Is ! even? (1) E=Q (2) Q=2

Question

Is  ! even?

(1) E=Q
(2) Q=2

ian7777 · Answer

I originally thought C, but I changed my mind. I think it's A. I thought originally that we had to be sure they weren't 0 or 1, because either of those factorial make 1, and 1 is odd. But knowing that the variables are equal means that even if they are 0 or 1, they both make 1, and 1 + 1 is even. So that's enough.

In 2, knowing that one variable is 2 doesn't tell us about the other one, which could be 0 or 1. So in either case, we'd get 3, which is odd, but in every other case we'd have even plus even which is even (every number other than 0 or 1 factorial must be even since it has at a minimum 2 times something in it).

So I'm going with A.

vprabhala · Answer

nice explanation Ian

stolyar · Answer

the only odd factorial is 0!=1!=1, all the rest are even.
Still A?

gayathri · Answer

I would go with D. Infact, from the stem, it looks like it will never be an odd number. You will never get 0! or 1! from E!+Q! :?:

Besides 1! factorial every other factorial is multiplied by atleast 2 an even number and any integer multiplied by an even number will always be even.

ian7777 · Answer

yeah. in fact, I think it would be even no matter what. I didn't see the exclamation point after the absolute value signs originally. I saw it without that, so there was the chance of getting 2+1=3.

ChallengeMaker · Answer

! = (positive integer + positive integer)! = (integer >=2)! = always even

stolyar · Answer

Yeah... I see.
I have f--cked up myself. Sorry about it.

I am growing old... gettin' stupid
remember me in my golden days?

MA · Answer

yes. i was wondering about the question...............

rxs0005 · Answer

my analysis is 

from statement 1
 

(1) E=Q then 0! + 0! = 2 Or 1! + 1! = 2 and so on so A is good


(2) Q=2 here we do not know what E is so if E = 1 0r 2 then u get 1+ 2 thats odd if E = 2 thne its even so statement 2 not suff

my answers to this is A

HongHu · Answer

Note the factorial sign outside of the bracket rxs.

MA · Answer

Guys, the question doesnot need any more information to answer the question. try without statement i and statement ii.

HongHu · Answer

That is a great question stolyar! And great discussions and explantions. You should drop by more often!

maneeshkumar · Answer

I will go with D. At first i missed the outside factorial sign the moment i saw i knew all number greater than 2 will give even number. So even the factorials are O or 1 you have 2.

Dan · Answer

C. 

unless Q & E are shown to be integers, they could otherwise be irrational.

Caspace · Answer

unless i am crazy you couldn't have factorials without using integers right?

Based on that assumption i throw in for D too.

praveen_rao7 · Answer

nice problem, D as well

anirban16 · Answer

It should be (d) as any factorial other than 0 and 1 is even.

rxs0005 · Answer

i did not notice the outer most factorial so it should be D

anirban16 · Answer

The outermost factorial makes all the difference.

Is ! even? (1) E=Q (2) Q=2

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