Question

I did these, but I got the wrong answers.
Please explain how ...


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

Answer 1

2. a is greater because it has the smaller reciprocal.

3. P/4<q/12
Multiply both sides by 12:
3P<q or q>3P.

(P-1)/4
Let P = 3
(3-1)/4 = 2/4 = 1/2.

(q-9)/12
Let q = 10 which greater than 3P.
(10-9)/12 = 1/12.
Therefore, (P-1)/4>(q-9)/12. This is
true for values of q up to 14.

4. 7<ab<21

This a compound inequality which states
that ab is greater than 7 but less than
21. Therefore, ab can be any whole number ranging from 8 to 20.

When ab = 8 = 1*8 = 2*4.
a+b = 1+8 = 9.
a+b = 2+4 = 6.

When ab = 20 = 1*20 = 2*10 = 4*5
a+b = 1+20 = 21
a+b = 2+10 = 12

The results show that a+b><ab depending
on the value of a and b.

5. -1<=x-3<=6. 5<=y+1<=9
2<=X<=9
Xmin = 2, Xmax = 9.

5<=y+1<=9.
4<=Y<=8
Ymin = 4, Ymax = 8.

X/Y = 9/4 =2 1/4,max.
Therefore,(x/y)>2.