Problem-Solving and Data Analysis practice question

Answer: 5000

Let n be the total number of boards. Line 1 contributes 0.02(0.6n) = 0.012n defective boards and Line 2 contributes 0.05(0.4n) = 0.020n defective boards, for a total of 0.032n. Setting 0.032n = 160 gives n = 5000. Check: Line 1 has 3000 boards with 60 defective; Line 2 has 2000 boards with 100 defective; 60 + 100 = 160. Common errors: adding the two percentages to get 7% and computing 160/0.07 ≈ 2286 (this ignores that each percent applies to only part of the batch); averaging the percentages to 3.5% and computing 160/0.035 ≈ 4571 (this incorrectly weights the two lines equally instead of 3:2); or applying a single rate such as 160/0.02 = 8000 or 160/0.05 = 3200 (using only one line's defect rate for the whole batch).

Common wrong answers

If you answered 2286

You added the two rates to get 7% and computed 160/0.07, but 2% applies only to the 3/5 on Line 1 and 5% only to the 2/5 on Line 2, so the combined rate is 0.012 + 0.020 = 3.2%.

If you answered 3200

You applied Line 2's 5% rate to the whole batch (160/0.05); Line 2 made only 2/5 of the boards, with the rest defective at 2%.

If you answered 4571

You averaged 2% and 5% to get 3.5% and divided 160 by 0.035; that weights the lines equally, but they split 3:2, giving a weighted rate of 3.2%.

If you answered 8000

You applied Line 1's 2% rate to the whole batch (160/0.02); only 3/5 of the boards came from Line 1, and the other 2/5 were defective at 5%.

More Problem-Solving and Data Analysis questions

• Hard
  The mean of five numbers is 12. If four of them are 8, 10, 14, and 16, what is the fifth number?
• Hard
  In a survey of 50 people, 30 like coffee, 20 like tea, and 8 like both. How many like neither?
• Hard
  A car travels at 60 mph for 2 hours, then 40 mph for 3 hours. What is its average speed for the whole trip?
• Hard
  Which statement correctly compares the standard deviations of the two sets?
• Hard
  Which statement best interprets the slope of the line of best fit?
• Hard
  How many milliliters of the 40% acid solution must the chemist add?