Two pipes, A and B, empty into a reservoir. Pipe A can fill the reserv GMAT data sufficiency

Question: Two pipes, A and B, empty 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?

Statement 1. By itself, pipe B can fill the reservoir in 20 minutes.
Statement 2. Pipe B has a larger cross-sectional area than pipe A.

A. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are not sufficient.

Answer: A

Solution and Explanation:

Approach Solution 1:
A and B are two pipes that empty into a reservoir. By itself, Pipe A can fill the reservoir in 30 minutes. How much time will it take pipe A and pipe B to fill the reservoir?
(1) Pipe B can fill the reservoir by itself in 20 minutes. —- We know that Pipe A's work was 1/30 of the total work done because of the question. B did everything we needed, thus his job was sufficient.
(2) Pipe B has a bigger cross-sectional area than pipe A - omits to discuss B's contribution. It's possible that the water is moving either too slowly or too quickly. therefore insufficient
Correct option: A

Approach Solution 2:
(1) Three angles of a quadrilateral are 90 degrees each:
We can use the information provided in both statements to determine how long it will take for pipes A and B together to fill up the reservoir.
Statement 1 tells us that pipe B can fill the reservoir in 20 minutes by itself. This means that the rate at which pipe B fills the reservoir is 1/20 of the reservoir per minute.
Using this information and the information from the question stem that pipe A can fill the reservoir in 30 minutes, we can calculate that the rate at which pipe A fills the reservoir is 1/30 of the reservoir per minute.
When pipes A and B work together, their rates of filling the reservoir will add up. Therefore, the combined rate at which pipes A and B fill the reservoir is:
1/30 + 1/20 = 1/12
This means that pipes A and B together can fill 1/12 of the reservoir in one minute. Therefore, it will take them 12 minutes to fill up the reservoir together.
Statement 2, which tells us that pipe B has a larger cross-sectional area than pipe A, is not needed to solve the problem. The time taken to fill up the reservoir depends only on the rates at which the pipes fill the reservoir, which is given in question stem and statement 1.
Correct option: A

Approach Solution 3:
Statement 1: Let the total capacity of the reservoir be 1 unit, which can be filled by pipe A alone in 30 minutes. Therefore, in 1 minute, pipe A can fill 1/30 of the reservoir.
Similarly, pipe B can fill the reservoir alone in 20 minutes. Therefore, in 1 minute, pipe B can fill 1/20 of the reservoir.
When pipes A and B work together, they fill the reservoir at a combined rate of 1/30 + 1/20 = 1/12 of the reservoir per minute.
Let the time taken for pipes A and B to fill the reservoir together be t minutes. Therefore, in t minutes, pipes A and B together can fill (1/12) x t of the reservoir.
According to the problem statement, the combined work done by pipes A and B in time t should be equal to the capacity of the reservoir, which is 1. Therefore, we can set up an equation as follows:
(1/12) x t = 1
Solving for t, we get:
t = 12 minutes
Statement 2: The information about the larger cross-sectional area of pipe B is not sufficient to determine the time taken for pipes A and B together to fill up the reservoir. This is because the rate at which each pipe fills the reservoir depends not only on the cross-sectional area of the pipe but also on other factors such as the pressure, the velocity of the water, and the length of the pipe.
Correct option: A

“Two pipes, A and B, empty into a reservoir. Pipe A can fill the reserv GMAT data sufficiency" - is a topic of the GMAT data sufficiency section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT data sufficiency questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and two statements. By using mathematics to answer the question, the candidate must select the appropriate response among five choices which states which statement is sufficient to answer the problem. The data sufficiency section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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