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All scientists expect the population of penguins on the 09 Jul 2006, 02:30
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All scientists expect the population of penguins on the island of Zeeberg is expected to rise by from 50,000 today to 800,000 18 years from now. Scientist A holds that the population will follow an arithmetic progression, that is that the absolute increase in population from year to year will be constant. Scientist B says that it will follow a geometric progression, which is to say that the percentage increase in population from year to year will be constant. If the two scientists are asked to predict the population of penguins in 9 years’ time, by how much will their predictions differ?

(A) 150,000 (B) 225,000 (C) 300,000 (D) 425,000 (E) none of these



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All scientists expect the population of penguins on the 09 Jul 2006, 10:45
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For AP

Tn = a + (n-1)*d
T18 = 800,000 = 50,000 + (18-1) * d
=> d = 750,000/17

For GP

Tn = a * r ^ (n-1)
T18 = 800,000 = 50,000 * r ^ (18-1)
=> r^17 = 16 => r = 16 ^ 1/17

Now calculating the 9th term for the AP and GP

For AP

T9 = a*r^8 = 50,000 * 16 ^ (8/17) ~ 50,000 * 16^(1/2) = 200,000

For GP

T9 = a + 8d = 50,000+8*(750,000/17)~ 50,000 + (750,000/2) = 420,000

The difference between to T9s

= 420,000 - 200,000 = 220,000

Hence the closest answer is 225,000.
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All scientists expect the population of penguins on the 09 Jul 2006, 15:28
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grepro


Now calculating the 9th term for the AP and GP

For GP

T9 = a*r^8 = 50,000 * 16 ^ (8/17) ~ 50,000 * 16^(1/2) = 200,000

For AP

T9 = a + 8d = 50,000+8*(750,000/17)~ 50,000 + (750,000/2) = 420,000

The difference between to T9s

= 420,000 - 200,000 = 220,000

Hence the closest answer is 225,000.
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I follow your methodology until calculating for GP
How does 16 ^ (8/17) become 16 ^ (1/2)
It must be my weakness with exponent properties coming through here...

Your thoughts please...
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All scientists expect the population of penguins on the 09 Jul 2006, 15:41
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grepro
For AP

Tn = a + (n-1)*d
T18 = 800,000 = 50,000 + (18-1) * d
=> d = 750,000/17

For GP

Tn = a * r ^ (n-1)
T18 = 800,000 = 50,000 * r ^ (18-1)
=> r^17 = 16 => r = 16 ^ 1/17

Now calculating the 9th term for the AP and GP

For AP

T9 = a*r^8 = 50,000 * 16 ^ (8/17) ~ 50,000 * 16^(1/2) = 200,000

For GP

T9 = a + 8d = 50,000+8*(750,000/17)~ 50,000 + (750,000/2) = 420,000

The difference between to T9s

= 420,000 - 200,000 = 220,000

Hence the closest answer is 225,000.
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I assume you are saying that T1 is the value now, at the beginning of the first year. Then T19=800,000

so r^18=16=4^2 and r^9=4
d=750,000/18 and 9d=375,000
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All scientists expect the population of penguins on the 09 Jul 2006, 18:14
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I thought that Geometric Progression is out of scope of GMAt. Am I wrong? Should I put it back on my "cheat-sheet"?
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All scientists expect the population of penguins on the 09 Jul 2006, 20:49
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The total terms are 19 not 18.

Using this I got 10th term (i.e after 9 years) of AP = 375,000

The 10th term for GP is = 200,000

Difference = 275,000

So answer should be E.



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