CAMANISHPARMAR wrote:
An ornithologist has studied a particular population of starlings and discovered that their population has increased by 400% every ten years starting in 1890. If the initial population in 1890 was 256 birds, how large was the population of starlings in 1970?
A) 102,400
B) 10,000,000
C) 16,777,216
D) 20,000,000
E) 100,000,000
Every 10 years, a population quintuples (see below). Take the start value, find the multiplier and the number of times it is used, and multiply. Answer choices have clues about the last step.
(1) Multiplier for "increase by 400%"
Increase by 10% = .10? (1 + .10) = 1.10
Increase by 100% = 1? (1+1)=2
Increase by 100% = *2
Increase by 400% = 4? (1 + 4) = 5
Increase by 400% = "times 5"
(2) # of times the population increases
Total years: (1970-1890) = 80
Increases every 10 years
# of increases: \(\frac{80}{10}=8\)
(3) Number by which P = 256 gets multiplied
For 8 decades we multiply P=256: \(*5*5*5*5*5*5*5*5 = 5^8\)
(4) 1970 population size
\(256*5^8=?\)
GMAT does not expect us to find the 8th power of 5, nor to multiply the result by 256
Answers B, D,and E indicate powers of 10: pairing of 2s and 5s. We have 5s. How many 2s?
\((256*5^8)=(2^8*5^8)=10^8=100,000,000\)
Answer E
*Useful to know
100% increase (over original) = twice = *2
200% increase = thrice = *3
300% increase = quadrupled = *4
400% increase = quintupled = *5
See, e.g., DmitryFarber here and here in this thread
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