PP-PS107

[max999]

The table above shows the total sales recorded in July for the 5 salespeople at Acme Truck Sales. It was discovered that one of Cal's sales was incorrectly recorded as one of Ann's sales. After this error was corrected, Ann's total sales were still higher than Cal's total sales, and the median of the 5 sales totals was $330,000. What was the value of the incorrectly recorded sale?

name sales
Ann $450,000
Bob $360,000
Cal $190,000
Dot $210,000
Ed $680,000

(A) $30,000 (B) $48,000 (C) $90,000 (D) $120,000
answer :D

[samgaetang]

由高到低排列5筆
<incorrected sales> ------> <corrcted sales>
Ed $680,000
Ann $450,000
Bob $360,000 (median) $330,000
Dot $210,000
Cal $190,000
表示說330,000一定是因為Cal或者是Ann的銷售額變動所來的, 所以產生以下兩種可能:
(1)由Cal's sales而來
330,000-190,000=140,000
但若ann's sales減去140,000會使得Ann's total sales "Lower" than Cal's
where 450,000-140,000=310,000<330,000
與題意不合

(2)由Ann's sales而來
450,000-190,000=120,000
驗證: 190,000+120,000=310,000(Cal's sales)<330,000(Ann's sales)
因此答案為120,000

[max999]

非常謝謝samgaetang大大