If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true?
(i) x is prime
(ii) y is even
(iii) xy is positive Answers
A) ii only
B) iii only
C) i and iii only
D) ii and iii only
E) i, ii and iii
Effectively y = 36x/41   (i) x is prime: now if y = 36x/41 and both x and y are integers; then if x= 41, 36(41)/41 .....so the 41s cancel each other out and you get x=36. Hunky dory. But if x = 82; you get y =72 which also works. Hence x is not necessarily prime.   (ii) y is even: y = 36(41)/41 = 36 (even). Or try 36(82)/41 = 72 (even). When you multiply even with odd, answer is even. So Y HAS TO BE EVEN.   (iii) xy is positive. Hmm. So if y is positive, then x is positive. Because if you have a -ve value of x, it leads to -ve value of y. Hence I would say iii is the answer. ANSWER:iii only
<result>B</result>
If x and y are both integers such that 41y = 36x and y is not negative, which of the following must be true?
(i) x is prime
(ii) y is even
(iii) xy is positive