PP T1 DS183.192.210

[emmaaqua]

不好意思~我知道一帖一題的版規...
可是我的問題實在太多了... 所以想說三題貼在同一帖....

192. 18939-!-item-!-187;#058&011984
Of the 75 houses in a certain community, 48 have a patio. How many of the houses in the community have a swimming pool?

(1) 38 of the houses in the community have a patio but do not have a swimming pool.

(2) The number of houses in the community that have a patio and a swimming pool is equal to the number of houses in the community that have neither a swimming pool nor a patio.

Ans:B

210. 20285-!-item-!-187;#058&012741
Is m + z > 0 ?

(1) m - 3z > 0

(2) 4z - m > 0

Ans:C

183. 18017-!-item-!-187;#058&011390
The positive integers x, y, and z are such that x is a factor of y and y is a factor of z. Is z even?

(1) xz is even.

(2) y is even.

Ans:D

請大家幫忙解答了~謝謝~!

[chris8888]

183.

列出式子
y = xa
z = yb

1. xz = even
even * even 帶入y = xa發現y必為even, 當y=even, x is even
even * odd 帶入y = xa, z必為even, 所以這條件不可能
odd * even 不用帶了, 因為z還是even
因此根據上面三個條件, 唯一會造成z = odd的已經排除, 不管x=even or odd, z都必為even

2. y is even, 帶入z = yb, 確認z is even as well.

[puja]

不好意思~我知道一帖一題的版規...
可是我的問題實在太多了... 所以想說三題貼在同一帖....

192. 18939-!-item-!-187;#058&011984
Of the 75 houses in a certain community, 48 have a patio. How many of the houses in the community have a swimming pool?

(1) 38 of the houses in the community have a patio but do not have a swimming pool.

(2) The number of houses in the community that have a patio and a swimming pool is equal to the number of houses in the community that have neither a swimming pool nor a patio.

Ans:B

[color=red]利用集合的觀念, n(AUB)=n(A)+n(B)-n(A交集B)

1) 可知缺少了neither patio nor swimming pool的資料 故不能求出有swiming pool house.------>不充分

2)令 both patio and swimming pool house=x,則 neither patio nor swimming pool =x , swimming pool house =s

75-(48+s-x)=x
s=27 --------->充分
210. 20285-!-item-!-187;#058&012741
Is m + z > 0 ?

(1) m - 3z > 0

(2) 4z - m > 0

Ans:C

這題我的理解是:

1)m-3z>0----> z<m/3 不充分

2)4z-m>0----> z>m/4 不充分

1) +2) ==> z>0 且 m/4 < z < m/3
所以 z>0且 m/4 < z < m/3 可知 m>0 ---->充分

有問題請指教~~~~ths

183. 18017-!-item-!-187;#058&011390
The positive integers x, y, and z are such that x is a factor of y and y is a factor of z. Is z even?

(1) xz is even.

(2) y is even.

Ans:D[/color]

請大家幫忙解答了~謝謝~!

[emmaaqua]

感謝chirs888及puja的熱心回覆喔~^^
解釋滴非常清楚明瞭~
謝謝~!!^^