400-1816-180
本題由chris提供
【OG20-P181-225題】
List T consists of 30 positive decimals, none of which is an integer, and the sum of the 30 decimals is S. The estimated sum of the 30 decimals, E, is defined as follows. Each decimal in T whose tenths digit is even is rounded up to the nearest integer, and each decimal in T whose tenths digit is odd is rounded down to the nearest integer; E is the sum of the resulting integers. If 1/3 of the decimals in T have a tenths digit that is even, which of the following is a possible value of E - S ?
1. -16
II. 6
III. 10
(A) 1only
(B) 1and II only
(C) 1and III only
(D) II and III only
(E) 1, II, and III
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文字解析
最優(yōu)情況
當(dāng)1/3的十分位為偶數(shù)的元素都是0.2xxx，則進(jìn)位時(shí)盈利0.8.
而剩下2/3的元素十分位為0.1xxx,則退位時(shí)虧損0.1.
E-S的差值就是0.8*10-0.1*20=6
最差情況：
當(dāng)1/3的十分位為偶數(shù)的元素都是0.8xxx，則進(jìn)位時(shí)盈利0.2
而剩下2/3的元素十分位為0.9xxx,則退位時(shí)虧損0.9
E-S的差值就是0.2*10-0.9*20=-16
可以舉兩個(gè)極端情況：（1）1.8和1.9；S=1.8*10+1.9*20=56，E=2*10+1*20=40，則E-S=-16；（2）1.2和1.1；S=1.2*10+1.1*20=34，E=2*10+1*20=40，則E-S=6
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