GWD4-31

[Emilyh]

Q31
The numbers x and y are three-digit positive integers, and x + y is a four-digit integer. The tens digit of x equals 7 and the tens digit of y equals 5. If x < y, which of the following must be true?


I. The units digit(個位數) of x + y is greater than the units digit of either x or y.
II. The tens digit of x + y equals 2.
III. The hundreds digit of y is at least 5.


A. II only
B. III only
C. I and II
D. I and III
E. II and III

Ans:B

麻煩可以講解這一題嗎?

感激!!

[FrankChang]

I.個位數和大於x或y,
1+2="3">2>1
7+4=1"1"<4<7
所以I.是未必
II.x的十位數=7,y的十位數等於5,
但是我們不知道x+y個位數相加是否會造成進位,
所以II.也未必
III.x+y會到達千位數,十位數相加確定會讓百位+1,
若y的百位為5,x的百位可以為4,加上十位進位可以產生出千位.
若y的百位為4,x的百位必須為5,加上十位進位可以產生出千位.
但是不符合y>x,所以y的百位最小必須為5.
若問為什麼x百位可以設為4或5,因為要求最小的y百位,
x百位我們就儘量設大,只要不違反條件.