Quant word problem strategy

[Eddie Gutia]

Lets take the below problem from "MGMAT Word problems", page 13:

A candy company sells premium chocolate at $5 per pound and regular chocolate at $4 per pound. If Barrett buys a 7-pound box of chocolates that costs him $31, how many pounds of premium chocolates are in the box?

MGMAT recommends us to follow the below process to answer any word problem question.

1) Identify what value the question is asking for.
2) Identify unknown values and label them with variables.
3) Identify relationships and translate them into equations.
4) Use the equations to solve for the desired value.

Question: Step 1 in the process asks you to identify what value the question is asking for. However, in order to find the desired value, you should fully comprehend the question. If you have to fully comprehend the question, you might as well finish steps 2 and 3, saving redundant work which in turn saves time. In summary, I think the below sequence of steps works better than
what MGMAT recommends.

Step 2
Step 3
Step 1
Step 4

Am I missing something? Thanks a lot for your help.

[StaceyKoprince]

Ah - "identify what the question is asking for" doesn't actually mean "find the exact answer." It means: know what you are trying to find. Make sure you have articulated clearly to yourself what you are working toward before you start taking steps to find it.

In this problem, for example, I want pounds of premium chocolate - as opposed to pounds of regular chocolate, or the total cost of the premium chocolate, or the total cost of the regular chocolate. There are lots of possible values, but I care ultimately about pounds of premium chocolate. If I keep that in mind, I am likely to be able to work efficiently (avoiding unnecessary steps) and I'm likely to avoid the trap of solving for the wrong thing.

Does that make more sense? :)

[Eddie Gutia]

Hi Stacey,

What you said makes total sense because I am the kind of guy who makes careless mistakes trying to solve for something that the question doesn't even ask :-)

From what I understand, you are suggesting that I first find out what the question is asking for and not necessarily understand the entire question. I practiced a few problems using this technique and it did work great on a few of them. Just to be super clear, for the below question what you are suggesting me to do is to first look at the what portion of the question, which in this case is "What is the value of y in terms of x and z?" and then follow the second (Identify unknown values and label them with variables.) and the third steps (Identify relationships and translate them into equations.) to better understand the question. Am I correct?
Or
Are you suggesting that I at least understand what the question is asking for? If yes, for the below question I wouldn't be able to understand what the question is asking for (value of y in terms of x and z) unless I understand the entire question (what is y, what is x etc..).

In summary, what approach do you suggest that I take for the questions like these?

Machine A, working alone at a constant rate, can complete a certain production lot in x hours. Machine B, working alone at a constant rate, can complete 1/5 of the same production lot in y hours. Machines A and B, working together, can complete 1/2 of the same production lot in z hours. What is the value of y in terms of x and z?

[StaceyKoprince]

I do just read the whole question from the start, but when it's a big long story like this, I don't even think about trying to solve anything until I get to the end and make sure I understand what the question is asking. First, I'm just trying to wrap my head around the story.

Then, once I understand the basic info, including the specific question, I ask myself: What would be the most efficient way to find that thing?

So, on the machine question that you posted, I would say something like this to myself, as I read:

Okay, there are two machines with some info about the machines working separately vs. together. They want y...what is y? Oh, it's how long it takes B to do 1/5 of the job...

NOTE: here, my thinking would change depending on whether this is PS or DS. From the way the question is worded, I'm guessing it's PS. I'm also guessing that the answer choices contain variable expressions, in which case I'm going to start thinking about picking real numbers to work through the problem. And since the problem has three variables, I'm going to start by thinking about what numbers would make the math "nice." I have to keep in mind any hidden constraints (eg, if I pick for x and y, that will determine z for me).

And then I would start to write down the specific info given for machine A by itself, machine B by itself, and the two together and see what I can do.

[Eddie Gutia]

Immensely immensely helpful! Thanks again.

[StaceyKoprince]

you're welcome!