and continue:

_X____X^2
------------
-1/2___1/4
0
1/2____1/4
------------

Is 1/4 < 1? Yes for both x = -1/2 and 1/2. But wait, one is negative the other is positive. INSUFFICIENT.

Now, (1+2) can be confusing but we have both tables built already. Let's merge the columns of each table and eliminate rows again. But wait, we've already eliminated certain rows based on (1) and (2) so we don't even need to incude them!

_X___X^3____X^5___X^2
-------------------------------- (x = -2 eliminated from (1) and (2) above)
-1/2__-1/8____-1/32__1/4
_0____0_______0_____0
1/2___1/8_____1/32__1/4
-------------------------------- (x = 2 eliminated from (2) above)

So now we just need to compare these values. Look at 0 first since it's so easy. Eliminate that row because 0^2 is not less than 1 and x^3 is not less than x^5. So:

_X___X^3____X^5___X^2
-------------------------------- (x = -2 eliminated from (1) and (2) above)
-1/2__-1/8____-1/32__1/4
-------------------------------- (violates both 1 and 2)
1/2___1/8_____1/32__1/4
-------------------------------- (x = 2 eliminated from (2) above)

Look at these last two rows. We cannot eliminate based on (2) since both (-1/2)^2 and (1/2)^2 is less than 1. Evaluate using statement (1) then. We know -1/8 < -1/32 because we evaluated it above for stmt 1. So let's check 1/8 and 1/32: 1/8 > 1/32 so it violates (1)- ELIMINATE! Now we have:

_X___X^3____X^5___X^2
-------------------------------- (x = -2 eliminated from (1) and (2) above)
-1/2__-1/8____-1/32__1/4
-------------------------------- (violates both 1 and 2)
-------------------------------- (violates 1 above)
-------------------------------- (x = 2 eliminated from (2) above)

So now we have only one row left and indeed x is negative. SUFFICIENT. C.

Things to note:
(1) Use the constraints given in (1) and (2) to eliminate rows first then go back to the root question and see whether the statement holds true or not for the rows remaining.
(2) Sometimes the constraints given in (1) and (2) will not eliminate a row, BUT a constaint given in the question stem will. For example, the question stem notes, "if x is not equal y," then if you see a row where x = y you must eliminate that row. In other words, DON'T FORGET about question stem constraints.
(3) As soon as you fill in the value for a row, check it against the constraints and either leave the row in or cross it out.
(4) As soon as you find two rows with contradicting results, you know it is INSUFFICIENT if the question is a DS question. Stop there and do not fill out the rest of the table.

So you see this picked number + constraints + elimination table/process that I've created made the process of picking numbers extremely simple and easy. All I had to do was do some simple calculations, use some logic to eliminate, avoid doing extra work as soon as I found two numbers that gave contradicting results, and combine the tables together (since I reached phase 3 where I had to combine 1 and 2). But this process, when practiced methodically becomes second nature and is very easy to use. Now, do me a favor and open up the OG11 to the official explanation provided for this problem and read that explanation and compare it to what I have just shown you. Which is easier to understand? Which is faster to do? Which will you be able to utilize on the real GMAT? Which one can be used again and again and again on number picking questions?

Does anyone want more examples of the application of this technique? Please say so if you would like more examples of it being applied. I can think of at least one other OG11 problem that can be solved very quickly this way.

Good luck with this technique and you can thank me later. =)

mayonnai5e · Posted: Wed Oct 17, 2007 6:33 pm Post subject:

Here are actual pictures from my error log so you can better visual the table handwritten out. My apologies for my terrible handwriting. In the last picture, you can see my lessons in blue ink. The first states that I should consider which strategy for attacking the question seems easiest (e.g. my table or the OG explanation) and the second states that I should stop testing values once I find two contradictory results.

aim-wsc · Posted: Wed Oct 17, 2007 7:27 pm Post subject:

meticulous! indeed! ( files are big though...)

By the way which one is in blue ink Wink

And just noticed cute little kids in your avatar. May I know who are they?