Miscellaneous Topics Diagnostic Test

15 Minutes — 12 Questions

Solve   problems    1–12.   Select  the best    answer  choice  for each    question.

1 . For all nonzero numbers x   and y,  the operation       is  defined by  the equation

when    x   >   y   and by  the equation     when   x   ≤   y.  If  x y <

0,  then    which   of  the following   could   be  true?

I. x^3  =   y^3

II. (y  +   x)(y    –   x)  >   0

III. x  –   y   >   0

(A) I   only

(B) II  only

(C) III only

(D) I   and II

(E) II  and III

2 . If   ,  then    which   of  the following   has the greatest    value?

(A) i^4     +   i^3     +   i^2     +   i

(B) i^8     +   i^6     +   i^4     +   i^2

(C) i^12    +   i^9     +   i^6     +   i^3

(D) i^16    +   i^12    +   i^8     +   i^4

(E) i^20    +   i^15    +   i^10    +   i^5

3 . “If a   zic is  a   zac,    then    a   zic is  not a   zoc.”