提问3道PREP数学，请大牛进！！

Lyssazhao · 发表于 2011-3-6 02:11:23

1/ Three grades of milk are 1%,2%, and 3% fat by volume, if x gallons of the 1% grade, y gallons of the 2% grade, z gallons of 3% grade are mixed together to give x+y+z gallons of a 1.5% grade, what's x in terms of y and z?

(1) y+3z (2) y+z/4 (3) 2y+3z (4) 3y+z (5) 3y+4.5z

2/ A certain stock exchange designates each stock with a one-, two-, or three-letter code,where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order consistute a different code, how many different stocks is it possible to uniquely designate with these codes?

(1) 2951 (2) 8125 (3) 15600 (4) 16302 (5) 18278

3/ The positive integer 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.

正确答案：D

sdcar2010 · 发表于 2011-3-6 02:28:20

1/ Three grades of milk are 1%,2%, and 3% fat by volume, if x gallons of the 1% grade, y gallons of the 2% grade, z gallons of 3% grade are mixed together to give x+y+z gallons of a 1.5% grade, what's x in terms of y and z?

(1) y+3z (2) y+z/4 (3) 2y+3z (4) 3y+z (5) 3y+4.5z

1*x + 2*y + 3*z = 1.5*(x + y + z)
0.5*y + 1.5*z = 0.5*x
y + 3*z = x

sdcar2010 · 发表于 2011-3-6 02:30:11

2/ A certain stock exchange designates each stock with a one-, two-, or three-letter code,where each letter is selected from the 26 letters of the alphabet. If the letters may be repeated and if the same letters used in a different order consistute a different code, how many different stocks is it possible to uniquely designate with these codes?

(1) 2951 (2) 8125 (3) 15600 (4) 16302 (5) 18278

26*26*26 + 26*26 + 26 = 18278

Lyssazhao · 发表于 2011-3-6 02:34:02

我是这么做的呀都。。。哦。。。算错数了。。。杯具。。。

sdcar2010 · 发表于 2011-3-6 02:35:17

3/ The positive integer 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.

y = a*x; z = b*y; a and b are integers. So x = y/a = z/(a*b); y = z/b

1) 2*n = x*z = z^2/(a*b). z^2 = 2*m. z is even
2) 2*n = y = z/b. z = 2* k. z is even

Lyssazhao · 发表于 2011-3-6 02:38:40

第三个明白了。特别清楚。谢谢。

rainbow582 · 发表于 2011-3-7 07:49:55

1楼的你太油菜了。

rainbow582 · 发表于 2011-3-7 07:56:33

2楼解答求解释！对不起我实在数学脑残，请多包容。

alexlixin · 发表于 2011-3-22 01:00:10

呵呵，路过。2楼的解题原理就是根据混合前后所含的脂肪总量保持不变列出方程。

sdcar2010 · 发表于 2011-3-22 07:13:16

2楼解答求解释！对不起我实在数学脑残，请多包容。

-- by 会员 rainbow582 (2011/3/7 7:56:33)

For 3-letter word, the possibilities are: 26*26*26
For 2-letter word: 26*26
For 1-letter word: 26

提问3道PREP数学，请大牛进！！

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