## Monday, November 21, 2011

### Elisson gets it

The answer to last week's MGRE Math Beast Challenge problem was indeed (E). MGRE's explanation:

First, let’s note that choice (A) is a pretty transparent trap. Increasing by x% and then by 2x% is not equal to increasing by 3x%, since the x and 2x are percents of different numbers (2007’s and 2008’s year-end populations). Similarly, the decrease needed to return to the original percent will be a percent decrease off a third number – the population at the end of 2009. So, 3x is an obvious trap based on a serious misunderstanding of percent change.

This problem is best solved by plugging in numbers! For example, let’s make x% equal to 50% and the original (end of 2007) population equal to 100.

If x = 50,
end of 2007: 100
end of 2008: 150
end of 2009: 300
end of 2010: 100

For Peopletown’s population to have gone back to the original 2007 levels at the end of 2010, it must have decreased 66.67% in 2010. Thus, plug in 50 for x and see which answer yields 66.67 (feel free to use your calculator):

(A) 3x = 150
(B) (100 + 50)(100 + 100)/100 = 300
(C) 1 – [100/(150)(200)] = 0.996
(D) 100 – [10,000/(50)(0)] = can’t divide by zero!
(E) 100 – [1,000,000/(150)(200)] = 66.67 (any slight discrepancy is just due to rounding off repeating decimals)

The correct answer is E.

MGRE's explanation goes on at some length to demonstrate the algebra behind the problem, but that explanation ends this way: "The answer is E, of course. But almost no one can do this in the time limits allotted, which is why we strongly suggest plugging in numbers. x = 50 was a very good example, since taking 50% of any number is pretty easy."

The brute-force "plug-and-play" strategy is something we also provisionally recommend at my place of work, if the situation warrants it.

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