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x is a positive integer. When x is divided by 2, 4, 6 or 8, the remainder is 1.
x is a positive integer. When x is divided by 2, 4, 6 or 8, the remainder is 1.
游客
2025-02-23
27
管理
问题
x is a positive integer. When x is divided by 2, 4, 6 or 8, the remainder is 1.
Quantity A: x
Quantity B: 24
选项
A、Quantity A is greater.
B、Quantity B is greater.
C、The two quantities are equal.
D、The relationship cannot be determined from the information given.
答案
D
解析
根据题目:x=2q+1=4p+1=6n+1=8m+1,其中q,p,n,m分别为x除以2,4,6,8后的商,得出x-1=2q=4p=6n=8m。当q,p,m≠0时,x-1是2,4,6,8的公倍数,即x-1是2,4,6,8四个数最小公倍数的倍数。又2,4,6,8的最小公倍数为24,故x-1可以为24,48,72,…,x可以为25,49,73,…。当q,p,m,n=0,x-1=0,所以x=1。故答案为D。时刻牢记,当被除数<除数时,商=0的特殊情况。
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