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Joined: 11 Feb 2015
Posts: 1195
An ornithologist has studied a particular population of starlings  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 48% (02:13) correct 52% (02:21) wrong based on 134 sessions

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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

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Manish
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An ornithologist has studied a particular population of starlings  [#permalink]

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Official Solution:-

Step 1: Analyze the Question
You know that the initial population of starlings in 1890 is 256, and you know that the population increases by 400% every 10 years.

Find the size of the population of starlings in 1970.

Step 3: Approach Strategically
Although this question does not deal with money, it is useful to notice that the given facts fit the compound interest formula perfectly. The formula, as applied to money, is (Total of principal and interest) = Principal × $$(1 + r)^t$$, where r is the interest rate per time period and t is the number of time periods. In this question, the total of “principal and interest” is the final population of starlings in 1970, the “principal” is the initial population (256), the “interest rate” is the population growth rate expressed as a decimal (4.00), and t is the number of 10-year periods from 1890 to 1970 (8). Thus, you have the following:

1970 population = $$256 × (1 + 4)^8 = 256 × 5^8$$

At this point, you could do the arithmetic, but without a calculator, this approach would be time-consuming and potentially
prone to errors. Remember that when seemingly complicated arithmetic arises on the GMAT, there is often a more strategic
way to get to the answer. If you notice that 256 is a power of 2, you can use the exponent rules to make your task much
simpler:

$$256 × 5^8 = 2^8 × 5^8 = (2 × 5)^8 = 10^8 = 100,000,000$$

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Manish

Originally posted by CAMANISHPARMAR on 05 Jun 2018, 08:34.
Last edited by CAMANISHPARMAR on 30 Jun 2018, 23:37, edited 1 time in total.
Senior SC Moderator V
Joined: 22 May 2016
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An ornithologist has studied a particular population of starlings  [#permalink]

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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?

$$(256*5^8)=(2^8*5^8)=10^8=100,000,000$$

*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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Manager  S
Joined: 04 Mar 2020
Posts: 76
Re: An ornithologist has studied a particular population of starlings  [#permalink]

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Number 2 increased by 100% means twice the number 2 = 2*2
Because 100% of 2 is 2 and increasing 2 by 2 means 2+2 = 4

Number 2 increased by 200% means thrice the number 2 = 3*2
Because 200% of 2 is 4 and increasing 2 by 4 means 2+4 = 6 or 3*2

Similarly, an increase in population by 400% means every decade the population becomes 5 times the population the previous decade

Population in 1890 = $$256$$
Population in 1900 = $$256 * 5$$
Population in 1910 = $$(256*5)*5$$
.
.
Population in 1970 = $$256 * 5^8$$

$$256= 2^8$$
$$2^8 * 5^8$$
$$10^8$$

Option E Re: An ornithologist has studied a particular population of starlings   [#permalink] 20 Jun 2020, 04:24

# An ornithologist has studied a particular population of starlings  