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03 Jun 2020, 09:14
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
53% (03:23) correct
47%
(03:16)
wrong
based on 64
sessions
History
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Not Attempted Yet
For every x celestial objects of the Sunny Way galaxy that can be seen from the Earth, there are x^3 – x celestial objects of the galaxy that cannot be seen from the Earth. In the years of research done on the Sunny Way galaxy, scientists have been able to see only 93 planets in the galaxy. These planets were seen to have an average of 7 satellites per planet. It is also known that the ratio of the number of stars in the galaxy that are seen from the Earth to the number of satellites in the galaxy that are seen from the Earth is 2600:1 Assuming the same ratios are followed for the invisible celestial objects, which of the following is closest to the number of celestial objects in the Sunny Way galaxy?
A. \(3 * 10^{12}\)
B. \(2 * 10^{16}\)
C. \(5 * 10^{18}\)
D. \(5 * 10^{21}\)
E. \(7 * 10^{23}\)
Are You Up For the Challenge: 700 Level Questions
A. \(3 * 10^{12}\)
B. \(2 * 10^{16}\)
C. \(5 * 10^{18}\)
D. \(5 * 10^{21}\)
E. \(7 * 10^{23}\)
Are You Up For the Challenge: 700 Level Questions
03 Jun 2020, 09:43
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Number of observable celestial objects of the Sunny Way galaxy, x \(= 2600*93*7\) ≈ \(2500*100*8\) ≈ \(2*10^6\)
The number of celestial objects in the Sunny Way galaxy \(= x^3-x +x = x^3 = (2*10^6)^3 = 8*10^{18}\) (Closest to C)
The number of celestial objects in the Sunny Way galaxy \(= x^3-x +x = x^3 = (2*10^6)^3 = 8*10^{18}\) (Closest to C)
Bunuel
06 Jun 2020, 00:31
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IMO C
# of celestial objects; x : # of stars. + # of satellites + # of planets
=2600*93*7 + 93*7 +93
= 93*(2600*7 + 7 +1)
# of celestial objects = \((# of celestial objects) ^3\)
= \(93*(2600*7 + 3)^3\)
~ 4 * \(10^8\)
# of celestial objects; x : # of stars. + # of satellites + # of planets
=2600*93*7 + 93*7 +93
= 93*(2600*7 + 7 +1)
# of celestial objects = \((# of celestial objects) ^3\)
= \(93*(2600*7 + 3)^3\)
~ 4 * \(10^8\)
