Q5:

If k, m, and t are positive integers and + = , do t and 12 have a common factor greater than 1 ?

(1) k is a multiple of 3.

(2) m is a multiple of 3.

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.

Answer: A

k/6+m/4=t/12

==>

2k+3m=t

12的质因数有2和3。要想有公因数至少得有公质因数。所以要证明t与12是否有公因数只要证明t是否是2或者3的倍数

(1)k是3的倍数：充分。设k=3n 则t=2k+3m=3(2n+m)是3的倍数 成立

(2)m是3的倍数：不充分。比方说m=3, k=2 t=2k+3m=13与12互质

所以原题选A

p.s若把(2)改成“m是偶数”则同样可以成立