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28 Feb 2025, 01:30
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
58% (02:03) correct
42%
(02:35)
wrong
based on 158
sessions
History
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Time
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Not Attempted Yet
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
A) 102,400
B) 10,000,000
C) 16,777,216
D) 20,000,000
E) 100,000,000
28 Feb 2025, 01:37
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Population increased by 400% means it became 5X
From 1890 to 1970, it must have had 8 iterations
Population = 256 * 5^8 = 10^8
From 1890 to 1970, it must have had 8 iterations
Population = 256 * 5^8 = 10^8
Bunuel
05 Apr 2025, 01:30
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Bunuel
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.
Step 2: State the Task
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:
\(256 × 5^8 = 2^8 × 5^8 = (2 × 5)^8 = 10^8 = 100,000,000\)
The correct answer is (E).
