Question

1. If xy>1 and z<0, which of the following statements must be true?

I. x>z
II.xyz<-1
III.xy/z<1/z

A. I. only
B. II. only
C. III. only
D. II. and III.
E. None

2.

ab>0
1/a<1/b

Which is greater, a or b?

3.

p/4<q/12

Which is greater, (p-1)/4 or (q-9)/12?

4.

a and b are positive integers.
7<ab<21

Which is greater, a+b or ab?

5.

-1<=x-3<=6
5<=y+1<=9

Which is greater, the largest possible value of x/y or 2?

6.

a+b=5
b<7/3

Which is greater, a or 8/3?

Answer 1

These require some thought, and it serves you not for someone to do that for you.

example 1.
xy>1 implies x,y are both positive, or both negative.
z<0 means z is negative. Not think out the choices
I. x>z cannot be true always, x could be -100 and z could be -88
II.xyz<-1 xy is positive, z is negative, so sign is right. but the product of xyz could be -1/2 (example xy=2, z=-.5
III
III.xy/z<1/z divide both sides by xy.
1/z<1/xyz . now consider z=-1/2, and xy 10
1/-.5<1/-5
-2<-.2 true the right side is always greater than the left,

A. I. only
B. II. only
C. III. only
D. II. and III.
E. None