21. The total amount that Mary paid for a book was equal to the price of the book plus a sales tax that was 4 percent of the price of the book. Mary paid for the book with a 10 bill and received that correct change which was less than $3.00
Which of the following statements must be true?
Indicate all such statements
A the price of the book was less than 9.50
B the price of the book was greater than 6.90
C the sales tax was less than 0.45
Ans: C
解析：设该书价格为x，Mary付费为书钱加上税钱，x(1+4%)=1.04x
Mary支付了10元，找零小于3，则Mary支付的钱大于7
即7<1.04x<10 得6.73
x可取9.51，则A项不对;x可去6.80，则B项不对。
对于C项，取x最大为9.61, tax=4%x=0.38<0.45，该项正确
解题要点：将文字形式转化为代数式。
22. If 1/211×517 is expressed as a terminating decimal, how many nonzero digits will the decimal have ?
A one
B two
C three
D six
E seven
Ans: B
解析： 1/211×517=1/(2×5)11×56
=(1/5)6×10-11
=(0.2)6×10-11
=26×10-6×10-11
=64×10-17
非零的数字为6和4
解题要点：分数向小数转换，尽可能先凑出10。
23. If s is a speed,in miles per hour,at which the energy used per meter during running is twice the energy used per meter during walking ,then according to the graph above ,s is between
A 2.5 and 3.0
B 3.0 and 4.5
C 3.5 and 4.0
D 4.0 and 4.5
E 4.5 and 5.0
Ans: A
解析： Running消耗的energy在300左右
当s>3.0后，walking消耗的energy大于150
则Running消耗的energy不再为Walking消耗的energy的两倍
当2.5
解题要点：图表题中有这么一类题要善于进行估算。
24. If n= 23, then nn =
A 26
B 211
C 218
D 224
E 227
Ans: D
解析： n=23=8
nn=(23)8=224
解题要点：求一个表达式的值前可以先看选项，确定最后求出的值的形式如何。
25. Which of the following statement individually provide sufficient additional information to determine the area of triangle ABC above?
Indicate all such statements
A DBC is an equilateral triangle (等边三角形)
B ABD is an isosceles triangle (等腰三角形)
C the length of BC is equal to the length of AD
D the length of BC is 10
E the length of AD is 10
Ans: AD
解析： A项：?DBC为等边三角形
角C=60
Rt?ABC中，根据三角函数值
可求出BC，A项正确
B项：?ABD为等腰三角形
可以AB=AD或者AD=DB，这两种情况都不影响BC长度变化，因此 B项错误
C项：BC=AD，但AD值也未知，必须借助其他条件求值，C项错误
D项：BC=10，D项正确
E项：AD=10，但AD与BC的关系未知，无法判断BC，E项错误
解题要点：?图形未必依比例画出，不要依据图形比例判断关系
?通过梳理关系，将一个复杂问题转化为求解另一个更简单问题的能力。
26. a1,a2,a3,……,an,……
In the sequence above,each term after the first term is equal to the preceding term plus the constant c. If a1+a3+a5=27,what is the value of a2+a4?
a2+a4=( )
Ans: 18
解析：该数列为一等差数列，公差c，通项为an=a1+(n-1)c
a1+a3+a5=a1+a1+2c+a1+4c=3a1+6c=3(a1+2c)=27
a1+2c=9
a2+a4=a1+c+a1+3c=2a1+4c=2(a1+2c)=18
解题要点：数列中常将一个代数式当成一个整体去计算，未必求出其中每个变量的值，如本题中a1+2c
27. A desert outpost has a water supply that is sufficient to last 21 days for 15 people.At the same average rate of water consumption per person,how many days would the water supply last for 9 people?
A 28.0
B 32.5
C 35.0
D 37.5
E 42.0
Ans: C
解析：题中假定每个人的耗水量相同，设为k，设d为要求的天数
21×15×k=9×d×k
d=35
解题要点：文字题，理解题意，将文字形式转化为代数关系
注意抓住前后不变的量，如本题中的k。
28. The fabric needed to make 3 curtains sells for $8.00 per yard and can be purchased only by the full yard. If the length of fabric required for each curtain is 1.6 yards and all of the fabric is purchased as a single length, what is the total cost of the fabric that needs to be purchased for the 3 curtains?
A $40.00
B $38.40
C $24.40
D $16.60
E $12.80
Ans: A
解析：每个窗帘需要1.6码布，3个窗帘需要3*1.6=4.8码布
布只能以整数码被交易，共需买5码布
花费5*8=$40
解题要点：文字题重在读懂题意，将文字表述的关系转化成代数式
29. In the xy-plane, line k is a line that does not pass through the origin.
Which of the following statements individually provide(s) sufficient additional information to determine whether the slope of line k is negative?
Indicate all such statements.
A The x-intercept of line k is twice the y-intercept of line k.
B The product of the x-intercept and the y-intercept of line k is positive.
C Line k passes through the points(a,b) and (r,s), where (a-r)(b-s)<0.
Ans: ABS
解析：如果一条直线的x轴截距和y轴截距是同号的，则它们的斜率一定为负。
如下图所示
A 直线k的x截距是y截距的两倍，x、y截距同号。
所以，由此判断斜率为负
B 直线的x截距和y截距的乘积为正，说明二者同号
所以，其斜率为负
C 已知(a,b)和(r,s)两点，直线斜率的两点式表达为b-s/a-r
C项中，已知(a-r)(b-s)<0，即b-s/a-r<0
所以，直线的斜率为负
解题要点：涉及到坐标系的问题，通常可作图将问题可视化、形象化，从而把较难判断的问题转化为简单的。
30.
The expressions in the table above give the distance from Centerville to each of two trains t hours after 12:00 noon. At what time after 12:00 noon will the trains be equidistant from Centerville?
A 1:30
B 3:30
C 5:10
D 8:50
E 11:30
Ans: B
解析： t hours F train 距 C的距离为 -10t+115
t hours P train 距 C的距离为 -20t+150
-10t+115= -20t+150
10t=35
t=3.5
从12:00以来过了3.5个小时，所以到3:30
解题要点：文字题+表格，理解题意，列出代数关系