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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除以3余2-->n=3a+2, t除以5余3-->t=5b+3
(1)n-2被5整除-->n-2=5c，因为n-2=3a，所以 n-2既能被5整除也能被3整除，则n-2能被15整除，n-2=15e，n=15e+2,所以n/15的余数是2；
(2)t被3整除-->t=3d，t拆成2个因数E和F， t/15=EF/15=E/3*F/5,余数是3
所以n除15余2，t除以15余3.继续用余数公式设n,t，n*t=(15a+2)*(15b+3)，乘开来最后只有2*3是不能被15整除的，余数是6
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