扫描二维码，直接登录
题库 / Prep2007E2-DS-129
If t is a positive integer and r is the remainder when ~$t^2 + 5t + 6$~ is divided by 7, what is the value of r ?
(1) When t is divided by 7, the remainder is 6.
(2) When t2 is divided by 7, the remainder is 1.
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.
还没有题目讲解（毕出老师会陆续发布对官方考题的解读，请保持关注）。
t^2+5t+6=(t+2)(t+3)
(1) 设t=7x+6（x为倍数）(t+2)(t+3)=(7x+8)(7x+9)=49x^2+49x+63x+72，前4项都是7的倍数，72不是7的倍数，余数为2，所以整个式子余数为2，充分。
(2) 设t^2=7x+1（x为倍数）t=根号7x+1 t^2+5t+6=7x+1+5根号7x+1+6=7x+7+5根号7x+1，前2项都是7的倍数，但5根号7x+1无法确定除以7以后的余数，不充分。
登录 或 注册 后可以参加讨论