Directions for question : The given problem contains a question and two statements giving certain data. You have to select the correct answer from (a) to (e) depending on the sufficiency of the data given in the statements to answer the question.Two pipes A and B emptied into a reservoir; pipe A can fill the reservoir in 30 minutes by itself. How long will it take for pipe A and pipe B together to fill up the reservoir?I. By itself, pipe B can fill up the reservoir in 20 minutesII. Pipe B has a larger cross - sectional area than pipe A.radio_button_uncheckedIf statement I alone is sufficient to determine the answer to the question.radio_button_uncheckedIf statement II alone is sufficient to determine the answer to the question.radio_button_uncheckedIf both I and II together are sufficient, but neither of the statements alone is sufficient to determine the answer to the question.radio_button_uncheckedIf either of the statements I or II alone is sufficient to determine the answer to the question.radio_button_uncheckedIf statements I and II together are not sufficient to determine the answer to the question.
Question
Directions for question : The given problem contains a question and two statements giving certain data. You have to select the correct answer from (a) to (e) depending on the sufficiency of the data given in the statements to answer the question.Two pipes A and B emptied into a reservoir; pipe A can fill the reservoir in 30 minutes by itself. How long will it take for pipe A and pipe B together to fill up the reservoir?I. By itself, pipe B can fill up the reservoir in 20 minutesII. Pipe B has a larger cross - sectional area than pipe A.radio_button_uncheckedIf statement I alone is sufficient to determine the answer to the question.radio_button_uncheckedIf statement II alone is sufficient to determine the answer to the question.radio_button_uncheckedIf both I and II together are sufficient, but neither of the statements alone is sufficient to determine the answer to the question.radio_button_uncheckedIf either of the statements I or II alone is sufficient to determine the answer to the question.radio_button_uncheckedIf statements I and II together are not sufficient to determine the answer to the question.
Solution
The answer is "If statement I alone is sufficient to determine the answer to the question."
Here's why:
The rate at which a pipe can fill a reservoir is inversely proportional to the time it takes to fill the reservoir. Therefore, if we know the time it takes for each pipe to fill the reservoir individually, we can determine how long it will take for both pipes to fill the reservoir together.
From statement I, we know that pipe B can fill the reservoir in 20 minutes. Therefore, the rate at which pipe B fills the reservoir is 1/20 reservoirs per minute.
From the question, we know that pipe A can fill the reservoir in 30 minutes. Therefore, the rate at which pipe A fills the reservoir is 1/30 reservoirs per minute.
When both pipes are filling the reservoir together, their rates add up. Therefore, the combined rate of pipes A and B is 1/20 + 1/30 = 1/12 reservoirs per minute.
Therefore, it will take 12 minutes for both pipes to fill the reservoir together.
Statement II, which tells us that pipe B has a larger cross-sectional area than pipe A, does not provide any additional useful information. The rate at which a pipe can fill a reservoir depends not only on its cross-sectional area, but also on other factors such as the pressure of the water and the height of the reservoir. Without knowing these other factors, we cannot determine the rate at which pipe B fills the reservoir from its cross-sectional area alone. Therefore, statement II alone is not sufficient to determine the answer to the question.
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