PRODUCT AND EVEN

[vishubn]

`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.

A WAS MY ANSWER CHOICE

i asssume m+t/2 is equal to p , as p is integer so m+t is always even

Correct me

Vishu

[stop@800]

P = (m+t)/2

ps is an integer
means (m+t)/2 is an integer
hence
(m+t) is even

but sum of two odds can also be even
3 + 3 = 6

We need to find mpt is even or not

I think you mistook mpt with something else

Hope this helps

IMO ans is E
whats the OA?

[drpawan]

`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.

A WAS MY ANSWER CHOICE

i asssume m+t/2 is equal to p , as p is integer so m+t is always even

Correct me

Vishu

I am sure it will be E.

Given m<p<t

Statement 1 --> t-p = p-m => p = (t+m)/2
Ex: 3<5<7 and also 5-3 = 7-5 = 2 => 7.5.3 = 105 not an even no
Ex: 1<2<3 and also 2-1=3-2 = 1 => 1.2.3 = 6..its an even no
So statement 1 is insufficent

Statement 2 --> we have t-m=16 and also m<p<t
Ex: 2<3<18 => 18-2 =16 => 2*3*18 is even
Ex: 3<7<19 => 19-3 = 16 => 3*7*19 is odd
So we cannot decide here too. Hence statement 2 is insufficent.

Even if we take both the statements,
Ex: 8<16<24 => 24-16=16-8 and also 24-8 = 16 => 8*16*24 is even.
7<15<23 => 23-15 = 15-7 and also 23-7 = 16 => 7*15*23 is odd

So ans is E

[yezz]

`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

from 1

t-2p+m = 0

t+m = 2p ie either t,m are both even or are both odd , p could be anything.....insuff

from 2

t-m = 16 ie: odd - odd or even - even., no info about p ......insuff

both

still insuff

[rohangupta83]

imo E

m<p<t

From statement 1: t - p = p - m
or
t + m = 2p

Pick numbers

2,4,6 --> 2*4*6 = Even
3,4,5 --> 3*4*5 = Even
1,3,5 --> 1*3*5 = Odd

Therefore, Not sufficient

Statement 2: t - m = 16

1,2,17 --> 1*2*17 = Even
1,3,17 --> 1*3*17 = Odd

Not sufficient

Now 1 and 2 together

3, 11, 19 --> 3*11*19 = Odd
4,12,20 --> 4*12*20 = Even

Not sufficient

Therefore Statements 1 and 2 are insufficient alone as well as together.

Correct answer - E

[eracnos]

yup, i think the best way to solve this problem is by plugging in answer.
IMO E i correct)