mpt even?

[nakul_anand]

If m,p, and t are positive integers and m<p<t, is the product mpt an even integer?

(I) t-p=p-m

(II) t-m=16

[November Rain]

I would say the answer is E.


For m.p.t to be even you need at least one of three values to be even.

The first sentence tells you that M=T, but it doesn't mention whether they're even or odd. So it's insufficient

The second sentence tells you that both M and T can be even or odd, because that's the only way the difference between the two is an even number.

Both sentences combined doesn't add any information to each other.

So, its E.

[mp2437]

first statement does not say M = T, it says T + M = 2P, and second statement says T - M = 16. Either statement by itself doesn't say anything, and combining them, you could add the equations to get:

2T = 2P + 16, or T = P + 8. This is still insufficient since P and T could take on any values, as well as M. For example, if P = 3, then T = 11, so P*T = 33. M could be 1 or 2, so product of mpt could be 33 or 66. Choice E.

[adi_800]

well..i am confused..
Consider statement 1..
t-p=p-m
=> t + m /2 = p
=> So, t + m has to be even so as to make the value of (t + m) /2 an even integer..
=> t and m are both odd or both even..
Case I:
t and m are both even ->product mpt even. Statement 1 sufficient.
Case II:
t and m are both odd -> value of p is even -> one even in product of three -> the product mpt is even..
Statement 1 is sufficient..

Statement II is insufficient..
So, I think answer is A..

where am i going wrong??

[harshavardhanc]

well..i am confused..
Consider statement 1..
t-p=p-m
=> t + m /2 = p
=> So, t + m has to be even so as to make the value of (t + m) /2 an even integer..
=> t and m are both odd or both even..
Case I:
t and m are both even ->product mpt even. Statement 1 sufficient.
Case II:
t and m are both odd -> value of p is even -> one even in product of three -> the product mpt is even..
Statement 1 is sufficient..

Statement II is insufficient..
So, I think answer is A..

where am i going wrong??

=> So, t + m has to be even so as to make the value of (t + m) /2 an even integer..

why are you assuming (t + m) /2 to be an even integer?

Case II:
t and m are both odd -> value of p is even -> one even in product of three -> the product mpt is even..

if t and m are both odd, for e.g, 7 and 3, 7+3 = 10 is divisible by 2 and p will be 5 , i.e all ODDs.

[dream700]

i find the best way always is to take examples...

first i take m,p and t to be 1, 9 and 17

it satisfies both the given statements. is product mpt even = NO

now we take m, p and t to be 2,10 and 18

again, it satisfies both the given statements. is product mpt even = YES

so no statement alone or even combinining two statements is enough to answer the question.

Hence the ans must be E.

Deutsch750