Take a really basic DS question to break it down.
Is x divisible by 10?
1. x is divisible by 5
2. x is divisible by 2.
You have the answer choices, that stay the same in every DS question. Here is what you need to do:
You do not need to know the value of x, you just need to check if the information in the two statements is sufficient to answer the question "is x divisible by 10?". The answer needn't be a "yes" or a "no" either, it can be whichever as long as it always holds true. To do that, you must first evaluate each statement separately and then, if necessary, analyze them together.
So, first off, we look at statement 1 and COMPLETELY IGNORE statement 2. Our problem reads:
Is x divisible by 10? We know that x is divisible by 5.
OK, with this sort of a problem, pick the smallest two or three numbers that fit the description "x is divisible by 5": 5, 10 and 15. Of these, only 10 is also divisible by 10, while 5 and 15 are not. Since we get two different answers to the question "is x divisible by 10" (yes, if x = 10; no if x = 15), this information is not sufficient. So 1 is insufficient to answer the question in a definitive manner. By definitive, I understand that we ALWAYS KNOW FOR SURE, no matter the value of x, that it is or is not divisible by 10.
Now we look at statement 2 and WE COMPLETELY IGNORE statement 1. The problem will be:
Is x divisible by 10? We know that x is divisible by 2.
Again, pick a few numbers: 2, 4, 6, 8, 10... As was the case with the first statement, we can't say it's a definitive "yes" or "no", because this depends on the values: 2 IS NOT divisible by 10, but 10 IS divisible by 10. So 2 is insufficient by itself as well.
So now we're at step 3 of the problem, when we look at the two statements TOGETHER. The problem reads:
Is x divisible by 10? We know that x is divisible by 5 and x is divisible by 2.
Now things change a bit. Since 10 = 2*5, any number that is divisible AT THE SAME TIME by both 2 and 5 will also be divisible by 10 (this is a simple rule that I'll write down as a "footnote"). Pick a few values: 10, 20, 30... In this case, we can give a definitive answer to the question "is x divisible by 10?". Yes, it is, because no matter the value of x, as long as it is divisible by both 5 and 2 at the same time, it will be divisible by their product, 10. So both statements together are sufficient to answer the question with certainty, without needing to know x: x can be 10 or x can be 1450, as long as it fits the description.
Rule
Let the greatest common divisor of a and b be 1 (in other words, a and b do not share any divisors except 1). If a number n is divisible by both a and b, then n will also be divisible by their product, a*b. \
Hope this helps!
