For every x celestial objects of the Sunny Way galaxy that can be seen

Question

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

nick1816 · Answer

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)

NitishJain · Answer

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

Gemmie · Answer

93 planets
93 * 7 sattelites
93 * 7 * 2600 stars that can be seen
 (93 * 7 * 2600)^3  celestial objects (can be seen + cannot be seen)

93 * 7 * 2600 \approx{90 * 8 * 25 * 100} \approx{90 * 200 * 100} \approx{18 * 10^5}

(93 * 7 * 2600)^3 \approx{(18 * 10^5)^3} \approx{(2 * 10^6)^3} \approx{8 * 10^{18}}

=> Closest to  5 * 10^18

For every x celestial objects of the Sunny Way galaxy that can be seen

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GMAT Problem Solving (PS) Questions

For every x celestial objects of the Sunny Way galaxy that can be seen

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