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

For the product mpt to be an even integer at least one of three has to be an even integer.
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

This is how i have approached:

We need to find if mpt is Even.
For this at least one out of m, p, t has to be Even

1. t-p = p-m
=> t+m = 2p

we know, Even + Even = Even
Odd + Odd = Even
Hence t and m both can either be even or odd..... hence Insuff

2. t-m = 16

we know, Even - Even = Even
Odd - Odd = Even
Hence t and m both can either be even or odd..... hence Insuff

Combining both we have
t-p = 8.... again insuff

hence E
Whats the OA?

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

For mpt to be odd, all 3 values (m, p and t) must be odd.

Question rephrased: Are m, p and t all odd?

Statement 1: t-p = p-m.
m+t = 2p
p = (m+t)/2.
The implication is that p is HALFWAY between m and t.
Thus, all 3 values could be even (2,4,6), or all 3 values could be odd (1,3,5).
INSUFFICIENT.

Statement 2: t = m+16.
If m=1, then t=17.
If p=9 , then all 3 values are odd.
If p=10, then all 3 values are not odd.
INSUFFICIENT.

Statements 1 and 2 combined:
To satisfy both statements, t = m+16, and p is halfway between m and t.
If m=1 and t=17, then p=9, in which case all 3 values are odd.
If m=2 and t=18, then p=10, in which case all 3 values are not odd.
INSUFFICIENT.

The correct answer is E.