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Posted on
01
Sep 2021

Additional Voters – GMAT Quant Problem

Additional Voters – GMAT Quant Problem

Hey guys, today we’re going to look at a particularly challenging GMAT Quant problem that just about everyone resorts to an algebraic solution path on, but there’s a very elegant part solution path. When we take a look at this problem we observe immediately that the difficulty is that we have no baseline for the number of voters that we start with. That’s the confusing part here and this is one of the ways that the GMAT modulates difficulty; when they give us a problem without fixed numbers, and where we’re not free to run a scenario because there are add-on numbers that change the relative values.

Additional Voters Problem Introduction

GMAT Quant Problem

Here they’re adding the 500 and the 600 which means there exist fixed values at the beginning, but we don’t know what they are. What we want to do here is remove ourselves a bit from the problem and let the ratios that they give us guide our way.

We start out with three parts Republicans, five parts Democrats. These eight parts constitute everything, but we don’t know how many voters are in each part – it could be one voter in each, or a hundred, or a thousand, and we can’t speculate yet. So, what we need to do is not worry about it, and this is where a lot of people get really uncomfortable. Let it go for a second, and notice that, after we add all the new voters, we end up with an extra part on the Republican side and the same number of parts on the Democrat side.

What does this mean? Well, the parts are obviously getting bigger from the before to the after. But because we have an overall equivalence between the number of parts we can actually reverse engineer the solution out of this.

Reverse Engineering the Solution

We’re adding 500 Democrats and we’re maintaining five parts from the before to the after. This means that each part is getting an extra 100 voters for the total of plus 500. On the Republican side, we’re adding 600 voters. We already know, from the Democratic side, that each part needs to increase by 100 to keep pace with all the other parts. So, 300 voters are used in the three republican parts, leaving 300 extra voters to constitute the entirety of the fourth part.

Now we know that each part after we add the voters equals 300 and therefore each part before we added the voters was 200. From there we get our answer choice. I forget what they were asking us at this point, and this is actually a really great moment because it’s very common on these complex problems to get so caught up, even if you’re doing it mentally, with a more conducive solution path, to forget what’s being asked. When you’re doing math on paper, which is something we really don’t recommend, it’s even easier to do so because you get so involved processing the numbers in front of you that you lose conceptual track of what the problem is about.

So, they’re asking for the difference between the Democratic and Republican voters after the voters are added. Now we know there’s one part difference and we know that after voters are added a part equals 300 voters so the answer choice is B, 300.

Something to Keep in Mind

This one is not easy to get your head around, but it’s easier than dealing with the mess of algebra that you’d otherwise have to do.
Review this one again. This is a GMAT Quant problem you may have to review several days in a row. It’s one where you might attain an understanding, and then when you revisit it four hours later or the next day, you lose it and you have to fight for it again. It’s in this process of dense contact and fighting that same fight over and over again that you will slowly internalize this way of looking at it, which is one that is unpracticed. The challenge in this problem isn’t that it’s so difficult. It’s that it utilizes solution pads and way of thinking that we weren’t taught in school and that is entirely unpracticed. So, much of what you see as less difficult on the GMAT is less difficult only because you’ve been practicing it in one form or another since you were eight years old. So, don’t worry if you have to review this again and I hope this was helpful.

Check out this link for another super challenging GMAT Quant problem.

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Posted on
10
Mar 2021

GMAT Ratio Problem – Mr. Smiths Class

GMAT Ratio DS Problem

Expressing Different Notations

Hey guys!

Expressing different notations is often challenging when you’re first starting out on the GMAT and by different notations mean percentages fractions decimals ratios. We learn all these separately and we tend to of them as separate systems of math when in fact they’re all different expressions of the same math. One half is no different from 0.5 is no different from 50 percent there are different ways of the same thing.

Breaking Down The Problem

In this problem all their testing is our ability to shift notations. We’re being asked what the ratio, keyword ratio, is between boys and girls in the or what do we need is just that a ratio it’s fairly straightforward. So they’re probably going to come to us with weird information that doesn’t quite look like a ratio. The big thing to note before we dive in is that when we’re being asked for a ratio. In fact, when we’re being asked for any sort of relative notation, fractions, percentages, anything that needs a base that is compared to a whole. We don’t need precise numbers.

Possible ways to solve this problem

So this leaves us open either to run scenarios if we want to or to deal entirely in the relative. So we’re looking for an expression of that ratio in a non-ratio sort of language. Number one tells us there are three times as many boys and girls. We can run a scenario with 3 boys, 1 girl, 75 boys, 25 girls, but we’re being given that ratio. It’s being expressed in language rather than with the term ratio or with the two dots : in between but it’s still a ratio. So it’s sufficient!

What Did You Miss?

Correction!! Number one states there are three times as many girls as there are boys. Why do we leave that error in? To point out that here it doesn’t matter. We’re not looking to determine whether the ratio is 1 boy to 3 girls or 3 girls to 1 boy or 3 boys to 1 girl. The only thing that matters, the threshold issue on this problem, is getting to a single specific ratio. What that is or in this case even reversing the boys and girls doesn’t matter because it’s a referendum on the type of information that we have. The moment we have a quantitative comparison of boys and girls coming from number one we know that number one is sufficient. Being able to have flexibility and even focus on the more abstract thing you’re looking for sometimes leads to careless errors on the details though and this is important. Many times those careless errors don’t matter, freeing yourself up to make those and understanding that you don’t have to manage the nitty-gritty once you have the big abstract understanding is very important.

Looking at Statement No. 2

Number two goes fractional, telling us that 1/4 of the total class is boys. We can break that into a ratio by understanding that a ratio compares parts to parts whereas a fraction is part of a whole so one out of four has a ratio of one to three. If this isn’t immediately obvious, imagine a pizza and cut it into four slices. One slice is one quarter of the total pizza the comparison of the one slice to the other three slices is the ratio one to three so if you get one slice and your friends get the other ones. The ratio of your slice to the others is 1:3. You have 1/4 of the total so two is also sufficient. Therefore, the answer choice here is D.

Hope this helped guys! Practice this skill of going in between these different notations because it’s one that pays off in dividends. Check out the links below for other problems and we’ll see you again real soon.

If you enjoyed this GMAT Ratio DS Problem, try your hand at this Triangle DS Problem.

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