Tuesday, January 17, 2012

got another one right!

I consider myself quite capable of teaching the Quantitative, Verbal, and Analytical Writing sections of the GRE, but I still need to keep myself on my toes. That's one reason why I do the weekly Math Beast Challenges that Manhattan GRE throws us. The challenges appear on Monday; I splash them up on this blog on Tuesday (since Tuesday is the designated math day here) and offer my own answers to the questions. When the solutions to the problems appear the following week, I recopy and display them here for your edification. This way, Dear Reader, you get to see two approaches to the problem, which allows you to decide what works best for you.

As it turns out, I got last week's problem right: the answer is, in fact, (C): the quantities are equal. Here's MGRE's explanation:

We can set up and simplify two equations, one for the calories consumed and the other for cost, using variables A and B for the number of servings of Snacks A and B, respectively.

200A + 350B = 3250
20A + 35B = 325 {divided by 10}
4A + 7B = 65 {divided by 5}

$1.70A + $0.60B = $11.00
17A + 6B = 110 {multiply by 10 to eliminate decimals}

So we now have a system of two equations and two variables, which could be solved for A and B. But, even in their simplified form, these two equations have awkward coefficients that will make solving messy.

Since this is a Quantitative Comparison question, it would be smarter to “cheat off of the easy statement.” That means we plug in the 4 from Quantity B as a possible number of servings of Snack A, and see what that tells us.

We’ll plug A = 4 in to each equation.

Calories: 4(4) + 7B = 65, so 7B = 65 – 16 = 49. Therefore B = 7.
Cost: 17(4) + 6B = 110, so 6B = 110 – 68 = 42. Therefore B = 7.

We have effectively shown that A = 4 and B = 7 is the solution we would have found had we solved this system of equations ourselves.

Thus, Quantity A and Quantity B are both 4.

The correct answer is C.

I'd say that's not so different from my own approach, until we get to the next-to-final step. MGRE and I certainly agreed on the fundamental issue: this was indeed a "systems of equations" problem. Where we disagreed was in how to reach the very end. I did the typical thing, and simply solved all the algebra. MGRE, by contrast, "cheated" by plugging in data from the chart to solve for one variable. This method is arguably quicker, although I think the difference between MGRE's and my respective methods amounts to just a few seconds. On the actual test, you've got a little more than a minute to solve each math problem, so there's a bit of a time buffer there, as long as you're fast on your feet.


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