I29-172

Question

At a mountain observatory, astronomers set exposure times for two types of targets. Each faint target requires R seconds per image, and each bright target requires a shorter exposure of S seconds per image. On Night 1, the team captured 35 images using a total of 625 seconds. On Night 2, they captured 140 images using a total of 1730 seconds. On both nights, both faint and bright targets were captured.
 
Select for  R  and  S  values for R and S that are jointly consistent with the information provided. Make only two selections, one in each column.

Bunuel · Answer

Official Solution:

Night 1 average = 625/35 ≈ 17.9
 
Night 2 average = 1730/140 ≈ 12.4
 
So S must be below both averages and R must be above both. Since R > S, that narrows to R = 19 or 21, and S = 10 or 12.
 
Night 1 equation is xR + (35 - x)S = 625, where x is the number of faint images on Night 1.
 
First test R = 19. Substituting gives 19x + S(35 - x) = 625. For S = 10, 12, or 14, this does not give an integer solution for x, so R cannot be 19.
 
Now test R = 21. Substituting gives 21x + S(35 - x) = 625.
 
For S = 10, this gives x = 25, which is an integer solution.
 
For S = 12 or 14, no integer solution exists.
 
Therefore the only consistent pair is  R = 21  and  S = 10 .

Correct answer:

R  "21"

S  "10"

SRIVISHUDDHA22 · Answer

Hi Bunuel !

How did you assume R > S. No where in the question its mentioned that R> S . Could you please clarify? Thanks

Bunuel · Answer

Read carefully. The question says faint targets require  R seconds per image  and bright targets require a   shorter exposure   of  S seconds per image .

That phrase “shorter exposure” means bright targets need less time, so R (faint) must be greater than S (bright). It’s not an assumption, it’s explicitly stated in the wording.

Karym · Answer

I like the solution - it’s helpful.

ananya022001 · Answer

Since "  S must be below both averages" our option for S shouldn't include 14 right?

Bunuel · Answer

Yes, you are right. Fixed the typo. Thank you!

I29-172

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