Probability of Scoring Perfect Score on multiple tests GMAT, GRE, LSAT

Question

Hello GMAT Clubbers, I was typing this reply (actually this is just one small part of it that I will post here now) to one ongoing discussion that was locked in the meantime. Of course, I could unlock original one, but there is no need to, some other people thought that conversation there heated, or some participants misbehaved. Instead of that, just on pure facts and research I want to present some data and raise some questions, without mentioning names. (actually just one name

) I have visited Manhattan page and checked all tutors, all 77 of them, we are talking here about one tutor's peers/ex colleagues, with approximately same experience, here are stats among them, regarding perfect scores : ACT 1 GRE 7 LSAT 1 GMAT 1 SAT 3 https://www.manhattanprep.com/gmat/instructors/ Now, here is the most important part (although I already expected that kind of distribution of perfect scores), we have one person with perfect ACT score, 7 instructors with perfect GRE score, one with perfect LSAT, one with perfect GMAT score....do you know how many of them have scored perfect score on at least two separate tests ? NONE. ZERO . Yesterday out of fun, I have started to calculate probability of scoring perfect scores on multiple tests...I will present only probability to score perfect score here on GMAT and GRE (perfect on verbal and perfect on quant) : 30/200,000 * 17,427/1,700,000 * 52,3269/1,700,000....it comes to approximately 0.00000045....and that's only for GMAT & GRE perfect score. Now, not only that none of Manhattan instructors did score perfect score on any two existing combination of tests, let me repeat all 77. of them...but one (ex-Manhattan) tutor supposedly scored perfect score on GMAT and GRE and GRE Mathematics Subject Test and SAT (only 10 times in a row) and LSAT and ACT. To put that mildly, I would say that is highly unlikely ! I was wondering what is your opinion about it, just from scientific point of view, for the sake of truth, without mentioning names please ?? *GMAT figures are annual, GRE are for 3 years period, but that doesnt change the outcome, since I would just divide both numerator and denominator with 3, scaled them down, and still get the same result.

mcelroytutoring · Answer

I agree with your math (and logic!), but I've scored perfectly on the SAT, ACT, and GRE—though I don't work for Manhattan. ; ) (I've "only" scored 99% on the LSAT and GMAT.)

It took me 7 tries to achieve a perfect score on the ACT, however, so hearing someone claim "10 consecutive perfect scores on the SAT" makes me laugh because of how outrageous the probability behind that is. Even if you can earn a perfect score 50% of the time, which is insanely good, then the odds are only (.5)^10 that you could do so 10 times in a row, or .09 percent (less than 1 in 1,000).

The more attempts you are given, the easier it is to eventually achieve a perfect score. The GRE is easy enough to score perfectly on, since you get unlimited lifetime attempts, and same with the LSAT. The GMAT is the hardest one to ace since you are limited to 8 lifetime attempts (I've used 5 so far), and you need every single question correct for a perfect 800.

-Brian

IanStewart · Answer

I'm not sure what this calculation is, but I gather you're multiplying the fraction of GMAT scores that are perfect with the fraction of GRE scores that are perfect?

It's not mathematically correct to do that, because these probabilities are not independent, and they're not random. When someone takes a GMAT, they don't have a 30/200,000 (or whatever the numbers are) chance to get a perfect score. It's not random. And if someone does get a perfect GMAT score, the probability they will also get a perfect GRE score is high. They're not independent (unrelated) things, which is the only situation where it is mathematically correct to multiply probabilities.

Perfect LSAT scores seem to be the rarest perfect scores on these standardized tests, but only slightly rarer than perfect GMAT scores. It's much easier to get perfect GRE, SAT and ACT scores (though obviously those scores still are uncommon). I don't understand any of the probability calculations in either of the two posts above though - some people will have a much higher than 0.5 probability of getting a perfect score on a single SAT or GRE, so you can't conclude anything about how likely it would be that one person could get ten consecutive perfect scores by computing the value of (0.5)^10.

mcelroytutoring · Answer

My estimate of a 50% perfect-score frequency, if anything, is too high and unrealistic, which is why I used it as an extreme example and an upper limit of what's possible.

A good comparison would be James Holzhauer, affectionately known as "Jeopardy James," who wowed the nation by winning 32 consecutive games of Jeopardy, while absolutely dominating with an average of $77,000 per game, obliterating nearly every single-game record and nearly breaking Ken Jenning's total money record of $2.5 million. Holzhauer is arguably the 2nd greatest Jeopardy contestant of all-time.

Although Holzhauer had 11 "perfect score" games during his 32-game streak (games where he won and answered every question he answered correctly), 35% of his overall games, he of course did not do so every time, and he was never able to earn a perfect score 10 times consecutively. In fact, Holzhauer was never able to do so more than 3 times in a row: https://thejeopardyfan.com/statistics/james-holzhauer-jeopardy-statistics

By comparison, although the Jeopardy GOAT, Ken Jennings, won twice as many (75) games, he only had 2 perfect games (3% of the time): https://thejeopardyfan.com/statistics/k ... statistics

Why? Because real people with real, verified test scores will inevitably make mistakes every few hundred questions or so—even the brightest human beings on this planet. Even if you have 80% odds of earning a perfect score on the SAT on any given attempt—and I would argue that there is no one alive who meets this description—you would only have 11% odds of doing so TEN TIMES IN A ROW.

For one final comparison's sake, I've taken the SAT 6 times and earned 2 perfect scores (33% of the time). I'm proud of that number, though, because I know it's real and not a figment of my imagination.

A little skepticism goes a long way. "Trust, but verify."

-Brian

IanStewart · Answer

Even if everyone makes mistakes, on a test the issue is only whether you can spot your mistakes and fix them before confirming your answer. Everyone I went to grad school with would get a perfect score on the Quant sections of these standardized tests effectively 100% of the time, because even in the rare situations where they made mistakes, they'd know how to find them when double-checking their work. Fortunately for GMAT test-takers, they aren't competing with many of those people with math PhDs!

If these tests were math-only, there would be a lot of people capable of scoring a perfect score on any number of consecutive attempts. It's the Verbal sections that make perfect scores rare, but some tests have easier Verbal sections than others, so I wouldn't know how to guess the probability that a top-level Verbal expert would get a perfect score on, say, an SAT. For obvious reasons, a comparison with Jeopardy is not meaningful, nor are your or anyone else's specific test scores, since test takers have differing ability.

Apparently this thread is discussing someone who claims to have ten perfect SAT scores. I have no idea even who that person is, and no idea if their claim is true, but I don't find it as implausible as you appear to.

Anupom · Answer

mcelroytutoring , You're technically showing up your 99 percentile scores in the forum!

You're too much funny.

Who says that you've to make every questions correct to get 99% in GMAT? For verbal, you've to make every questions correct, but for Quant...? You are just judging everyone as your own knowledge! If you got 2 times perfect score that doesn't mean that nobody will get more than 2 times perfect score in SAT. At first try to get perfect score in GMAT, then suspect other's perfect score, please. Most importantly, you and billionaire is going to make a probability on someone's score, but remember: Probability can't be the evidence! IanStewart He is no one but GMAT god, RonPurewal N.B. We should honor Ron for the unlimited time for his contribution in GMAT WORLD. Here you go for the whole discussion: https://gmatclub.com/forum/any-good-res ... l#p2284808

IanStewart · Answer

Thanks for the info, Anupom. Over the years, I've known of a few instructors who claim 800 GMAT scores who don't have them. So it's not unreasonable to question those claims, because those claims are genuinely questionable some of the time. But I've seen Ron on this and the BTG forum for about ten years, and he can answer anything, Quant or Verbal -- he is obviously capable of getting an 800. Of all the people claiming to have an 800 score, he'd be the last person I'd doubt. I otherwise don't want to participate in this conversation, because it seems to have become contentious (I wasn't aware of the background to this thread when I first posted here), but I did at least want to be sure someone's character wasn't being unfairly maligned.

mcelroytutoring · Answer

Yes, you need every question correct in Verbal and Quant for a perfect 800 on the GMAT.

If you answer 1 or even 2 questions wrong on Quant, then you might still technically score a perfect Q51, but even with a perfect V51 you will not earn a composite 800 unless you answered every (counted) question on Quant and Verbal correctly. That's why there are people on this forum with verified Q51/V51/790 scores, for example:  https://gmatclub.com/forum/q51-v50-253258-20.html

I know this because I've done extensive studies on GMAT Club user ESRs--and I've also had access to dozens of ESRs from my own private students.

houston1980 · Answer

I believe Ron Purewal should confirm his scores if he is not lying. His claims are outrageous. I personally believe Ron Purewal is lying about his scores. The burden is on him to disabuse our suspicions.  RonPurewal   SarahPurewal

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Probability of Scoring Perfect Score on multiple tests GMAT, GRE, LSAT

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