The paper that was pulled from the pile

Question

A class of 12 exam papers averages 70. One paper is pulled out for a re-grade, and the remaining 11 papers average 72. Solve in your head. What did the pulled paper score? Aim: under 15 seconds.

Accepted Answer

Removing one paper raised the average, so the pulled paper must have been a low one. Work in deviations from the old average of 70. After removal the 11 survivors each sit 2 points above the old average, a surplus of 11 	imes 2 = 22 points. Because the total is fixed, that surplus is exactly what the pulled paper was below the old average: 70 - 22 = 48. Slow route for contrast: totals give 12 	imes 70 - 11 	imes 72 = 840 - 792 = 48. Same answer, larger numbers. Takeaway. Removing an item shifts the average by an amount that reveals the item: "removed value = old average - (new count) 	ime…

The paper that was pulled from the pile

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