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13 Mar 2026, 07:07
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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:
43% (02:30) correct
57%
(02:03)
wrong
based on 46
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Not Attempted Yet
In a certain part of the universe, p percent of all galaxies contain at least one solar system.
p percent of those solar systems contain at least one planet.
p percent of those planets are livable.
p percent of those livable planets contain intelligent life.
On p percent of those planets with intelligent life, beings have been to outer space.
Galaxies that contain planets from which beings have been to outer space account for what percent of all galaxies?
A. p^5 / 10^4 percent
B. p^5 / 10^6 percent
C. p^5 / 10^8 percent
D. p^5 / 10^10 percent
E. p^5 / 10^12 percent
p percent of those solar systems contain at least one planet.
p percent of those planets are livable.
p percent of those livable planets contain intelligent life.
On p percent of those planets with intelligent life, beings have been to outer space.
Galaxies that contain planets from which beings have been to outer space account for what percent of all galaxies?
A. p^5 / 10^4 percent
B. p^5 / 10^6 percent
C. p^5 / 10^8 percent
D. p^5 / 10^10 percent
E. p^5 / 10^12 percent
18 Mar 2026, 11:35
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kevincan
Let there be \(g\) galaxies
\(\frac{p}{100}*g = ss \)
\(\frac{p}{100}*\frac{p}{100}*g\) = At least one planet
{\(\frac{p}{100}\)}\(^3\)*g= Livable
{\(\frac{p}{100}\)}\(^4\)*g=IL
{\(\frac{p}{100}\)}\(^5\)*g= outer Space
Required \(\%\) = {\(\frac{p}{100 }\)}\(^5\)* \(\frac{g}{g}\) *\(100 \)
\( =\frac{p^5}{10^8}\) Percent.
Ans C
Hope it helped
19 Mar 2026, 00:59
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Let's walk through this step by step.
Key Idea: every time we say "p percent of something," we are multiplying by p/100.
We do this 5 times in a row:
1. p% of all galaxies have solar systems
2. p% of those have planets
3. p% of those have life-possible planets
4. p% of those have intelligent life
5. p% of those have sent a spaceship
Each step multiplies by p/100. So after 5 steps, the fraction of all galaxies that have sent a spaceship is:
(p/100) × (p/100) × (p/100) × (p/100) × (p/100) = p^5 / 100^5 = p^5 / 10^10
Now here's the crucial part that trips people up: p^5 / 10^10 is a fraction (a decimal), NOT a percentage yet. The question asks "what PERCENT," so we need to convert this fraction into a percentage by multiplying by 100.
p^5 / 10^10 × 100 = p^5 / 10^8
So the answer is p^5 / 10^8 %, which is choice C.
Quick check with easy numbers: Let p = 100 (meaning 100% at every step — every galaxy qualifies at each stage). Then 100% of all galaxies should have sent a spaceship. Plugging in: 100^5 / 10^8 = 10^10 / 10^8 = 100%. That checks out!
The common mistake is stopping at p^5 / 10^10 and picking choice D, forgetting that the question asks for a percent, not a plain fraction.
Answer: C
Key Idea: every time we say "p percent of something," we are multiplying by p/100.
We do this 5 times in a row:
1. p% of all galaxies have solar systems
2. p% of those have planets
3. p% of those have life-possible planets
4. p% of those have intelligent life
5. p% of those have sent a spaceship
Each step multiplies by p/100. So after 5 steps, the fraction of all galaxies that have sent a spaceship is:
(p/100) × (p/100) × (p/100) × (p/100) × (p/100) = p^5 / 100^5 = p^5 / 10^10
Now here's the crucial part that trips people up: p^5 / 10^10 is a fraction (a decimal), NOT a percentage yet. The question asks "what PERCENT," so we need to convert this fraction into a percentage by multiplying by 100.
p^5 / 10^10 × 100 = p^5 / 10^8
So the answer is p^5 / 10^8 %, which is choice C.
Quick check with easy numbers: Let p = 100 (meaning 100% at every step — every galaxy qualifies at each stage). Then 100% of all galaxies should have sent a spaceship. Plugging in: 100^5 / 10^8 = 10^10 / 10^8 = 100%. That checks out!
The common mistake is stopping at p^5 / 10^10 and picking choice D, forgetting that the question asks for a percent, not a plain fraction.
Answer: C
