GWD 5-21

[saikang]

Theater M has 25 rows with 27 seats in each row. How many of the seats were occupied during a certain show?

(1)During the show, there was an average (arithmetric mean) of 10 unoccupied seats per row for the front 20 rows.
(2)During the show, there was an average (arithmetc mean) of 20 unoccupied seats per row for the back 15 rows.

Answer:(E)

我的想法是, 劃一條數線, 線上有 0, 13, 20, 27 四個點, 0~20 代表 front 20 rows, 13~27 代表 back 15 rows. 而 0~20 排的座位人數為 17*20=340, 13~27 排的座位人數為 7*15=105

既然上述只是利用平均數求出來的數字, 那我為什麼不能假設 13~20排都沒有坐人?如此一來, 0~13 排坐 340人, 13~20 排坐 0人, 20~27 排坐 105人, 這樣前20排和後15排的平均數依然符合要求不是嗎? 然後 total (340+0+105)/27 就是題目的答案了, (c)可以 ?

我知道這想法有瑕疵, 但找不出來, 請解惑 ! (H) ||

[homaru]

題目問:某場秀裡面多少座位有人坐?
依照你的假設
應該是設1~20=340,11~25=105(是25排不是27排)
共20*(27-10)+15*(27-20)=340+105=445人

但是如果假設11~20排平均都坐7個人好了(7*10=70)
那1~10排被坐滿的有:340-70=270
21~25排被坐滿的有:105-70=35
1~25總共:270+70+35=375
因11~20排坐滿的情況而異....so E

[saikang]

好犀利！多謝 :P