If XY is divisible by 4, which of the following must be true?
(A) If X is even then Y is odd --> X=4 Y =4 XY is disivible by 4, X is even and Y is not odd--> Eliminate
B) If X=2^1/2 then Y is not a positive integer --> keep
(C) If X is 0 then X + Y is not 0 --> X = 0 and Y =0 , then XY divisible by 4 --> eliminate
(D) X^Y is even --> X=3, Y = 4 then XY is divisible by 4 and X^Y=81 even--> eliminate
(E) X/Y is not an integer.--> X=4 and Y=4 then X/Y=1--> eliminate
Hence can only be B by elimination. Prove that B is true:
if X=2^1/2 there is no integer such as XY is divisible by 4 except 0. In fact Y needs to be divisible by 4 but XY divided by 4 will have a reminder as X = 2^1/2 Hence saying Y is not a positive integer is correct as 0 is the only solution. Please correct me if I am wrong
XY divisible by 4:
X= √2, Y= 0 => XY = 0 (divisible by 4)...satisfied
X= √2, Y= 8√2 => XY = 32 (divisible by 4)...satisfied
X= √2, Y= -8√2 => XY = -32 (divisible by 4)...satisfied
In the first case, Y=0 - not a positive integer...satisfied
In the 2nd case, Y=8√2 -not a positive integer...satisfied
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