If x and y are positive integers, is x even?

S1: x-3y=27

This means that x=27+3y. The value of x is dependent on y, ie. if y is odd then x is even and if y is even then x is odd.

eg. y=3 then x = 36
y=2 then x= 33

S2: x+2y=37

This means that x=37-2y. Please note that here 2y is even so no matter what the value of y. So this expression will always be odd. Hence the statement is sufficient.

Ans - B

statement 1 = x-3y=27
i.e x= 27+3y
x can be even if y=odd and it can be odd when y= even so= not suff
statememt 2 = x+2y = 37
i.e x =37-2y (odd - odd = odd)= suff
ans b

We are given that x and y are positive integers, and we need to determine whether x is even.

Statement One Alone:

x - 3y = 27

Simplifying statement one, we have:

x = 27 + 3y

x = 3(9 - y)

x/3 = 9 - y

We see that x must be divisible by 3; however, that is not enough information to determine whether x is even. For instance x could be 6, which is even, or x could be 9, which is not even. Statement one alone is not sufficient to answer the question.

Statement Two Alone:

x + 2y = 37

Simplifying statement two, we have:

x = 37 - 2y

Because 37 is odd and (2y) is even, we see that x = odd - even, which is always an odd number. Since we know that x is odd, statement two is sufficient to answer the question.

Answer: B