Multiple choice

Directions: The following question has two statements, (1) and (2). Answer the question using the following instructions: How many hours does it take 12 machines with identical production rates, running simultaneously without stopping, to fill a certain production order? (1) It takes each machine, running alone continuously, 60 hours to fill the production order. (2) It takes 10 of these machines, running simultaneously without stopping, 6 hours to fill the production order.

  1. Statement (1) alone is sufficient but statement (2) alone is not

  2. Statement (2) alone is sufficient but statement (1) alone is not

  3. Both (1) and (2) together are sufficient but none of them alone is sufficient

  4. Both independently are sufficient

  5. Both statements (1) and (2) together are not sufficient
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Statement (1) gives the rate of one machine (1/60 per hour). 12 machines together have a rate of 12/60 = 1/5 per hour, so time = 5 hours. Statement (2) says 10 machines take 6 hours, so 1 machine takes 60 hours, which is consistent with (1). Both are sufficient.

AI explanation

The total work equals the number of machines multiplied by the time taken. Statement (1) states one machine takes 60 hours, so using the formula time equals total work divided by the number of machines, the time for 12 machines is 60 divided by 12, which is 5 hours. Statement (2) states 10 machines take 6 hours, meaning the total work is 60 machine-hours; dividing this total work of 60 by the 12 machines gives 5 hours. Both statements independently provide enough data to find the required time, so both statements independently are sufficient.

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