Multiple choice

At a large manufacturing plant, the assembly line's output speed is measured and forecast at various times of the day. At 3:00 p.m. on a certain day, was the forecast output speed exactly 120 units per hour? (1) At 12:00 noon, the forecast output speed was 105 units per hour, and at 4:00 p.m., it was forecast to be 125 units per hour. (2) The forecast output speed followed a uniform linear trend throughout the day.

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

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

  3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

  4. EACH statement ALONE is sufficient.

  5. Statements (1) and (2) TOGETHER are NOT sufficient.
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C Correct answer
Explanation

Statement 1 gives two points. Statement 2 confirms a linear trend. With a linear trend, two points define the line, allowing calculation of the value at any time. Both are needed.

AI explanation

Statement 1 provides the forecast speeds of 105 units per hour at 12:00 noon and 125 units per hour at 4:00 p.m., but without knowing the pattern of change, we cannot assume the value at 3:00 p.m. Statement 2 states the trend is uniformly linear, but provides no data points to anchor the calculation. By combining both statements, we can use linear interpolation over the four-hour interval to find the exact speed at 3:00 p.m., meaning both statements together are sufficient.

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