GWD 18-05

[yvetteytseng]

A department manager distributed a number of pens, pencils, and pads among the staff in the department, with each staff member receiving x pens, y pencils, and z pads. How many staff members were in the department ?
(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2 : 3 : 4, respectively.
(2) The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
為什麼我覺得答案是c阿?
明明加起來可以解出9個員工阿,可是答案是E
誰可以救我阿?

[Winni]

這題跟天山4 Q5一模一樣喔
兩條件合併會有2組以上答案
若每人拿2隻pen,3隻pencil,4個pad -->則共有9個stuff
若每人拿6隻pen,9隻pencil,12個pad -->則共有3個stuff
若每人拿18隻pen,27隻pencil,36個pad -->則只有1個stuff (不知道這個算不算）
所以合併後依然不充分
只能選E

[mcpopcorn2001]

選e的原因是不是因為b 給的18,27,36並不一定全部"發完"
所以和併也不充份?

[vantreal]

選e的原因是不是因為b 給的18,27,36並不一定全部"發完"
所以和併也不充份?

應該不是哦, 是全部都有發完了.
我的方法是用比例下去算.

(1) The numbers of pens, pencils, and pads that each staff member received were in the ratio 2 : 3 : 4, respectively.
-> x:y:z = 2:3:4 (insufficient)
因為不知道實際物品的數量.

(2) The manager distributed a total of 18 pens, 27 pencils, and 36 pads.
-> (insufficient)
只能知道全部東西發完, 發給誰又發給誰多少無從知道.

now combine (1) and (2)

from (1) 的比例,
設 x= 2a, y=3a, z=4a
2a + 3a + 4a = each staff member 拿到的pen, pencil and pad.
如果有b個staff,
total number: b(2a +3a+4a) 的pen, pencil and pad.

from (2)
total number: pen + pencil + pad = 18 + 27 +36

(1) + (2)
b(2a +3a+4a) = 18 + 27 +36 = 9 (2+3+4)
b x (9a) = 9 (2+3+4)
b x a = 9
所以就像Winni說有3種組合
b=1, a=9
b=3, a=3
b=9, a=1

希望我的解答不會太亂

[chris8888]

上面的大大寫的很複雜,

我是這樣看的,

請把
3 |18, 27, 36
　3 | 6, 9, 12
　　　2, 3, 4 <== 有沒有發現當比例是2:3:4時候, 旁邊的公因素有3^1 or 3^2, 所以你知道(1)的比例關係, 但卻其實有兩種可能的員工人數, insufficient, 解答完畢