gmat prep If r and s are positive integers is r/s an integer

[Guest]

Hi guys need help with this. Does it matter if r>s or s>r?

If r and s are positive integers is r/s an integer?

1. Every factor if s is also a factor of r
2. Every prime factor of s is also a prime factor of r

[Guest]

Hi guys need help with this. Does it matter if r>s or s>r?

If r and s are positive integers is r/s an integer?

1. Every factor if s is also a factor of r (32/16) etc...can't beat this example
2. Every prime factor of s is also a prime factor of r (4/8) They are both made up of all 2's! NO! (8/4) YES!

[RonPurewal]

Hi guys need help with this. Does it matter if r>s or s>r?

If r and s are positive integers is r/s an integer?

1. Every factor if s is also a factor of r
2. Every prime factor of s is also a prime factor of r

well sure it matters which one is greater. if s is greater than r, it's impossible for r/s to be a whole number (it will automatically be a fraction less than 1).

first, rephrase the question: is s a factor of r? or, is r a multiple of s? or, is r divisible by s? etc.
you shouldn't leave the question in its original form; the original form is just sort of ugly.

(1)
here's the easiest way to handle this one:
s is a factor of itself.
therefore, since every factor of s (including s itself) is a factor of r, s is a factor of r.
sufficient.

you can do this part with a whole lot of song and dance involving prime numbers, but i like this argument because it's simple and elegant.

(2)
this just means that r and s are combinations of the same prime factors, but you don't know how many times each of those prime factors appears. for instance, 10 and 1000 are both made up of 2's and 5's. therefore, (r, s) could be (10, 1000), in which case the answer is 'no', or (1000, 10), in which case the answer is 'yes'.
insufficient.

ans = a

[vicvishal_81]

Ron, you are a genius. I have seen many of your responses to GMAT questions and I am very much impressed. You make the most tough things look easy. Thanks a lot.

[RonPurewal]

Ron, you are a genius. I have seen many of your responses to GMAT questions and I am very much impressed. You make the most tough things look easy. Thanks a lot.

thanks for the kind words.

[mazurd]

I see that this thread is pretty old, but I am just now discovering the joys of some of these tricky questions...

I have a concern about this question that has been driving me nuts. I chose D instead of A. Looking at your explanation (and the GMAC explanation), I see what I did wrong. I read statement 2 as "Every single prime factor of s is also a prime factor of r," while the statement actually meant "every unique prime factor of s is also a unique prime factor of r." The annoying part is that I actually thought of that possible distinction when I was doing this question, but then decided that the question would have specified "unique" if it meant "unique," and thus said that statement 2 was suff since if every single prime factor of a x is also in the prime factor tree of y then y is divisible by x.

So, since it is unlikely that I will change the minds of the GMAC on this one, what is a good way to not fall into this "trap" of misinterpretation again?

Thanks,
Dave

[RonPurewal]

It actually doesn't matter whether you regard the "repeated" primes as things or not.

E.g., let's say I have list A = 2, 2, 2, 2, 2, 3, 5, and list B = 2, 3, 5, 7.

Is every member of list A in list B?
You can consider all the 2's if you want, but the answer is still the same:
Is 2 in list B? Yes.
Is 2 in list B? Yes.
Is 2 in list B? Yes.
Is 2 in list B? Yes.
Is 2 in list B? Yes.
Is 3 in list B? Yes.
Is 5 in list B? Yes.
There you go.

Really, the issue here (or, more accurately, non-issue) boils down to whether you should ask the first question ("Is 2 in list B?") five times, because there are five 2's, or just once.

[RonPurewal]

--

If there's any misinterpretation here, it's happening because you aren't reading these like normal statements, in everyday normal English.

Consider the following 2 examples:

1/
A, A, A, A, A, C, E, Q, Q, Z
Are all the members of this list in the English alphabet?
Yes.
(You're not going to complain that "the alphabet" fails to contain five different A's, because ... well, because you just aren't. That thought probably wouldn't even occur to you until you read this.)

2/
You eat hamburgers, hot dogs, and fries, but also vegetables and fruits and rice and chicken and so on.
I eat 10 hamburgers and 22 hot dogs every day, and nothing else.
Is every food that I eat also in your diet?
Yes.

Same deal here. You just have to import similar thinking into the test.