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by shankar.ashwin » Tue Nov 15, 2011 4:19 pm
You're looking at a number lesser than 100%, so you can eliminate A,B and C

Now just substitute easy numbers, Let population = 100, 1st year increase =10% and 2nd yr increase = 20%

So after 2 years 100 becomes (110+122) = 132.

132 becomes 100 again, or (100/132) * 100 = 75.75%

Sub x = 10 and 2x = 20 in D and E, only E gives 75.75. E IMO

You can also use algebra.

Let population = P

After 1 yr population = P (100 + X)/100
After 2 yrs = P (100 + X)/100 * (100+2X)/100 = P (100+X) (100+2X)/10000

Now let decrease = Y%

P (100+X) (100+2X)/10000 * (100-Y)/100 = P (given 2007=2010)

(100+X) (100+2X) (100-Y)/1000000 = 1

100 - Y = 1000000/(100+X)(100+2X)

Y = 100 - 1000000/(100+X)(100+2X)
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by GmatMathPro » Tue Nov 15, 2011 4:21 pm
Let P=population at the end of 2007
population at the end of 2008=P(100+x)/100
population at the end of 2009=P[(100+x)/100][(100+2x)/100]
Population at the end of 2010=P[(100+x)/100][(100+2x)/100][(100-y)/100]

We also know that the population at the end of 2010 is equal to population at the end of 2007, so:

P[(100+x)/100][(100+2x)/100][(100-y)/100]=P

[(100+x)/100][(100+2x)/100][(100-y)/100]=1 (Divide both sides by P)

(100-y)/100 = [100/(100+x)][100/(100+2x)] (Multiply both sides by the reciprocals of the first two terms.

(100-y)/100=10,000/[(100+x)(100+2x)] (Simplify the right side)

100-y=1,000,000/[(100+x)(100+2x)] (Multiply both sides by 100)

y=100-1,000,000/[(100+x)(100+2x)] (solve for y)

Ans: E

The key is probably just making sure you know how to handle percentage increases and decreases when they deal with abstract terms, like 'x', rather than real numbers. If you don't see it, you can probably convince yourself that multiplying a quantity by (100+x)/100 is the same as increasing it by x% by trying a few simple examples.
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by GMATGuruNY » Tue Nov 15, 2011 6:25 pm
To make the math easy, plug in x=100.
Let the starting population = 100.
Starting population increased by 100% = 100+100 = 200.
New population increased by 200% = 200+400 = 600.
Percent decrease from 600 to 100 = (600-100)/600 * 100 = 500/6. This is our target.

Now we plug x=100 into the answers to see which yields our target of 500/6.

Only answer choice E works:
100 - (1,000,000) / (100+100)*(100+200) = 100 - 1,000,000/60,000 = 100 -100/6 = 500/6.

The correct answer is E.
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