### Another Way to Solve Data Sufficiency Value Problems, The Goldilocks Method, & Finding a Number That’s Just Right

One of the hardest parts about becoming an instructor with Manhattan GMAT was relearning how to solve GMAT questions. That sounds absurd, considering I had already scored a 780 on the GMAT when I applied to become an instructor, but it’s true. During the interview process, I went through online and in-person classroom simulations with 99th percentile instructors playing students, testing my ability to explain a question using algebra instead of plugging numbers or using a rate chart instead of adding rates. Over the years, I’ve found that many of our instructors felt the same way: overwhelmed by how hard it is to go along with someone else’s preferred method without skipping a beat. Ultimately, I realized that teaching the GMAT is a hundred times harder than taking the GMAT because every question has several valid ways of being solved.

Which leads to the problem of what solution is the BEST solution. Any student who has worked with me over the years has heard me say the following- I don’t care what method you use to solve a problem. But I do care that you get great at that method. It’s the reason why the Official Guide has an explanation for each quant problem and Manhattan has an OG Companion with different explanations, along with online video explanations that will sometimes differ from either of those methods. With so many different ways of solving a question, it’s important to not get bogged down finding the best way to solve a problem, but instead focus on finding the fastest way from start to submit.

So with that said, over the next few months, I’d like to share a few methods that I personally use when solving a few different types of GMAT questions. Some of these methods might click for you, and I hope you practice them. Some of them won’t and I hope you stick with a method that works better for you. So without further ado- let’s take a look at a fairly straightforward GMATPrep problem and think about how you would attack this question:

A sum of $200,000 from a certain estate was divided among a spouse and three children. How much of the estate did the youngest child receive?

(1) The spouse received 1/2 of the sum from the estate, and the oldest child received 1/4 of the remainder.

(2) Each of the two younger children received $12,500 more than the oldest child and $62,500 less than the spouse.

The first two things that I notice about this problem is that it is a word problem, giving us a real-world scenario, and a value Data Sufficiency question, asking us to find a single value for the amount that the youngest child received. And if I wanted to set this up algebraically, I could assign variables (*s* = spouse, *x*, *y*, *z* = oldest, middle, youngest child), write out several equations (*s *+* x *+* y *+* z* = 200,000. (1) *s* = 1/2*200,000; *x* = 1/4 * (1/2*200,000); *y* + *z* = 75,000. (2) *y* = *z*; *z* = *x* + 12,500; *z* = *s* âˆ’ 62,500), and eventually solve for *z* using Statement 2: the correct answer is (B). Different students at different levels of comfort with Data Sufficiency will be able to stop at different points after realizing that there either will or will not be a single variable in the equation that they’ve set up.

On my scratch paper though, you’ll find no equations. What you will find are the letters S, O, M, & Y representing the four people in the problem, and a circle around Y to remind me which value I’m trying to find. For the first statement, I would have numbers written under the variables I could solve for: S = 100K, O = 25K, or maybe even just a check mark to represent that I COULD solve for those variables. And at that point, I’d be finished with Statement 1, because it’s clear that I can’t find the amount of money that the youngest child received. It could be as much as $75K or as little as $0.

But the real speed trick for me with this question is in the second statement. At first, this might seem less helpful than the first statement because there are no obvious amounts that I can solve for. So I try the Goldilocks method: I try to find a number that’s too small, one that’s too big, and think if there’s just one number in the middle that would be just right. I would start in this case by finding who gets the least amount of money in this problem: the oldest child. Let’s say that oldest child got nothing. This would mean that the middle and youngest children received $12.5K and the spouse received $75K. Without adding these four numbers up, I can tell that they will not add up to the $200,000 that was left from the estate. I could then add an extra, let’s say, $100K to everyone and those same relationships would still hold true: O = $100K, M = $112.5K, Y = $112.5K, and S = $175K. Now the numbers are much larger than $200,000. But the trick with this method is to recognize that somewhere between the oldest child receiving $0 and $100K, there must be some number that would allow this equation to perfectly add up to $200K. The great thing about Data Sufficiency is that I don’t have to actually find that number.

In this particular problem, the reason why Statement 2 is sufficient is because there is a cap on the total amount and a relationship between each of the variables. In other words, this is a four variable equation and the second statement allows us to put all variables in terms of the youngest child. But for me, being able to come up with one set of numbers that fit Statement 2 allows me to more quickly understand that those numbers can all go up or down. But only one set of numbers will be just right.

This method doesn’t work well for quadratic equations where there can be two different answers to a problem or with values that don’t have any restrictions to how large or small they can be. But most problems in the real world don’t involve multiple right answers. It’s the same reason why someone on the Price is Right bids $1 on a prize package when he or she thinks that the other contestants have all over-bid. That person doesn’t think the prize is worth $1, but thinks that the right number is some number in between the values that have already been selected. And just like on the GMAT, your job isn’t to guess that number, but to hope that somewhere in the middle lies the correct value.

* GMATPrep text courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

nitestr- good catch! The spouse should be getting $62.5K MORE than $12.5K, or $75K. I’ve updated the article. Another reason to not hate DS problems. Even if you make a mistake with your math, you can still get a right answer!

Hi Joe,

For the second statement can you help explain how did you come up with “the spouse received $62.5K” ?

I understand the part – “middle and youngest children received $12.5K each”

Thanks,

ns