请教tt-9-12,tt-9-32

其中绿色为正确答案。。

Q32:

What is the remainder when the positive integer x is divided by 8?

(1)     When x is divided by 12, the remainder is 5.

(2)     When x is divided by 18, the remainder is 11.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

Q12:

From Leland’s gross pay of p dollars last week, t percent was deducted for taxes and then s dollars was deducted for savings.  What amount of Leland’s gross pay last week remained after these two deductions?

(1)     p - s = 244

(2)     pt = 7,552

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.

C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. EACH statement ALONE is sufficient.

E. Statements (1) and (2) TOGETHER are NOT sufficient.

恩，我觉得１２的数字确实给错了，Ｐ－Ｓ＝２４４，怎么还能减７５５２？

the remained gross pay=p(1-t)-s=p-pt-s

1+2 正好满足

第一题选c

应该是余2吧？

希望更具体一些。。。

1) X=12M+5

2) X=18N+11

结合条件1和2，可得出 2M=3N+1,由于2M是偶数，可退出N为奇数

故可设N＝2K+1,将其带入条件2，可得到 X=36K+29

这是能满足上面两个条件的X的通项，由于36不是8的倍数，故X被8除，其余数不固定。

五楼的兄弟很厉害，可是对于我这种菜鸟，那个方法比较难掌握，想半天也不见得想得出来，所以考试的时候只能用点相对容易一点的笨办法。我就先化简式再用数字代，相对来说速度也还可以（虽然笨点，比想半天也想不出来要强，比较直观)。。。

(1) ＝12m＋5 =8m + 4m +5, 所以，只用看4m＋5被8除的余数是多少，用0，1，2，3，代m 进去可得余为1或5

（2）＝18n＋11＝16n ＋ 2n ＋ 8＋3，只用看2n＋3 被8 除余数是多少，用0，1，2，3代n发现余为3，5，7，1

即使（1）（2）一起看也得不出一个确定的余数来，所以选E

真高招，我怎么没想到呢？