Data Sufficiency

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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

OA is E. IMO A
In option A, p=(t+m)/2 .
P is a positive integer, therefore t+m has to be even.
Therefore product mpt is even , so sufficient.
CAn someone explain where I am going wrong.......

gmat009 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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

OA is E. IMO A
In option A, p=(t+m)/2 .
P is a positive integer, therefore t+m has to be even.
Therefore product mpt is even , so sufficient.
CAn someone explain where I am going wrong.......

Sum of two numbers can be even , when

(a) Both are even 2 + 2 = 4
(b) Both are odd 3 + 3 = 6

So, ur assumption that because m + t is even, m or t is even is incorrect

statement 1

t-p=p-m
t+m=2p
t+m results in an even integer
so either both must be even or both must be odd
and moreover we don't know whether p is even or odd
so this statement is insufficient

statement 2

t-m=16
Again both t and m can be odd or even
insufficient

Combining both the statements we have
2t=16+2p
t-p=8
Both t and p can be even or odd...

Hence E is the ans

gmat009 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

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

OA is E. IMO A
In option A, p=(t+m)/2 .
P is a positive integer, therefore t+m has to be even.
Therefore product mpt is even , so sufficient.
CAn someone explain where I am going wrong.......

If p/2 = (t+m) the p will have to be even. But A tells you p is half of t+m.