pp-T2-DS197

[mupeane]

197. 19016-!-item-!-187;#058&012397
The integers m and p are such that 2 < m < p and m is not a factor of p. If r is the remainder when p is divided by m, is r > 1 ?

(1) The greatest common factor of m and p is 2.

(2) The least common multiple of m and p is 30.

Ans:A

[amazingslim]

2 < m < p

(1)最大公因數=2
所以m,p為2的倍數
m=2*2,p=2*3
m=2*100,p=2*199
......
無論如何，p最少ㄧ定比m多乘ㄧ次2
所以餘數最小為2

(2)最小公倍數=30
m=5,p=6=>餘數為1
m=10,p=15=>餘數為5

[mupeane]

謝謝你喔，我懂了

[pimi]

請原諒我的白痴＞<
還是不太瞭amazingslim大大所說的"無論如何，p最少ㄧ定比m多乘ㄧ次2
所以餘數最小為2"

可否再解釋多一點呢??

[mupeane]

請原諒我的白痴＞<
還是不太瞭amazingslim大大所說的"無論如何，p最少ㄧ定比m多乘ㄧ次2
所以餘數最小為2"

可否再解釋多一點呢??

因為

(1)m跟p的最大公因數=2
所以m,p為2的倍數
又2 < m < p
無論如何，p最少ㄧ定比m多乘ㄧ次2
所以餘數至少大於2

[pimi]

感恩~