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题库 / Prep2007E2-DS-123
When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15 ?
(1) n - 2 is divisible by 5.
(2) t is divisible by 3.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.
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n=3a+2，t=5b+3，n*t=15ab+10b+9a+6
(1)n-2=5c,n=5c+2,5c+2=3a+2-->5c=3a-->5c=a3,a是5的倍数，9是3的倍数，所以9a是15的倍数
(2)t=3d,3d=5b+3,d=5/3b+1,因为d,b都是整数，所以b是3的倍数，10b是15d的倍数
(1)+(2), n*t=15ab+10b+9a+6除6外，都能被15整除，余数是6.
列了几种方法，看哪种能最直观地反应过来，临场考试时间太紧张，只能靠最直接的反应去解题；二利用解题的过程发现因数的规律，再有题目利用了该规律时，也能反应过来。
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