A pipe company produces an average of 420 pipes per day for 6 days and

Official Explanation

The problem poses an initial series of numbers for a 10-day period of production. For the first 6 days, the company produced 420 pipes per day and for the final 4 days, the company produced x pipes per day. Over the entire 10-day period, the company produced 450 pipes per day. The first task is to solve for x.

Use the over-under average shortcut. For each of the first 6 days, the company produced only 420 pipes per day, 30 pipes per day less than the 10-day average of 450 pipes per day. Over the 6 days, then, the company was “under” by (6)(30) = 180 pipes.

In order to hit the average of 450 for the entire period, the company has to “overproduce” 180 pipes during the subsequent 4-day period. Spread those 180 pipes over 4 days: 180 / 4 = 45 pipes per day. This is 45 pipes per day over the average, so the company produced 450 + 45 = 495 pipes per day during the final 4-day period.

Next, the question stem changes the scenario: If the company had instead produced 480 pipes per day during the final 4-day period (and still produced 420 per day in the first 6 days), then what would the new overall average be for the entire 10-day period?

You can use the average formula to solve for the exact average—but don’t do all that math! There’s a shortcut.

The company produced 420 pipes per day for 6 days and 480 pipes per day for 4 days. If the two time periods had been 5 days each, then the overall average would be 450 (exactly halfway in between 420 and 480). The company actually produced 420 pipes per day for 6 days, though, not 5, so the overall overage must be less than 450. Only one answer, 444, is less than 450, so it must be the correct answer.

Column 1: The correct answer is (E).
Column 2: The correct answer is (A).