GMAT Tip of the Week: The Remainder Remix

GMAT Tip of the WeekR. Kelly. Jermaine Dupri. Mariah Carey. The Graduate Management Admissions Council (GMAC). What do they all have in common?

It’s the remix.

All four artists above are masters of the remix, taking the same song and making it different and, in most cases, better by simply changing a few things around. To the casual observer the end result may be entirely different (hey R. Kelly – is there even a non-remixed version of “Ignition”? It almost doesn’t matter with the remix being that good…), but to those who seek to understand the art of either music or the GMAT, it’s extremely helpful to recognize the way that these artists ply their trade. To get a feel for it, let’s look at two almost-identical-but-beautifully-remixed problems from the Official Guide for GMAT Review:

1. If a and b are positive integers such that a/b = 97.16, which of the following cannot be the remainder when a is divided by b?

(A) 4
(B) 12
(C) 22
(D) 28
(E) 96

In this question, it’s extremely helpful to understand the concept of a remainder and how it relates to the overall process of division. This problem is one that we term at Veritas Prep “Reverse Engineering” – you know how to do division from start to finish, but you likely haven’t thought much about how the individual steps relate to each other conceptually. You just know how to run through the process. To master these concepts in a GMAT fashion, it’s helpful to do small problems to remind yourself of the process. So let’s take 11 divided by 4, a problem you should be able to do without much thought. The answers are:

2 remainder 3
2 and 3/4
2.75

And how does the remainder factor into the problem? This is the reverse-engineering step – the question is asking you which cannot be the remainder, which means you need to reverse-engineer the idea of a remainder and how it relates to the rest of the calculation. And here’s how – to get to the 2.75 decimal version of the answer, you take the remainder (3) and divide it back by the denominator (4). So you can reteach yourself the concept – Remainder / Denominator = Decimal Points, and it does so by way of taking that fraction (3/4) and turning it into a decimal (.75).

In the actual problem, you’re given the decimal (.16) and asked which answers could be the remainder. And since you know from that smaller problem (11 divided by 3) that the conversion of fraction to decimal is what relates the remainder to the decimals, when you’re given the decimals you should look to convert it to a fraction to relate back to the remainder. 0.16 = 16/100, which you can reduce (since that’s what you typically have to do when you’re dealing with fractions) to 4/25.

Now how does this relate to the problem? We know that the Remainder / Denominator must be able to reduce to 4/25, which means that the remainder has to be a multiple of 4 and the denominator (b) has to be a multiple of 25. So when you look at the answer choices, one should stick out – 22 is not a multiple of 4, so it cannot be the remainder, making the correct answer C. (And for more breakdown on this problem, you can check out this article)

But back to the “Remix” theme of this post – in order to achieve high quant scores on the GMAT you CANNOT simply memorize that one problem setup as a step-by-step structure (1) express decimal as fraction; 2) reduce fraction; 3) remainder must be multiple of numerator of new fraction). Because in order to test conceptual thinking and problem solving ability, the GMAT will find multiple ways to remix that problem. When Mariah or R. need a new hit single, they can always get Jay-Z or T-Pain to appear on the remixed version of the original and then cash their checks. When the GMAT needs to truly test your reasoning ability, it does just about the same – it remixes the problem you’ve seen so that the concepts are the same but you need to figure out a new process. Take a look at another problem, also from the Official Guide for GMAT Review…we present the remix:

2. When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

(A) 96
(B) 75
(C) 48
(D) 25
(E) 12

Here the concept is the same but the steps are not. They give you the remainder and ask you about the denominator, and for those who simply memorized the format of the previous problem this one can look entirely different. Remember – the remainder divided by the denominator gives you the decimal points, so:

9/y = 0.12

In this case, you actually now have a linear equation to solve for, so reducing the left-hand fraction won’t do you any good (you don’t know y, so you can’t reduce any factors), and you’ll have to just solve:

9 = 0.12y
900 = 12y
300 = 4y
75 = y, so the answer is B (and you can find a more detailed version of *this* problem in this article)

The lesson in all this? One, you should get comfortable with remainders because the GMAT does test them (as the linked articles attest), but even more so it’s that the GMAT loves the remix, so you can’t get too familiar with just the problems you’ve seen. It’s not enough to memorize problem structures and hope to follow the same couple of steps over and over – it’s a matter of making sure you understand these three things:

  1. The concepts being tested (how do remainders relate to the rest of the division problem?)
  2. The process for reverse-engineering these concepts (if you need to remind yourself how a calculation process works, do a small-number problem like we did with 11/4)
  3. That no two problems are identical, but even when a problem looks like something you’ve never seen before, chances are it’s the remix of a problem you have seen. Arguably your foremost strategic goal on the GMAT is to take what looks new and unique and find what’s familiar about it so that you can leverage what you do recognize to make the unknown clearer.

So as you study, remember that your job is bigger than knowing how to do *that* problem; it’s to teach yourself the concepts that underlie it and how to make sense of those concepts even when they look abstract or unfamiliar. The key to the GMAT is conceptual knowledge and the ability to make what looks unfamiliar (the remix) look more like what is familiar. Now take that key and stick it in the (remix to) Ignition.

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