48. 30% of paintings were by Picasso, 25% by Renoir. If 24 were Picasso's, how many were Renoir's?
Answer: A
Renoir's paintings total 20.
Given that 30% of the paintings were by Picasso and that amounted to 24 paintings, we can determine the total number of paintings. If 30% is equal to 24, then 100% corresponds to 80 paintings. Subsequently, 25% of these total paintings represents Renoir's contributions, which amounts to 20 paintings.
A) 20
This option is correct as it directly reflects the calculation of 25% of the total number of paintings. With 80 paintings in total, 25% results in 20, accurately representing the number of Renoir's works.
B) 18
Option B is incorrect because it underestimates the number of Renoir's paintings. If 25% of the total is calculated based on the correct total of 80, the result is 20, thus 18 does not align with the percentage calculation.
C) 12
This option is also incorrect as it significantly misrepresents the number of Renoir's paintings. With 25% of 80 being 20, 12 does not reflect the accurate calculation and thus is not a valid answer.
D) 6
Option D is incorrect for similar reasons, as it drastically undercounts the number of Renoir's paintings. The calculation based on 25% of the total 80 yields 20, making 6 an implausible figure in this context.
Conclusion
The definitive correct answer is 20, as it correctly represents the percentage of Renoir's paintings out of the total calculated. All other options fail to align with the mathematical derivation based on the total number of paintings, emphasizing the importance of accurate percentage calculations.