HMMT 二月 2000 · 代数 · 第 5 题

HMMT February 2000 — Algebra — Problem 5

A ja k et w as originally pri ed $100. The pri e w as redu ed b y 10% three times and in reased b y 10% four times in some order. T o the nearest en t, what w as the nal pri e?

解析

Ev ery da y Edw ard w orks, he gets of the test done. Similarly , ev ery da y Barbara 9 1 1 w orks, she gets of the test done, ev ery da y Abhina v w orks, he gets of the test 10 11 1 done, and ev ery da y Alex w orks, he gets of the test done. So, after 4 da ys (after 12 1 1 1 1 ev ery one has w ork ed on the test one da y , they ha v e ompleted + + + = 38 : 535% 9 10 11 12 of the test. After 8 da ys, they ha v e ompleted t wi e that, or 77 : 0707% of the test. After Edw ard, Barbara, and Abhina v ea h w ork one more da y , the test will b e omplete in the minim um amoun t of time, so the test will tak e 11 da ys to omplete. If the least eÆ ien t w ork ers w ork after the 8th da y , the test still tak es 11 da ys to omplete. 2 4 8 12 24 25 50 100 200