GMAT Prep Story Problem: Make It Real
In the past, we’ve talked about making story problems real. In other words, when the test gives you a story problem, don’t start making tables and writing equations and figuring out the algebraic solution. Rather, do what you would do in the real world if someone asked you this question: a back-of-the-envelope calculation (involving some math, sure, but not multiple equations with variables).
If you haven’t yet read the article linked in the last paragraph, go do that first. Learn how to use this method, then come back here and test your new skills on the problem below.
This is a GMATPrep® problem from the free exams. Give yourself about 2 minutes. Go!
* “Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?
“(1) Machines X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone, does.
“(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does.”
You work in a factory. Your boss just came up to you and asked you this question. What do you do?
In the real world, you’d never whip out a piece of paper and start writing equations. Instead, you’d do something like this:
I need to figure out the difference between how long it takes X alone and how long it takes Y alone.
Okay, statement (1) gives me some info. Hmm, so if machine X takes 1 hour to do the job by itself, then the two machines together would take two-thirds…let’s see, that’s 40 minutes…
Wait, that number is annoying. Let’s say machine X takes 3 hours to do the job alone, so the two machines take 2 hours to do it together.
What next? Oh, right, how long does Y take? If they can do it together in 2 hours, and X takes 3 hours to do the job by itself, then X is doing 2/3 of the job in just 2 hours. So Y has to do the other 1/3 of the job in 2 hours.
If Y does 1/3 of the job in 2 hours, it can do the whole job in 6 hours.
6 hours for Y – 3 hours for X = 3 hours
Now, if this had been a Problem Solving question where you could use Smart Numbers, you’d pretty much be done. But it’s data sufficiency. Could you pick different numbers that would still work but give a different answer?
Sure. Double everything. If X takes 6 hours alone, then the two machines would take 4 hours together. Machine X would still do 2/3 of the job in that time, so Machine Y would still do 1/3, and therefore Machine Y could do the whole job in 12 hours. (You don’t, of course, have to take the calculation this far. Stop when you know that the calculation can be done.)
Statement (1) is not sufficient. Cross off answers (A) and (D).
Try the same process for statement (2).
Whenever you’re testing cases (using real numbers to see how the scenario would play out), try to re-use the numbers that you already used for the first statement, if possible.
Case 1: X = 3 hours alone, Y = 6 hours alone
Can I use this for statement (2)? Definitely! It actually says that Y takes twice the time of X, so this works perfectly! I already know that these numbers will give one answer, and then…
Case 2: X = 6 hours alone, Y = 12 hours alone
…this one also fits but gives a different answer. (Note: If you hadn’t completed the math during statement (1), you’d need to complete it now to see that when X = 6, Y = 12.)
Great! Statement (2) is not sufficient either.
Cross off answer (B). Now, you can revel in the beauty of trying the same numbers for both statements: you’ve already evaluated the two statements together as well! Even when used together, the two statements yield multiple possible answers to the question, so none of the given information is sufficient to answer the question.
The correct answer is (E).
Key Takeaways: Make Stories Real
(1) Put yourself in the problem. If someone really asked you to figure out this scenario as part of your job, you wouldn’t whip out a piece of paper and start jotting down equations. You’d plug in some real numbers and logic it out.
(2) Some problems allow for multiple possible scenarios—Data Sufficiency problems in general as well as Problem Solving “must be true” questions. When you get one of these, test different cases to see whether you can get contradictory answers. If so, that statement is not sufficient.
(3) When testing cases for the second statement, think about what you tried for the first statement. Whenever possible, re-use the same numbers (check to ensure that the numbers are allowed by the second statement!). This way, if you eventually have to test the two statements together, some of your work is already done for you.
* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.
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