If x and y are positive integers, is x an even int? i. (y+5)

Question

If x and y are positive integers, is x an even int?

i. (y+5) (x) is an even int
ii. 6y^2 + 41y + 25 is even int

My take :

(i) - since y+5 or x either can be even for the entire statment to be even - insufficient
(ii) 6(odd/even) + 41(odd/even) + odd = even therefore y should be odd. - insufficeint

combined - x could be even or odd. 

Answer E. did this in 30 sec. Not sure if it's right. Please provide your help. thanks

KillerSquirrel · Answer

statement 1 e = even o = odd (y+5)(x) = e (o+o)*e = e ---> true sufficient statement 2 6y^2 + 41y + 25 = e e+o+o = e ---> true No info on x insufficient the answer is (A)

alimad · Answer

What if for statement I

y = 1 x = 1
(6) (1) = even

this statement makes x an odd 
y =1 x =2
6(2) = 14 
this statement makes x an even

both of them satisfy statement I

KillerSquirrel · Answer

You are correct

alimad · Answer

So statement I is insufficent. 


So the answer is C

tarek99 · Answer

If x and y are positive integers, is x an even int? 

i. (y+5) (x) is an even int 
ii. 6y^2 + 41y + 25 is even int

Answer is E.

statement 1: either X is even or (y+5) is even...not suff.

statement 2: 6y^2 will always be even because 6 is even. then we have 25 (odd), so when you add even to odd, you will get odd. the third number has to be odd in order for the total to be even, hence, y for 41y must be odd because 41(odd) * odd number will always be odd.


Statement 1 & 2:
Since Y is odd, (Y+5) will be even. however, the final product will be even by multiplying either with 2 even numbers or with 1 even and 1 odd. Whether X is even or not, the final product will still end up as an even integer, therefore E is the answer.

FN · Answer

ooops my bad E..

1)
(y+5)(x) is even

if y is odd then x can be odd or even ..we dont know..insuff

2)
6Y^2+41Y has to be odd 

6Y^2 is never odd..so the only way the above is going to be odd is y is odd i.e 41y has to be odd..which is only when y is odd


Ok now we know y is odd

but we dont know if x is even or not..

pmenon · Answer

made a silly mistake at the start thinking that if 41y has to be odd, then y had to be even.

corrected it and end up with E, because x can be even or odd and the final product is still even

alisag · Answer

consider first case- if Y is Odd(say 3), (Y+5) is even bcos Odd + odd = Even.
now since Y + 5 is Even, X can be odd or Even bcos Even*Even= EVEN and Even*odd=EVEN.
so from this we cant say that X is even or odd. So 1st is Insufficient.
So options A, D are out of scope.
-------
6y^2 +41y+25 
watever is the value of Y,6y^2 is always Even
therefore EvEN +41y+25 to be an EVEN no., Y must be ODD.
now combining the above two conditions:- 
Since Y is ODD from 2nd so putting Y =3 in first Condition we get 8*X, but this alos have to be even.In this case X again can be even or odd.
therfore the NAS is E(Undoubtedly)

spider · Answer

For 
1. take y = 1 then x can be odd or even
take y=2 then x has to be even so InSUff

2. take y = odd then - its even.

so taking both together ==>

y - odd and when its odd statement 1 - x can be even or odd.

so answer is E

If x and y are positive integers, is x an even int? i. (y+5)

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