Hey guys,
Great question, and great work on statement 1. I've always found the words-and-not-equations problems to be a little tricky (your mind wants to see "math", but you're seeing more verbal-style logic), but manageable if you take the time to flush out the statements and even use examples to help yourself get the point of what the statement is saying.
Statement 1:
EVERY factor of s is also a factor of r
This means that whatever you can divide into s, you can also divide into r. If s is divisible by 2, 3, and 6, then r is also divisible by 2, 3 and 6. You can't, therefore, put anything into the denominator that wouldn't cancel with the numerator...whatever is in s will automatically be in r (which may or may not have extra factors), so there's no choice but to say that r is divisible by s.
Statement 2:
EVERY PRIME factor of s is also a prime factor of r
Here, the difference is that we're only talking about prime factors. Say that s has the prime factors 2 and 3...that means that r will also have prime factors 2 and 3. But that's all we know about r - we can guarantee that it's a multiple of 6 in that case, but s could have as many 2s and 3s as we want to give it and we'd still only be able to know that r is divisible by 2 and 3. Say that s is 36 - its prime factorization is 2*2*3*3...but we only know that x has the same "prime factors", not the same "prime factors and number of prime factors". Because statement 2 allows for both r/s = 6/6 and r/s = 6/36, it's not sufficient.
For really any DS problems, but especially those that give written rules that may seem mathematically nebulous because you don't quite have an equation/inequality, I like to test each statement by trying to stretch the rule as far as it will go. If you come up with a hypothetical that isn't specifically prohibited by the rule (like that 6/36 above), it's allowable.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
Looking for GMAT practice questions? Try out the Veritas Prep Question Bank.
Learn More.
