In the third century BC, Greek mathematician and astronomer Eratosthenes calculated the circumference of the Earth to be 252,000 stadia. The stadion (plural: stadia) was a unit of length used in ancient Greece and the value of 1 stadion in terms of later units of length has been the subject of much debate. One belief is that 1 stadion is equivalent to 157.5 metres while another is that 1 stadion equals 185 metres. If the circumference of the Earth is now known to be 24,902 miles (where 1 mile is approximately 1.61 kilometres), depending upon the chosen equivalent measure of a stadion, the error in Erastothenes calculation is the closest toa)1% or 16%b)15% or 75%c)84% or 99%d)523% or 631%e)98896% or 116181%Correct answer is option 'A'. Can you explain this answer?

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In the third century BC, Greek mathematician and astronomer Eratosthenes calculated the circumference of the Earth to be 252,000 stadia. The stadion (plural: stadia) was a unit of length used in ancient Greece and the value of 1 stadion in terms of later units of length has been the subject of much debate. One belief is that 1 stadion is equivalent to 157.5 metres while another is that 1 stadion equals 185 metres. If the circumference of the Earth is now known to be 24,902 miles (where 1 mile is approximately 1.61 kilometres), depending upon the chosen equivalent measure of a stadion, the error in Erastothenes’ calculation is the closest to

a)
1% or 16%
b)
15% or 75%
c)
84% or 99%
d)
523% or 631%
e)
98896% or 116181%

Correct answer is option 'A'. Can you explain this answer?

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In the third century BC, Greek mathematician and astronomer Eratosthen...

Given:

Calculated circumference of Earth = 252,000 stadia
- 1 stadion = 157.5 meters or 185 meters
Actual circumference of Earth = 24,902 miles
- 1 mile = 1.61 kilometer approx.

To Find: % error in Erastothenes’ calculation

Approach:

We’ll do the calculation for each of the 2 possible conversions of 1 stadion into meters.

Working out:

Calculating % Error for 1 stadion = 157.5 meters
- So, the Calculated circumference of Earth = 252,000*157.5 meters

252*100 miles approx.
= 25200 miles approx

The Actual circumference of Earth = 24,902 miles = 24,900 miles approx.

(Looking at the answer choices, we’ll already know that the answer will be Option A, but still for the sake of completeness of the solution, we’ll also show below the calculation of % Error for the other possible value of 1 stadion)

Calculating % Error for 1 stadion = 185 meters
- So, the Calculated circumference of Earth = 252,000*185 meters

63*460 miles approx
The Actual circumference of Earth = 24,902 miles = 24,900 miles approx

Evaluating the given answer choices
- Thus, depending on which conversion of stadion into meters is chosen, the % error in Erastothenes’ calculation is either about 1% or about 16%

Looking at the answer choices, we see that the correct answer is Option A

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In the third century BC, Greek mathematician and astronomer Eratosthenes calculated the circumference of the Earth to be 252,000 stadia. The stadion (plural: stadia) was a unit of length used in ancient Greece and the value of 1 stadion in terms of later units of length has been the subject of much debate. One belief is that 1 stadion is equivalent to 157.5 metres while another is that 1 stadion equals 185 metres. If the circumference of the Earth is now known to be 24,902 miles (where 1 mile is approximately 1.61 kilometres), depending upon the chosen equivalent measure of a stadion, the error in Erastothenes’ calculation is the closest toa)1% or 16%b)15% or 75%c)84% or 99%d)523% or 631%e)98896% or 116181%Correct answer is option 'A'. Can you explain this answer? for GMAT 2024 is part of GMAT preparation. The Question and answers have been prepared according to the GMAT exam syllabus. Information about In the third century BC, Greek mathematician and astronomer Eratosthenes calculated the circumference of the Earth to be 252,000 stadia. The stadion (plural: stadia) was a unit of length used in ancient Greece and the value of 1 stadion in terms of later units of length has been the subject of much debate. One belief is that 1 stadion is equivalent to 157.5 metres while another is that 1 stadion equals 185 metres. If the circumference of the Earth is now known to be 24,902 miles (where 1 mile is approximately 1.61 kilometres), depending upon the chosen equivalent measure of a stadion, the error in Erastothenes’ calculation is the closest toa)1% or 16%b)15% or 75%c)84% or 99%d)523% or 631%e)98896% or 116181%Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for GMAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In the third century BC, Greek mathematician and astronomer Eratosthenes calculated the circumference of the Earth to be 252,000 stadia. The stadion (plural: stadia) was a unit of length used in ancient Greece and the value of 1 stadion in terms of later units of length has been the subject of much debate. One belief is that 1 stadion is equivalent to 157.5 metres while another is that 1 stadion equals 185 metres. If the circumference of the Earth is now known to be 24,902 miles (where 1 mile is approximately 1.61 kilometres), depending upon the chosen equivalent measure of a stadion, the error in Erastothenes’ calculation is the closest toa)1% or 16%b)15% or 75%c)84% or 99%d)523% or 631%e)98896% or 116181%Correct answer is option 'A'. Can you explain this answer?.

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