请教几道GWD数学题 求思路、过程

cxks01

Q13:
An integer greater than 1 that is not prime is called composite.If the two-digit integer n is greater than 20, is n composite?
(1)The tens digit of n is a factor of the units digit of n.
(2)The tens digit of n is 2.

Q15:
If w, x, y, and z are integers such that 1 < w < x < y < z and wxyz = 462, then z =?



Q18:
On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship.If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?


Q23:
AMOUNT OF BACTERIA PRESENT

Time	Amount
1:00 P.M.	10.0 grams
4:00 P.M.	x grams
7:00 P.M.	14.4 grams

Data for a certain biology experiment are given in the table above.If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?
Q24:
The value of (9´10⁷)(9´10⁸) is closest to which of the following?
Q25:
A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster.If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?
Q31:
There are 8 magazines lying on a table; 4 are fashion magazines and the other 4 are sports magazines.If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?
Q32:
What is the remainder when the two digit, positive integer x is divided by 3?
(1)The sum of the digits of x is 5.
(2)The remainder when x is divided by 9 is 5.
Q33:
In Town X, 64 percent of the population are employed, and 48 percent of the population are employed males.What percent of the employed people in Town X are females?




Q15:
If w, x, y, and z are integers such that 1 < w < x < y < z and wxyz = 462, then z =?



Q18:
On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship.If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?


Q23:
AMOUNT OF BACTERIA PRESENT

Time	Amount
1:00 P.M.	10.0 grams
4:00 P.M.	x grams
7:00 P.M.	14.4 grams

Data for a certain biology experiment are given in the table above.If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?
Q24:
The value of (9´10⁷)(9´10⁸) is closest to which of the following?
Q25:
A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster.If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?
Q31:
There are 8 magazines lying on a table; 4 are fashion magazines and the other 4 are sports magazines.If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?
Q32:
What is the remainder when the two digit, positive integer x is divided by 3?
(1)The sum of the digits of x is 5.
(2)The remainder when x is divided by 9 is 5.
Q33:
In Town X, 64 percent of the population are employed, and 48 percent of the population are employed males.What percent of the employed people in Town X are females?

王小睿

Q13，应该是A吧
如果十位是个位的factor，那么这个数肯定就不是prime了

王小睿

Q15  wxyz=2*3*7*11， Z=11

无敌可爱多

Q13:
An integer greater than 1 that is not prime is called composite.If the two-digit integer n is greater than 20, is n composite?
(1)The tens digit of n is a factor of the units digit of n.
(2)The tens digit of n is 2.

条件1，n>20，所以tens digit=2,3,4,5,6,7,8,9  满足条件的有20+2a, 30+3a, 40+4a, 50+5a, 60+6a, 70+7a, 80+8a, 90+9a,
因此条件1成立
条件2，n=20+a, a可以为任何数。因此当a=3, n=23时，是质数，条件2不成立。

综上，选A



Q15:
If w, x, y, and z are integers such that 1 < w < x < y < z and wxyz = 462, then z =?

把462进行因子分解，分解到质因数的次方形式，就一目了然了。

Q18:
On a certain transatlantic crossing, 20 percent of a ship’s passengers held round-trip tickets and also took their cars abroad the ship.If 60 percent of the passengers with round-trip tickets did not take their cars abroad the ship, what percent of the ship’s passengers held round-trip tickets?

这题如果你错了，也许你是把范围看错了。
20% 是 (R&C)/All
60%这句说的是 R&C占 R的 40%   而 R&C占all的20%
那么问题问的是R:All
All=5R&C
R=2.5 R&C
那么R:All= 1/2= 50%



Q23:
AMOUNT OF BACTERIA PRESENT
Time

Amount


1:00 P.M.

10.0 grams


4:00 P.M.

x grams


7:00 P.M.

14.4 grams





Data for a certain biology experiment are given in the table above.If the amount of bacteria present increased by the same fraction during each of the two 3-hour periods shown, how many grams of bacteria were present at 4:00 P.M.?

这个，14.4=10*(1+R)^2
R是增长的速率，同理可推其他银行利率问题，增长速率问题。是复利概念，都是考察的等比数列。

Q24:
The value of (9´107)(9´108) is closest to which of the following?

=81*10^15  ，自己看看和哪个最接近吧。
Q25:
A certain roller coaster has 3 cars, and a passenger is equally likely to ride in any 1 of the 3 cars each time that passenger rides the roller coaster.If a certain passenger is to ride the roller coaster 3 times, what is the probability that the passenger will ride in each of the 3 cars?


如果不加任何条件，一共27种选择： 3*3*3（每次3种） 那么依照不重复坐车的条件，设A,B,C三个车厢，则第一次可以在A,BC中任选1，那么就是3种选法，第二次选择除了第一次选了的之外的任意两个（第一次选了A,第二次就只能选BC)因此是2种选法。第三次没得选。所以一共是3*2=6种方法。因此答案是6/27=2/9

Q31:
There are 8 magazines lying on a table; 4 are fashion magazines and the other 4 are sports magazines.If 3 magazines are to be selected at random from the 8 magazines, what is the probability that at least one of the fashion magazines will be selected?

用C3,8 (8本里任选三本）做分母
C3,4(只选sports magazine)做分子

然后1-上面的分数，得到答案。
Q32:
What is the remainder when the two digit, positive integer x is divided by 3?
(1)The sum of the digits of x is 5.
(2)The remainder when x is divided by 9 is 5.

设这个数是10a+b, a和b为1-9之间的自然数
a+b=5--->b=5-a,则这个数是10a+5-a=9a+5  9a+5除以3 余数是2，因此1可以

条件2，x=9n+5   用9n+5除以3， 余数依然是2，因此2也可以

选D

Q33:
In Town X, 64 percent of the population are employed, and 48 percent of the population are employed males.What percent of the employed people in Town X are females?

比例问题，做法同18。

这道题就当做是你思考18题的作业了，所以你自己再做一次吧，如果还是做不出来再跟帖问。

cxks01

高手再请教一题，是GWD第二套第30题，有个图，我不会怎么插图上来，题目是In the figure, each side of square ABCD has length 1, the length of line segment CE is 1, and the length of line segment BE is equal to the length of line segment DE.What is the area of the triangular region BCE?分不清是平面还是立体图，立体图的话应该是1/2吧？

还有Q24:
The value of (9´10⁷)(9´10⁸) is closest to which of the following?


A.10¹⁶
B.10¹⁷
C.10⁵⁶
D.10⁵⁷
E.10⁵⁸
81*10的15次方，接近的应该选A吧，可是答案是B


Q24:
The value of (9´10⁷)(9´10⁸) is closest to which of the following?


A.10¹⁶
B.10¹⁷
C.10⁵⁶
D.10⁵⁷
E.10⁵⁸
81*10的15次方，接近的应该选A吧，可是答案是B

无敌可爱多

对了，刚刚重新看这次的JJ，发现了一道题你看看思路

PS：一个立方体6个面,用蓝，绿，红三色涂其表面，必须满足任意边所在面颜色不同，问几种方案，题目写了6-faced,答案也没有1，最小是4
参考答案：
任意边所在面颜色不同可以理解为任意两个相邻面的颜色不同。蓝，绿，红三色设为A,B,C.
设立方体的长宽高不一样，当长宽面选A,则宽高面可以选B或C，2种方案。当宽高面选A，长宽面可以选B或C，2种方案。当长高面选A，则长宽面可以选B或C，2种方案。2+2+2=6种方案。



也算是给你的作业吧，呵呵

GWD的课我也听了，算是同学互助啦~

你看看，这题跟你问过的一道题思路是一样的哦~~~~

无敌可爱多

还有Q24:
The value of (9´107)(9´108) is closest to which of the following?


A.1016
B.1017
C.1056
D.1057
E.1058
81*10的15次方，接近的应该选A吧，可是答案是B



啊啊啊啊啊，这道题差点被你绕进去。

81X10^15 近似于 8*10^16  近似于 10^17
另一个角度，9直接当做10，因此就是10^8*10^9=10^17

怎么都是选B的。


高手再请教一题，是GWD第二套第30题，有个图，我不会怎么插图上来，题目是In the figure, each side of square ABCD has length 1, the length of line segment CE is 1, and the length of line segment BE is equal to the length of line segment DE.What is the area of the triangular region BCE?分不清是平面还是立体图，立体图的话应该是1/2吧？

是平面图。

答案是B

这题需要画辅助线，链接AC，从B点做一条垂直于AE的线段，根据45°角性质求出这条线段，就是BCE的高，底边就是CE=1, 然后底乘以高除以2得出B选项