Let's understand that rule for divisibility of 0 here before start answering the question. 0 is divisible by any number, however, we can not divide any number with 0. Another rule, even number which is divisible by 5 will also be divisible by 10.
Option 1:
If xy/5 is an integer, is x divisible by 3?
X value can be anything 3,6 and 9.... To divide the product xy by 5, y must have to be divided by 5. Sufficient.
Option 2:
y is divisible by 10. X can be any value 2,3,4,5.... Some of them divide by 5 and some of them not... Not sufficient.

Answer is A.... I hope I am right...

Case 1 ->
y = 30
x = 1

NO, x is not divisible by 5

Case 2 -->
y=30
x=5
YES, x is divisible by 5


Use the above test case to reject A,B,C

and then off-course -> Smash that E
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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (x and y) and 0 equations,C is most likely to be the answer. So, we should consider 1) & 2) first.

Conditions 1) & 2):

x = 5, y = 30 : Yes
x = 1, y = 30 : No

Since the answer is not unique, both conditions together are not sufficient.
Therefore, the answer is E.

Normally, in problems which require 2 equations, such as those in which the original conditions include 2 variables, or 3 variables and 1 equation, or 4 variables and 2 equations, each of conditions 1) and 2) provide an additional equation. In these problems, the two key possibilities are that C is the answer (with probability 70%), and E is the answer (with probability 25%). Thus, there is only a 5% chance that A, B or D is the answer. This occurs in common mistake types 3 and 4. Since C (both conditions together are sufficient) is the most likely answer, we save time by first checking whether conditions 1) and 2) are sufficient, when taken together. Obviously, there may be cases in which the answer is A, B, D or E, but if conditions 1) and 2) are NOT sufficient when taken together, the answer must be E.
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