Multiple choice

Phoebe's factory manufactures toys for small kids. She has compiled data on the number of toys manufactured by her factory workers over the past seven days: 184, 122, 167, 120, 132, 209, 109. If she added the number of toys manufactured on the 8th day, the average for the seven days would increase by 2. What is the difference between the increased average and the number of toys manufactured on the 8th day?

  1. 14

  2. 13

  3. 11

  4. 9

  5. 7
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A Correct answer
Explanation

Let S be the sum of 7 days. Average = S/7. New average = (S+x)/8 = S/7 + 2. S/8 + x/8 = S/7 + 2. x/8 = S/56 + 2. The difference between new average and x is (S+x)/8 - x = (S+x-8x)/8 = (S-7x)/8. This simplifies to 14.

AI explanation

The wording of the question contains a contradiction. It states the average for the seven days would increase by 2 after adding the 8th day, which is mathematically impossible since the new average must cover eight days. Interpreting this as the original seven-day average increasing by 2 to form the new eight-day average, the original sum of the toys is 184 + 122 + 167 + 120 + 132 + 209 + 109 = 1043. The original average is 1043 / 7 = 149, making the new average 151. The sum of 8 days is 151 * 8 = 1208, so the 8th day's production is 1208 - 1043 = 165 toys. The difference between the increased average (151) and the 8th day (165) is 165 - 151 = 14.

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