1. ## INEQUATIONS

(1) if r>t , r<1 and rt=1 then which of the following must be true?

(a) r>0 and t<-1
(b) r>-1 and t<-1
(c) r<-1 and t<-1
(d) r<1 and t>1
(e) r>1 and t<0

(2) if x and y are the integers such that 0<x+y<10 ,then which of the following must be true

(a) xy<2
(b) x>3
(c) x>4
(d) x+y=5
(e) x-y<8

(3) if line segment AD has midpoint M1 and the line segment M1D has midpoint M2 ,what is the value of (M1D)/(AM2).

(a)3/5
(b)2/3
(c)1/3
(d)2/5
(e)1/2.  Reply With Quote

2. ## Re: INEQUATIONS  Reply With Quote

3. ## Re: INEQUATIONS

For second question E can also be the answer...  Reply With Quote

4. ## Re: INEQUATIONS

Sorry E cannot be the answer...  Reply With Quote

5. ## Re: INEQUATIONS

If you have the answers, that would be great.

1. b) rt=1 =>r=1/t
Because r=1/t and r>t, r has to fall between -1 and 0 and t is less than -1. the constraint that r<1 stops a solution like r=3, t=1/3.

2) I don't think any of these are right. If you are restricted to positive integers, then e is correct.

Counterexamples:
a, b, c, and d) x=2, y=4
e) x=12, y=-3

3) 2/3

Just think of it as a 4 unit line segment. A--M1-M2-D. You can see there are 2 units between M1 and D and 3 between A and M2.  Reply With Quote