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# GMAT Prep Software Analysis and What If Scenarios

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GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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Updated on: 16 Jul 2018, 23:31
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GMAT Prep Software Analysis and What If Scenarios

We will try to run different scenarios with GMAT Prep Software to find out whether various myth about scoring algorithm are legit.

Reports from the Real GMAT:

Added a few points to my verbal score: http://gmatclub.com/forum/600-to-740-al ... 47029.html

1. What is the importance of the first 10 questions?

Experiment: We will try to disprove the myth the way OG/GMAC positions it: the first 10 questions are not critical
Methodology: we will attempt the worst case scenario and will answer the first 10 questions incorrectly (not guess but incorrectly); then we will attempt to answer the remaining 27 questions correctly (not guess)

Result: Q38 (48th percentile - ouch) with only 10 wrong answers
Analysis: obviously something is not right with the myth about the first 10 questions. They appear to be very important on the Quant. If you miss the first 10 (probably not a very realistic scenario for most) you have no way of climbing out of the hole - almost all questions that were offered to me were generally easy/medium difficulty. Let's try a different scenario next to check this myth (we'll miss the last 10 questions). Also interesting to note, when simulated in the previous GMAT Prep version, this scenario resulted in Q41 (so there have been changes in the scoring algorithms of the GMAT Prep).
Total Score: every question in the verbal section was answered as "E" and it resulted in the final score of V8, 1st percentile. Total score: 380 - 10th percentile
Questions: 20PS and 17 DS. Also, see what question topics were encountered in this scenario:

2. What is the importance of the last 10 questions?

Experiment: We will try to analyze the importance of the last 10 questions and if it equals the important of the first 10
Methodology: we will attempt the worst case scenario and will answer the first 27 Q questions correctly and then will answer the remaining 10 questions incorrectly (not guess but incorrectly).

Result: Q50, 92nd percentile - Nicely done though not great. I think it is possible to get Q51 with 10 incorrect ones.
Analysis: The questions were much harder this time with some new topics/types appearing on the test such as coordinate geometry DS. Conclusion: the last 10 don't count as much as the first 10. This myth is True (as long as you can get the first 27 right). Please note that I have not guessed the last 10 but rather answered them incorrectly (which means I still had to solve those questions too). If you are guessing, you will most likely get a higher score.
Total Score: every question in the verbal section was answered as "E" (again) and it resulted in the final score of V8, 1st percentile. Total score: 470 (90 points higher than when we missed the first 10 questions)
Questions: 20PS and 17 DS. Also, see what question topics were encountered in this scenario:

3. What is the importance of the middle 10 questions?

Experiment: We will try to analyze the importance of the middle 10 questions and see how it compares to the results of the previous 2 experiments
Methodology: we will attempt the worst case scenario and will answer the first 14 Q questions correctly; then I will answer incorrectly the following 10 questions, and will answer the remaining 13 questions correctly.

Result: Q49, 85th percentile - not as good of a result as in the case of missing the last 10 questions but it was much less effort (fewer hard questions than in the second case)
Analysis: The questions were not much easier than in the second scenario above even though I have made 10 consecutive mistakes. So, it may be a slightly better value in terms of effort/score but not by far
Total Score: every question in the verbal section was answered as "D" this time and it resulted in the final score of V6, 1st percentile. (Interestingly enough, it was a slightly worse result than "E"). Total score: 450

4. What is the penalty if I miss every third question?

Experiment: I will try to test a scenario in which a test takers answers every third question incorrectly (e.g. 3, 6, 9, etc. Thus giving themselves an extra 2 mins on quant). This scenario will simulate someone who takes 3 mins instead of 2 per question and then guesses every third question. Please note that this is the worst case scenario (we do not get any guesses right)
Methodology: Every 3rd questions answered incorrectly. So, 13 incorrect and 24 correct answers.
Results: Q49, 85th percentile
Analysis: Slightly lower score than in the case of missing the last 10 questions but it was much less effort in getting here(fewer hard questions than in the second or third scenarios I have tested). So far this is the best value in terms of effort/final score
Total Score: This time every question in the verbal section was answered as "C" this time and it resulted in the final score of V8, 1st percentile. Total score: 460, 23rd percentile.

5. Best Guessing Strategy: Part I - What if we guess a bunch of questions in the middle?

Experiment: I will attempt 3 different scenarios that will examine guessing strategies to figure out where the time should be invested.
Methodology: First 10 questions answered correctly, then GUESSED the next 17 questions (answered C to all of them and got 4 out of 17 correct) and finally answered the remaining 10 questions correctly.

Result: Q46, 73rd percentile.
Analysis: This is a pretty similar to the scenario above where we tried to figure out the importance of the middle 10 questions; missing 3 more (13 wrong vs 10 wrong) resulted in a lower score by 3 points (46 vs. 49).
Total Score: Every question in the verbal section was answered as "B" this time and it resulted in the final score of V6, 0 percentile. Total score: 420, 16th percentile.
Questions: 21PS and 16 DS.

6. Best Guessing Strategy: Part II - guess every third question

Experiment: I will try to test a scenario in which a test takers GUESSES every other question (e.g. 2, 4, 6, etc). I was answering C to all even numbered question and guessed correctly 3 out of 18

Result: Q40, 55th percentile. (22 correct answers and 15 incorrect answers, I guessed 3 questions correctly.)
Analysis: Not sure what I was expecting guessing every other question. I guess I got the 55th percentile (half the ultimate score but I also only invested half the effort and gottend double the time to answer my other questions). So far, I don' think this is the best strategy in terms of guessing since my goal would be to get the most return for the least amount of effort. However, I do think this score is too low to be seriously considered by anyone.
Total Score: Every question in the verbal section was answered as "A" this time and it resulted in the final score of V6, 0 percentile. Total score: 380, 10th percentile.

7. Best Guessing Strategy Part III - Variable Guessing

Experiment: first 10 questions answered correctly, GUESSED the next 9 questions (answered C to all of them, guessed 2 out of 9), then answered the next 9 questions correctly and finally GUESSED the remaining 9 questions (answered C to all of them, guessed 2 out of 9). So, 23 correct, 14 incorrect.

Result: Q49, 85th percentile. (23 correct answers and 14 incorrect answers, I guessed 3 questions correctly.)
Analysis: I was amazed to see Q49 as my final score. So far I think this is the best guessing strategy. It has resulted into the highest score (49) with 14 incorrect answers (compare that to scenario #5 above where I guessed the 17 middle questions and gotten 4 of them correct. I made 13 mistakes mistakes on that test but the final score was only 46. In this scenario I still only solved half the questions (guessed the other half). However, that's pretty darn good for solving only half the questions.
Total Score: Every question in the verbal section was answered as "E" and it resulted in the final score of V9, 2 percentile. Total score: 470, 26th percentile.

8. PS vs DS: what is the importance of DS questions?

Experiment: first 10 questions answered correctly. After that, I answered incorrectly to 12 DS questions only. So, 25 correct and 12 incorrect answers (all DS).

Result: Q50, 92th percentile.
Analysis:
Total Score: Every question in the verbal section was answered as "E" and it resulted in the final score of V8, 1 percentile. Total score: 470, 26th percentile.

9. PS vs DS: what is the importance of PS questions?

Experiment: first 10 questions answered correctly. After that, I answered incorrectly to 12 PS questions only. So, 25 correct and 12 incorrect answers (all PS).

Result: Q49, 85th percentile.
Analysis:
Total Score: Every question in the verbal section was answered as "E" and it resulted in the final score of V11, 3rd percentile. Total score: 490, 31st percentile.

9 and 10. Importance of answering ALL the questions in time.

Experiment: two scenarios:
A. Answered first 30 questions correctly and the remainder 7 questions incorrectly. Result Q50, 92nd percentile.
B. Answered first 30 questions correctly and didn't answer the remainder 7 questions at all (ran out of time). Result Q45, 71st percentile.
Analysis: As we can see it's extremely important to finish the test and manage to answer ALL the questions in time.

Do you have any questions or ideas what you would like to try?
I will be running a few more scenarios - feel free to suggest what other scenarios would be interesting to test. Thank you!

Important Clarification: we have a strong reason to believe that even though GMAT Prep is the closest algorithm to the GMAT, it is most likely not identical. Some of these scenarios may result into a different outcome when attempted on the real test. We so far have no reports to confirm or dismiss these results based on the test day experience.

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Attachment:

myth.gif [ 24.93 KiB | Viewed 405046 times ]

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Originally posted by Bunuel on 21 Jan 2013, 09:18.
Last edited by Bunuel on 16 Jul 2018, 23:31, edited 45 times in total.
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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21 Jan 2013, 10:20
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GMAT Prep Software Analysis and What If Scenarios -- VERBAL

1) What if you get all the LAST 11 questions incorrect ?

Testing Scenario:

All the last 11 questions incorrect and others correct.

Result:

V38 ( 83 percentile, not bad after getting 11 questions incorrect in a row)

Analysis:

The 11 incorrect questions at the end of the Verbal section did not bring the score down greatly. It is unlikely that someone after attempting first 30 correctly would go so wrong in the last 11. The results show that the momentum gained by the first 30 questions is not significantly beaten by the last 11.

Conclusion:

Can we conclude that one should not worry about the last 11 questions, probably not. But, a few glitches at the end of the test would not destroy your hopes of getting a good score. This will be more clear from the results below.

2) What if you get some of the MID 11 questions (I took 11 to 20) incorrect ?

Testing Scenario:

The MIDWAY 11 questions (11 to 20) incorrect and others correct.

Result:

Again V38 ( 83 percentile, once again, not bad after getting 11 questions incorrect in a row)

Analysis:

The 11 incorrect questions at the mid gave the same results as the previous experiment. The results show that the momentum lost by the mid 11 questions could be gained by answering remaining questions correctly.

Conclusion:

Again can we conclude that one should not worry about the mid 11 questions, probably not. But, the results show that you should not loose hope if you got a few questions incorrect somewhere in the midway.

3) What if you get all the FIRST 11 questions incorrect ?

Testing Scenario:

All the first 11 questions incorrect and others correct.

Result:

V22 ( 27 percentile, not a good score in verbal. I was surprised by this result)

Analysis:

The first 11 questions literally spoiled the score. Furthermore, even the successful attempts of remaining questions could not recover from the damage done by the first 11 questions.

Conclusion:

Once again can we conclude that one should worry about the first 11 questions, definitely yes. The results show that first 11 are very important to your score. We considered an extreme scenario here; it is highly unlikely that someone would perform this way during the test. Therefore I considered somewhat realistic scenarios in the next experiments.

4) What if you get all the LAST 6 questions incorrect ?

Testing Scenario:

All the last 6 questions incorrect and others correct.

Result:

V44 ( 97 percentile, an awesome score)

Analysis:

The last 6 incorrect questions were insignificant in bringing down the score.

Conclusion:

We can confidently say that if you are able to solve first 35 questions correctly, you have reached the 94+ percentile mark. Even if something bad happens in the last 6 questions, you will still be happy to see your score.

5) What if you get all the MID 6 questions(21 to 26) incorrect ?

Testing Scenario:

All the MID 6 questions(21 to 26) incorrect and others correct.

Result:

V44 ( 97 percentile, wow again the same awesome score)

Analysis:

With the same results, the middle 6 incorrect questions were insignificant in bringing down the score. Moreover, the placement of these 6 incorrect questions seems to have no effect on the overall score.

Conclusion:

We can say that if you are able to solve first 35 questions correctly and the other middle 6 questions incorrectly, you have reached the 94+ percentile mark. Can we be sure about the fact that getting 35 questions correct in Verbal would give you a score of around V44 no matter what; the answer is no. The following experiments will prove why.

6) What if you get all the FIRST 6 questions incorrect ?

Testing Scenario:

All the FIRST 6 questions incorrect and others correct.

Result:

V33 ( 66 percentile, a good score, but definitely not an awesome score)

Analysis:

Getting first 6 questions incorrect is more realistic than getting the first 11 incorrect. As compared to the last two results the first 6 question greatly damaged the overall verbal score.

Conclusion:

The first incorrect 6 questions can destroy someones' hope of reaching even the 70+ percentile mark in verbal, no matter how well he/ she performs on the remaining questions. The apparent conclusion is that one should not take the initial questions lightly.

7) What if you get EQUALLY SPACED 7 questions incorrect ?

Testing Scenario:

7 EQUALLY SPACED questions incorrect with a gap of 5 correct questions in-between. Therefore, the incorrect questions are 1, 7, 14, 21, 28, 35, 41, the rest are correct.

Result:

V42 ( 96 percentile, My actual GMAT score)

Analysis:

A good score indeed, even after breaking the consistency after every 5 correct questions. One incorrect question between 10 correctly answered questions has not significantly lowered the overall score.

Conclusion:

The results are inline with our assumption that the more questions you solve consistently the higher your score. In testing scenarios 4 and 5 we got V44 where we solved 35 and 20 questions correct in a row respectively. In this test there was a small breaks in consistency, so we got a slightly lower score.

8) What if you get ALTERNATE questions incorrect/correct ?

Testing Scenario:

Alternate questions incorrect starting with first question incorrect. So, every odd question is incorrect and every even question is correct.

Result:

V16 ( 10 percentile)

Analysis:

This is a somewhat expected result. With around half questions incorrect and none correct in a row will in fact, result in a bad score. Some say that the first question that you receive is of medium difficulty level, a 50 percentile or a 500 level question. Moreover, if you get one question correct then incorrect probably you will maintain the level. The result was not a 50%ile score but a 10 %ile score.

Conclusion:

From the analysis we can conclude that alternate correct and incorrect question would gradually lower your percentile.

9 i) What if you get All SC questions incorrect: Test1 ?

I have conducted two tests to prove the point that SC is not individually adaptive and the location of SC question matters more than the number of SC questions that you got incorrect.

Testing Scenario:

All theSentence Correction questions incorrect anywhere in the test. In this iteration I got SC questions at following question numbers: 1, 4,6, 7, 14, 15, 16, 17, 19, 23, 24, 27, 29, 30, 31, 36, 41. 17 SC questions in total.

Result:

V25 ( 35 percentile)

9 ii) What if you get ALL SC questions incorrect: Test2 ?

Testing Scenario:

All theSentence Correction questions incorrect anywhere in the test. In this iteration I got SC questions at following question numbers: 6, 7, 8, 13, 19, 23, 24, 25, 27, 28, 29, 30, 31, 32, 33 ,40 ,41. 17 SC questions in total.

Result:

V35 ( 74 percentile)

Analysis:

In both the tests I got all the 17 SC questions incorrect, but the different in the two scores was huge. In the first started with an SC question, moreover 3 out of first six were SC.

Conclusion:

SC is not individually adaptive and where you got an SC question matters more than the number of SC questions that you got incorrect. So, initial SC questions (of any other initial questions) are really more important for your overall score.

10 i) What if you get All RC questions incorrect: Test1 ?

I have conducted two tests to prove the point that RC is not individually adaptive and the location of RC question matters more than the number of RC questions that you got incorrect.

Testing Scenario:

All theReading Comprehension questions incorrect anywhere in the test. In this iteration I got RC questions at following question numbers: 10-13, 16-18, 23-25, 33-35. 13 RC questions in total.

Result:

V36 ( 79 percentile)

10 ii) What if you get ALL RC questions incorrect: Test2 ?

Testing Scenario:

All theReading Comprehension questions incorrect anywhere in the test. In this iteration I got RC questions at following question numbers: 4-6, 13-15, 18-20, 33-36. 13 SC questions in total.

Result:

V33 ( 66 percentile)

Analysis:

In both the tests I got all the 13 RC questions incorrect, but the different in the two scores was not very significant good enough. In the first test I encountered the first RC passage at the 10th question, but in the second it came early at 4th. This could be one of the reasons for the score difference.

Conclusion:

like SC, RC is also not individually adaptive and again where you got an RC question matters more than the number of RC questions that you got incorrect. So, initial RC questions (of any other initial questions) are really more important for your overall score. By observing the results we can see that scenario 10 resulted in a better score overall than scenario 9. The possible reason for this observation could be that the number of SC questions (17) is greater than that of RC questions (13).

11) What if you marked the last answer choice, but did not click submit and confirm, and the allotted time for the section gets over?

Testing Scenario:

Answered 40 verbal questions and marked the last question and waited for the time to finish.

Result:

The result was a positive one, favoring of the test taker. The test will register your answer choice and will not reward you any penalty.

Analysis/ Conclusion:

As soon as you reach the last question it's better to mark one answer choice and then attempt the that question, so even if you are not able to determine the correct answer in time, the question would still be considered for your overall score and you will receive any penalty on your score.

Quant Guessing Strategy

Testing Scenarios:

Marked the same option in all the questions.

 Quant Guessing Strategy Test # Marked Choice Correct Score 1 Marked All Bs 2 6 2 Marked All Bs 4 6 3 Marked All As 7 6 4 Marked All Es 7 6 5 Marked All Ds 7 6 6 Marked All Cs 9 6 7 Marked All Cs 9 6 8 Marked All Cs 10 6 9 Marked All Ds 10 6 10 Marked All Cs 11 6 11 Marked All Cs 13 9 12 Marked All Bs 5 6 13 Marked All Ds 9 6 14 Marked All Ds 7 6 15 Marked All Cs 10 7

Analysis/ Conclusion :

Results from 15 tests show that on average an Option 'C' carries a higher probability of being correct and option B carries the lowest. I tested 'C' option the 5 times after I saw 13 correct "flukes" in the quant section. I think the reason is the DS questions in which many answers may in fact be 'C'. Another conclusion that we can derive from our results is that if you guess all the answers you are likely to get a '0' percentile no matter what answer you mark. But if you have to guess one or two and you have no idea/ time for the question mark 'C'. After the next tests it seems that D is the next after 'C' while guessing in quant. In test 15 again C resulted in 10 correct questions and a score of 7. Once again marking all Cs resulted in more number of correct answers as compared to others.

I will be posting results from new test scenarios. If you have any other interesting suggestions please let me know, I'll be happy to run the test.

Thanks,

Vercules

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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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24 Jan 2013, 09:09
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7th scenario: first 10 questions answered correctly, GUESSED the next 9 questions (answered C to all of them, guessed 2 out of 9), then answered the next 9 questions correctly and finally GUESSED the remaining 9 questions (answered C to all of them, guessed 2 out of 9).

So, 23 correct, 14 incorrect.

Result:
Q49, 85th percentile.
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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22 Jan 2013, 09:34
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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25 Jan 2013, 10:37
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Updated with the verbal results (see the second post)
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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23 Jan 2013, 06:57
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carcass wrote:
another scenario could be 2 right one wrong (the third) regardless the difficulty and the question.

A sort of a balance approach. I think is woth to taste

best regards

carcass

Just tested this scenario (4th): Q49, 85th percentile.
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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25 Jan 2013, 10:42
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Excellent stuff Vercules
One thing that I needed to clarify
I am not entirely sure if I interpreted GMAC correctly but what I understood was that:
For example in the first 10 questions for example, if you answer all the SC questions correctly but all the CR questions incorrectly, the next SC question is going to be difficult but the CR question is going to be easier.
Do you think its right in the GMATPrep scene?
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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01 Feb 2013, 15:52
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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21 Jan 2013, 10:56
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another scenario could be 2 right one wrong (the third) regardless the difficulty and the question.

A sort of a balance approach. I think is woth to taste

best regards

carcass
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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21 Jan 2013, 10:28
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2
Great work.

Scenario 1: 7 or 8 correct in first 10 question. Then ,
- how many consecutive wrong answers will not allow to score 90+ %?
- And where it effects the most? For e.g. 5 consecutive wrong between 10 & 20 or 20 & 30 or 30 & 37?

Scenario 2: Does any particular type of question (s) gives us any indication of our performance (during exam)? For e.g. Probability or P&C question
in exam indicates that we have reached 700+ level
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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24 Jan 2013, 08:32
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kapsycumm wrote:
I would love to see the outcome if we answer every other question wrong. Thanks in advance.

Tested a similar scenario (#6): answered correctly every odd numbered question and GUESSED every even numbered question (asnwered C to all of them and guessed correctly 3 of them).

Result:
Q40, 55th percentile.
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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24 Jan 2013, 23:43
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Are the results for each scenario consistent if you repeat the experiment?
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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28 Jan 2013, 01:12
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soumens wrote:
Awesome initiative!! The use of crystal clear language unties all knots.

Eagerly waiting for the Verbal What-if scenarios...

Just a quick Q, does GMATPrep simulate experimental questions in the same way as the test???

I think you might have even conducted multiple cycles of the same scenario. Was there no difference in the end scores?

Because I guess only experimental questions can introduce an error margin and it would be great to quantify that if possible...

Thanks to all...

Important Clarification: we have a strong reason to believe that even though GMAT Prep is the closest algorithm to the GMAT, it is most likely NOT identical. Some of these scenarios may result into a different outcome when attempted on the real test. We so far have no reports to confirm or dismiss these results based on the test day experience.
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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30 Jan 2013, 00:15
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Just wanted to add that GMAC has since confirmed that the adaptivity is by the SECTION, not the question type:

http://officialgmat.mba.com/2012/12/11/ ... questions/

Hence, the verbal section itself is adaptive, not the individual question types like RC, CR or SC.

So we will never reach harder CR questions if we screw up big time in SC or RC.
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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02 Feb 2013, 12:59
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GMAC Continues to emphasize that the first 10 questions are not important.... which I think is a very absolute statement which does not appear so absolute based on our observations.
http://www.mba.com/the-gmat/prepare-for ... -that.aspx
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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11 Feb 2013, 09:40
3
Archit143 wrote:
Hi
I have been following this thread long...but i was bit skeptical, whether GMAT prep software has the same algorithm as actual gmat has.....
Can we follow the scenarios, if we get into any such scenario on actual test, for i have heard that first 10 questions are not that important.

Archit

Hi Archit,

Well, GMATPrep is the only thing which is closest to the actual GMAT algorithm. But is it exactly the same as the actual GMAT algorithm, probably not. In my opinion, GMAC, the makers of the GMAT must be continuously working on the algorithm and the questions so that the test maintains its standardized nature and accuracy level. GMAT says that first 10 questions are not that important, but the GMAT prep indicates the contrary.

Moreover there are a few experimental questions in the actual GMAT, a feature absent in the GMATPrep tests. So, if 6 questions in Verbal and Quant are experimental then the real determiners of your score are the 31 verbal questions and 35 quant questions. This thing is impossible to test on GMATPrep tests. So, even if they are using the same algorithm in the GMATPrep tests, the absence of experimental questions feature makes it slightly less accurate. But again, it is the closest one; I think that the variation from the actual would not be more than 30 score point. So, if you score 700 on GMATPrep then in the actual test you might score 670 on a bad day and 730 on a good day. I scored 720 on GMATPrep two days before my actual test, and on the real GMAT I scored 750.
Bottomline: GMATPrep tests are one of the most accurate predictors of your score among all the tests present in the real world.

Hope that helps,

Vercules
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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10 Jun 2013, 10:46
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I actually verified the "guess the last 10" strategy on an ACTUAL GMAT about 18 months ago. The quant score was 49. While I can't be absolutely sure that my first 27 questions were correct, I was probably sitting on a 50 or 51 before I ditched (guessed A on all) the last 10. So my score only dropped 1-2 raw points. I had seen the results you have seen on the GMATPrep software and wanted to verify that the same pattern held for the actual test. It does.
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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24 Jul 2017, 20:23
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Bunuel wrote:

1. What is the importance of the first 10 questions?

Experiment: We will try to disprove the myth the way OG/GMAC positions it: the first 10 questions are not critical
Methodology: we will attempt the worst case scenario and will answer the first 10 questions incorrectly (not guess but incorrectly); then we will attempt to answer the remaining 27 questions correctly (not guess)

Result: Q38 (48th percentile - ouch) with only 10 wrong answers
Analysis: obviously something is not right with the myth about the first 10 questions. They appear to be very important on the Quant.

I've been meaning to post this for a year or two, but to me this experiment proves the exact opposite - it proves that the first ten questions are not especially important, or at least that they're not more important than later questions. That might seem counterintuitive, so I'll explain in more detail, first in a loose way, then in a mathematically precise way.

There's one crucial observation about this experiment: answering the first ten questions incorrectly is just an unspeakably bad performance. If you put a cat in front of the computer, and let it paw away at the keyboard, the cat would normally get 2 right answers in the first 10 questions, just by random guessing. So before looking at the Q38 and drawing a conclusion just from that score, it's important to define expectations. What should we think that test taker's Quant level is? At that point in the test, what would you guess, and how certain would you be? That's the question the algorithm is asking, and with that performance, the algorithm is going to be almost 100% certain that the test taker is below the 200 level, because essentially no test taker ever performs that badly.

To roughly guess what score the test taker ought to get in this experiment, it's important to know how the algorithm works. The algorithm assumes that if a question is at your level, you have a 60% chance to get it right. So if the difficulty levels of your first ten questions were 500, 400, and then eight 300-level questions, you need to get your next twelve 300-level questions right just to prove you're a 300-level test taker. And then you still have a lot of work to do to prove you're above that level. It's impressive that you can even reach a Q38.

The reverse happens when you answer the first 27 questions correctly. By that point you've almost certainly answered fifteen Q50-level questions correctly already, with no wrong answers on anything easier than that, so even with ten wrong answers on Q50-level questions, you still have a 60% hit rate at that level. So while the performance at the end is unusually bad, it's completely understandable that you'd still get a Q50.

Using the actual math behind the algorithm, if the test does proceed as above (500, 400, the rest 300) for the first ten questions, then a true 700-level test taker should have nearly a 99% chance of answering those 300-level questions correctly*. The chance a random 700-level test taker would answer the first ten questions incorrectly is roughly 1 in 6.6 million trillion (6.6 quintillion, or 6.6 * 10^18). It will simply never happen, so of course the algorithm will never give a Q49-Q50 score to a test taker who does that badly early in the test. Even the 300-level test taker only very rarely does that badly - they will only do that about 3 times in 10,000.

Put another way, if you knew before a test that a test taker was either a 300-level, 500-level, or 700-level test taker (with equal probability), and he or she answered the first ten questions on the test incorrectly, at that point in the test the probability would be 1 in 40 trillion that the test taker was 700-level, and 1 in 500,000 that the test taker was even just 500-level. At that point, if 300, 500 or 700 are our only options, you should be willing to bet a small house to win just \$1 that the test taker is the 300-level test taker. The odds are astronomically against the test taker being even average. That you can recover from that position to get even a Q38 should indicate that the first ten questions are not weighted any more than the later ones.

It's the fact that there are so many wrong answers on easy questions that makes it so likely the test taker is a very low level test taker -- high level test takers almost never answer easy questions incorrectly. And that's the takeaway test takers should take from this: be careful not to get easy questions wrong, because that will hurt you a lot. It doesn't matter where they are in the test, beginning, middle or end. And if you get a really hard question early in the test, and get it wrong, you shouldn't worry about that at all - that's what you're supposed to do unless you're an 800-level test taker.

* (technical details for people who know about parameter values: here I'm using a=1 and c=0.2, along with b values of 0, -1, -2, for 500, 400 and 300 level, and ability values of -2, 0 and 2 for 300, 500 and 700 level)
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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22 Jan 2013, 18:15
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Gr8 initiative by Bunuel. Interesting stuff!

I feel to get a more realistic assessment that can be close to the test day performance we can test -

scenario 1] 3-4 questions wrong per every 10 questions ie around 12-14 questions wrong out of 37

scenario 2] getting alternate questions wrong (may be 2 correct then 2 wrong and so on..)
Thanks
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Re: GMAT Prep Software Analysis and What If Scenarios  [#permalink]

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23 Jan 2013, 08:52
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5th scenario: first 10 questions answered correctly, then GUESSED the next 17 questions (answered C to all of them and got 4 out of 17 correct) and finally answered the remaining 10 questions correctly.
Result: Q46, 73rd percentile.
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Re: GMAT Prep Software Analysis and What If Scenarios   [#permalink] 23 Jan 2013, 08:52

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# GMAT Prep Software Analysis and What If Scenarios

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