BruceNornia

11.

Is the integer n odd?

(1)   n is divisible by 3

(2)   2n is divisible by twice as many positive integers as n

 

条件(1) n能被3整除，明显不能判断n是不是奇数，NOT SUFFICIENT

条件(2) 将n分解质因数计为：n = a1^n1 * a2^n2 * ... * am^nm 这里a1 ... am均为质数 而n1 ... nm分别表示其质因数的指数

那么n的正整数因子个数为：(n1+1) * (n2+1) * ... * (nm+1)

当n为奇数时，a1 ... am均为奇数

从而2n的质因数分解为 2n = 2 * a1^n1 * a2^n2 * ... * am^nm 其正整数因子个数为：(1+1) * (n1+1) * (n2+1) * ... * (nm+1) 为n的正整数因子个数的2倍

当n为偶数时，可知a1 ... am 中存在一个2，取a1 = 2 即 n = 2^n1 * a2^n2 * ... * am^nm

从而2n的质因数分解为 2n = 2^(n1+1) * a2^n2 * ... * am^nm 其正整数因子个数为： (n1+2) * (n2+1) * ... * (nm+1) 为n的正整数因子个数的(n1+2)/(n1+1)倍 由于n1 != 0 所以不可能为2倍

则在条件(2)的约束下 只有奇数n能满足，从而n为奇数可以判断，SUFFICIENT

 

The correct answer is B

Statement (2) ALONE is sufficient

BruceNornia

10.
Store S sold a total of 90 copies of a certain book during the seven days of last week, and it sold different numbers of copies on any two of the days. If for the seven days store S sold the greatest number of copies on Saturday and the second greatest number of copies on Friday, did Store S sell more that 11 copies on Friday?

(1)   Last week Store S sold 8 copies of the book on Thursday.

(2)   Last week Store S sold 38 copies of the book on Saturday.

 

条件(1) 周四卖出了8本 ，无法判断周五是不是卖了11本，事实上，周一到周日卖书 分布为 1 2 3 8 11 61 4 满足题目要求， 分布为 1 2 3 8 12 60 4 同样满足要求，NOT SUFFICIENT

条件(2) 周六卖出了38本，可以判断周五是不是卖了11本，事实上如果 周六卖出38本 而周五卖了11本的话 剩下5天 最多能卖出 10 + 9 + 8 + 7 + 6 = 40本书 这样整周数量为89本 不足90，从而周五不可能卖出11本 SUFFICIENT

 

The correct answer is B

Statement (2) ALONE is sufficient

BruceNornia

In May Mrs.Lee’s earnings were 60% of the Lee family’s total income. In June Mrs.Lee earned 20% more than in May. If the rest of the family’s income was the same both months, then, in June, Mrs.Lee’s earnings were approximately what percent of the Lee family’s total income?

-          64%
-          68%
-          72%
-          76%
-          80%

 

假定5月李太太收入为 X 那么家庭总收入为 X/(60%)=5/3 X  家庭剩余人员的收入为：5/3 X - X = 2/3 X

6月 李太太收入增加20% 为X (1+20%) = 6/5 X 家庭剩余人员收入不便 2/3 X

从而李太太收入所占百分比为：6/5 X / [6/5 X +2/3 X]= 64.3%

 

The correct answer is A

BruceNornia

8.
In the figures above, if the area of the triangle on the right is twice the area of the triangle on the left, then in term of s, S=√2s
两个三角形，左边的底边为s 右边的底边为S,他们的内角都相等
没想通？

...

没想通就慢慢想... 相似三角形的性质而以，相似三角形面积之比为对应边长比的平方 （可以背下来）

事实上我们假定三个角分别为A B C 其中B所对的那个边的长度分别为S和s

 

那么

大三角形的面积 = S^2 * sinA*sinC/(2sinB)

小三角形的面积 = s^2 * sinA*sinC/(2sinB)

大三角形的面积/小三角形的面积 = S^2/(s^2) = 2 从而S=√2s

BruceNornia

7.

in the rectangular coordinate system, are the points(r,s) and (u,v)equidistant from the origin?

(1)   r+s=1

(2)   u=1-r and v=1-s

KEY:C

 

(r,s)与(u,v)到原点的距离分别为 √(r^2 + s^2) 与 √(u^2 + v^2)

 

条件(1) r+s=1 无法证明 √(r^2 + s^2) = √(u^2 + v^2)； NOT SUFFICIENT;

条件(2) u=1-r  v=1-s √(r^2 + s^2) = √[(1-u)^2 + (1-s)^2]，仍然无法证明 √(r^2 + s^2) = √(u^2 + v^2)； NOT SUFFICIENT;

条件(1)+(2) √(r^2 + s^2) = √[(1-u)^2 + (1-s)^2] = √(v^2 + u^2)；SUFFICIENT

 

The correct answer is C

Tow statements together are sufficient 

BruceNornia

6.

of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes or dislikes Brussels sprouts. Of these students, 2/3 dislike lima beans; and of those who dislike lima beans, 3/5 also dislike Brussels sprouts. How many of the students like Brussels sprouts but dislike lima beans?

(1)       120 students eat in the cafeteria

(2)       40 of the students like lima beans

KEY

 

题目说 所有人中2/3不喜欢利马豆，其中3/5不喜欢芽甘蓝 问多少人喜欢芽甘蓝不喜欢利马豆

条件1 总人数120，则不喜欢利马豆的为 120*2/3=80 而不喜欢利马都喜欢芽甘蓝的为80*(1-3/5) = 32 SUFFICIENT

条件2 40人喜欢利马豆，从而不喜欢利马豆的为 [40/(1-2/3)]*2/3 = 80 而不喜欢利马都喜欢芽甘蓝的为80*(1-3/5) = 32 SUFFICIET

 

The answer is D;

Each statement alone is sufficient.

BruceNornia

5.

A certain library assesses fines for overdue books as follows. On the first day that a book is overdue, the total fine is $0.10. for each additional day that the book is overdue, the total fine is either increased by $0.30 or doubled, whichever results in the lesser amount. What is the total fine for a book on the fourth day it is overdue?

- $0.60

- $0.70

- $0.80

- $0.90

- $1.00

 

逐步计算 第一天$0.10，第二天翻倍比增加$0.30少，所以为0.20$，第三天翻倍比增加$0.30少，所以为$0.40，第四天增加$0.30比翻倍少，所以为$0.70

 

The correct answer is B

BruceNornia

4.

For which of the following functions is f(a+b)=f(a)+f(b)for all positive numbers a and b?

-f(x)=x^2

-f(x)=x+1

- f(x)=√x

-f(x)=2/x

-f(x)= -3x

 

逐个计算：

A f(a+b) = (a+b)^2 = a^2 + b^2 + 2ab 而 f(a)+f(b) = a^2 + b^2 不满足

B f(a+b) = (a+b) +1 = a + b + 1 而 f(a)+f(b) = a +1 + b +1 = a + b +2 不满足

C f(a+b) =√(a+b)  而 f(a)+f(b) = √a + √b 不满足

D f(a+b) =2/(a+b)  而 f(a)+f(b) = 2/a + 2/b 不满足

E f(a+b) =-3(a+b) = -3a + -3b  而 f(a)+f(b) = -3a + -3b 满足

 

The correct answer is E

BruceNornia

3.

If each term in the sum a1+ a2+ …….an is either 7 or 77 and the sum equals 350, which of the following could be equal to n?

- 38

- 39

- 40

- 41

- 42

 

枚举所有可能，

39个7 1个77，n=40

28个7 2个77，n=30

17个7 3个77，n=20

6个7 4个77，n=10

选项中只有40合适

 

The correct answer is C

BruceNornia

2.

According to the directions on a can of frozen orange juice concentrate,1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12-ounce cans of the concentrate are required to prepare 200 6-ounce serving of orange juice?

- 25

- 34

- 50

- 67

- 100

 

1厅浓缩液要和3厅水混合，所以混合比为1：3

准备200个6盎司的橙汁，即共1200盎司

按照上述比例 需要浓缩液300盎司 水900盎司

而准备300盎司的浓缩液一共需要25个12盎司的浓缩罐 300/12 = 25

 

The correct answer is A