## 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)