If m,p, and t are positive integers and m<p<t, is the product mpt an even integer?
1. t-p=p-m
2. t-m=16
1. t-p=p-m
2. t-m=16
For the product mpt to be an even integer at least one of three has to be an even integer.alex.gellatly wrote:If m,p, and t are positive integers and m<p<t, is the product mpt an even integer?
1. t-p=p-m
2. t-m=16
statement 1 :INSUFFICIENT
t-p = p-m
=>2p = t+m
=>p = (t+m)/2
If p is a +ve integer, then t+m should be a +ve even integer.
This means either both t and m are even or both t and m are odd.
also p can be either even or odd.
statement 2: INSUFFICIENT
t-m= 16
t = 20, m = 4 (both even)
t = 21, m = 5 (both odd)
both can be either odd or even.
combining both the statements
t+m = 2p
t-m = 16
=>2t = 2p+16
=> t= p + 8
nothing can be concluded.
hence IMO the correct answer is E
