GMAT Tip of the Week: Trial, Error, and Success

GMAT Tip of the WeekOne of the most fascinating parts of being a GMAT instructor is getting to watch successful adults relive the math they did as kids. In many cases, an instructor can actually see that concept or point in time when the student stopped trying to really understand the math and just started relying on that combination of memorization and partial credit to get their Bs in math and search for a career path that would include no more of it. How many students decided at some point in junior high or high school that they just weren’t a “math person”?

While that’s sad on so many levels, it’s a particular challenge for many GMAT students in that somewhere down the line the binary nature of math – there’s always exactly one right answer, as opposed to an essay that you can write and back up your opinion of “To Kill A Mockingbird” in English – taught them that there wasn’t much value in trial and error. You either had the right answer or you didn’t, but for many math was never a discussion or a process. And so directly related to the GMAT the lesson that many students never embraced is this:

On the GMAT quant section, it’s okay to try and fail. And actually it’s more than okay – it’s absolutely necessary on some questions.

GMAT math is often not about “how DO I do this problem?” but much more about “how MIGHT I do this problem?”. There’s no one blueprint for most questions, but rather you need to be able to try out a concept and see if your reasoning holds up. Consider an example:

If x is the smallest positive integer that is not prime and not a factor of 50!, what is the sum of the factors of x?

(A) 51
(B) 54
(C) 72
(D) 162
(E) 50! + 2

Now, this is a unique problem structure – were you to see this problem on the test, you wouldn’t likely have seen a problem written all that closely to it before, so you probably don’t have a direct method to be able to solve it. For most of us, the thought process will have to include some trial and error. You may just have to have a conversation with yourself, thinking of numbers and trying to determine whether or not they’ll work:

-How about 51…I know that all the numbers 1 through 50 are factors of 50!. But wait – 51 is 3*17, and so both of those are factors of 50! so 51 doesn’t wok.
-How about 52 – well, no, that’s even and can quickly be broken down into 2*26, both factors of 50!.
-53 is prime and it’s bigger than all the individual components of 1*2*3*4*…49*50, so it would work. But wait – the question specifically says that it can’t be prime.
-If you keep going with other numbers like 54 (27*2) and 55 (5*11), if they’re not prime they’ll have smaller factors that fit within 50!, and if they are prime, well, the definition of the problem says they don’t work. So how do I lean on that smallest prime number of 53?
-Oh, I can make it “not prime” by multiplying it by the smallest possible number, 2, and then I have 106. It’s not a factor of 50! and that’s as small as you can get. So factor it out: 1, 106, 2, 53, and the sum is 162, answer choice D.

Now the takeaway from this – very few people will have a system to pick up that 106 is that number in question, but by thinking through several “wrong” numbers and finding out why they don’t work, you can incrementally develop a better understanding of the framework and lead yourself to the right number. Math is a conversation in many cases. So if a problem looks complicated and you don’t have a formula or system ready to go, start trying things and holding them up to logic until you realize that you’ve stumbled on the method. GMAT math requires a lot of trial and error. Often you need to fail in order to succeed on that very same question.

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By Brian Galvin

2 Responses

  1. Jesse says:

    Can you explain how you got the answer in more specific detail? I don’t know how you came up with 106 (I realize that it’s 53*2 but why did you even think to use that?)

    • Brian says:

      Sure thing – and quite honestly I thought of this particular problem for this post mainly because I had recently seen and solved it and it was that exact logic of “let’s try a few things to see what’s going on” that led me there. I definitely didn’t fully grasp the situation immediately.

      Since the stipulations are:

      -Not prime
      and
      -Not a factor of 50!

      You need to find a number that:

      1) Has a prime factor bigger than 50 (since all primes less than 50 are contained within 50!)
      2) Is not prime

      So if you look at the first number that fits the first requirement, it’s 53. But that’s prime. How do you make it “not prime” but keep the same prime factor? Multiply by another integer that’s greater than 1. And the smallest such integer is 2, so if you take 53*2 that’s going to give you the first number that works.

      Now, like I said…that takes some trial/error to fully conceptualize, at least for most of us. So that’s why this question makes this post – you might try a high prime less than 40 (say, 47) and try multiplying that by 2, but 47 and 2 are each called out within 50! (50*49*48*47*…..3*2*1). So you can’t go lower than 50 with a prime, so you need to go above, back to 53. That kind of thinking – try a few types of numbers to better understand the setup – can be really helpful on some of these more “philosophical” number questions.

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