请教2道毫无思路的数学题

Rainbeauty

170. 16927-!-item-!-187;#058&010946
If n and t are positive integers, what is the greatest prime factor of the product nt ?
(1) The greatest common factor of n and t is 5.
(2) The least common multiple of n and t is 105.
这个答案B 我问A怎么不可以，最大质因数就是5么~~~还有B怎么证明出来sufficient？？？
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If m, k, x, and y are positive numbers, is mx + ky > kx + my ?
(1) m > k
(2) x > y
这个毫无思路呀~~~

sdcar2010

1) The greatest COMMON factor of n and t is 5. Then n can have a prime factor of 7, while t does not. Then n*t can have a prime factor of 7, bigger than 5.

2) The least common multiple of n and t is 105. 105 = 7*5*3 = n*a = t*b.  Then n*t can only have prime factors of 7, 5, and 3. Seven would be the bigger prime factor of n*t

Rainbeauty

Thank you~~~

supertina

第二道：
1.移项   m(x-y)>k(x-y)
2.结合选项

1222093

第二道：
1.移项   m(x-y)>k(x-y)
2.结合选项

-- by 会员 supertina (2011/3/25 15:37:50)

(m-k)(x-y)>0
选C吧

mijianture

第二道：
1.移项   m(x-y)>k(x-y)
2.结合选项

-- by 会员 supertina (2011/3/25 15:37:50)

(m-k)(x-y)>0
选C吧

-- by 会员 1222093 (2011/3/25 15:52:50)

怎么好像是选D，两个都SUFFIENT额

脏兮兮

厉害！终于找到答案了。。呜呜呜！！那道105的！

fallwater

第二道：
1.移项   m(x-y)>k(x-y)
2.结合选项

-- by 会员 supertina (2011/3/25 15:37:50)

(m-k)(x-y)>0
选C吧

-- by 会员 1222093 (2011/3/25 15:52:50)

怎么好像是选D，两个都SUFFIENT额

-- by 会员 mijianture (2011/3/25 20:27:02)

应该选C。
m(x-y)>k(x-y)移项变成(m-k)(x-y)>0.要么两项同时大于零，要么同时小于0，一个条件是不够的。