Multiple choice

Machine X runs at a constant rate and produces a lot consisting of 100 cans in 2 hours. How much less time would it take to produce the lot of cans if both Machines X and Y were run simultaneously? 1) Both Machines X and Y produce the same number of cans per hour. 2) It takes Machine X twice as long to produce the lot of cans as it takes Machines X and Y running simultaneously to produce the lot.

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

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

  3. Both statements (1) and (2) TOGETHER are sufficient to answer the question, but neither statement ALONE is sufficient.

  4. Each statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are not sufficient to answer the question, and additional data is required.
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let X be the rate of machine X. Statement 1 says Y = X, so combined rate is 2X. Time taken is half the original time. Statement 2 says time(X+Y) = 0.5 * time(X), which is equivalent to saying the combined rate is twice the rate of X. Both statements are sufficient to determine the time reduction.

AI explanation

Statement (1) implies Y also produces 100 cans in 2 hours (50 cans/hour), so together they take 1 hour, meaning it takes 1 hour less. Statement (2) says the combined time is half of X's alone time, so since X takes 2 hours, together they take 1 hour, yielding the exact difference of 1 hour. Each statement alone is sufficient.

Keep practicing — related questions