第一题：ifa,b,candfarefournonzeronumbers,thenallofthefollowingproportionsareequivalentEXCEPT:a,a/f=b/cb,f/c=b/ac,c/a=f/bd,a/c=b/fe,af/bc=1第二题：forallnumbersxandy,lettheoperation#bedefinedbyx#y=xy-y.ifa

Question

第一题：if a,b,c and f are four nonzero numbers,then all of the following proportions are equivalent EXCEPT:
a,a/f = b/c
b,f/c = b/a
c,c/a = f/b
d,a/c = b/f
e,af/bc = 1
第二题：for all numbers x and y,let the operation # be defined by x#y=xy-y.if a and b are positive integers,which of the following can be equal to zero.
I.a#b
II.(a+b)#b
III.a#(a+b)
第三题：the number that results when as integer is mutiplied by itself CANNOT end in which of the folowing digits?
a,1
b,4
c,5
d,6
e,8

Answer 1

第一题：如果a,b,c 和f 是四个非零实数,那么下面选项中除哪个之外其余的都是等价的：
选A,将选项全部去分母得
A、ac = bf B、 af=bc C、 af=bc D、 af=bc E、 af=bc
第二题：对于所有的实数x和y,定义#的运算为：x#y=xy-y.如果a和b是正整数,下面哪一项可能等于零?
选I和III.
I.a#b=ab-b=(a-1)b,当a=1时,式子可等于0
II.(a+b)#b=(a+b)*b-b=(a+b-1)*b,因为a≥1,b≥1,所以a+b-1≥1,式子不可能等于0
III.a#(a+b)= a*(a+b)-(a+b)=(a-1)*(a+b),因为a=1,式子可等于0
第三题：一个整数与它自身相乘后所得的结果,其个位数不可能是下列哪个数?
选E