PP- DS- T1Q70

[小花]

70. 6067-!-item-!-187;#058&004849
Is the integer x divisible by 6 ?

(1) x + 3 is divisible by 3.

(2) x + 3 is an odd number.


ANS:C

各位有快速解法嗎
我用土法煉鋼 一個個數字慢慢代
又慢又容易錯

[chris8888]

70. 6067-!-item-!-187;#058&004849
Is the integer x divisible by 6 ?

(1) x + 3 is divisible by 3.

x + 3 = 3a
x = 3a -3
x = 3(a-1)
if a = 1, x = 0 (is divisible by 6)
if a = 2, x = 3 (is not divisible by 6)
if a = 3, x = 6 (is divisible by 6)
if a = 4, x = 9 (is not divisible by 6)

(2) x + 3 is an odd number.
if x = 2, x+3=5 odd number, 2 is not divisible by 6

(1)+(2),
x = 3(a-1) and x+3 is odd number
a = 1, x = 0, 0+3=3 (x+3 is odd but x is not divisible by 6)
a = 2, x = 3, 3+3=6 (x+3 is not odd)
a = 3, x = 6, 6+3=9(x+3 is odd and x is divisible by 6)
a = 4, x = 9, 9+3=12(x+3 is not odd)
a = -1, x = -6, -6+3=-3(x+3 is odd and x is divisible by 6)

Answer 應該是 E, 除非限定x > 0, 那就會是C


ANS:C

各位有快速解法嗎
我用土法煉鋼 一個個數字慢慢代
又慢又容易錯

[小花]

(2) x + 3 is an odd number
我認為他給的條件是告訴我們X是偶數
(偶+奇)=奇
(奇+奇)=偶
(偶+偶)=偶

(1)(2)合起來看
(1)x = 3(a-1) =>3是X的因數
(2)X是偶數
故C

[puja]

(2) x + 3 is an odd number
問認為他給的條件是告訴我們X是偶數
(偶+奇)=奇
(奇+奇)=偶
(偶+偶)=偶

(1)(2)合起來看
(1)x = 3(a-1) =>3是X的因數
(2)X是偶數
故C

但若x=0 則 x+3=3不能為6整除,故還是 E比較合理~~~ 投 E一票!!

[mupeane]

由(1)，x+3是3的倍數
由(2)，條件不足

so由(1)+(2)
when x+3=3, 不可被6整除
when x+3=9,不可被6整除
以此類推

[小花]

(2) x + 3 is an odd number
問認為他給的條件是告訴我們X是偶數
(偶+奇)=奇
(奇+奇)=偶
(偶+偶)=偶

(1)(2)合起來看
(1)x = 3(a-1) =>3是X的因數
(2)X是偶數
故C

但若x=0 則 x+3=3不能為6整除,故還是 E比較合理~~~ 投 E一票!!

謝謝puja加入討論的行列
我剛剛檢查PP給的答案 答案的確是C
0好像不是偶數