Hey Lime,

Questions like this are a little dangerous on the GMAT, because they encourage you to worry about things that, if you worried about them on the real test, would be an enormous waste of time. If you were doing this on the GMAT, you'd simply try the first few x values, and extrapolate out:

x = 1 --> 11/8; x = 2 --> 19/14; x = 3 --> 27/20; x = 4 --> 35/26; x = 5 --> 43/32

You can immediately see that nothing's ever going to reduce. If you wanted to know the reason, it's nothing particularly interesting, merely that the primes don't ever line up. The numerator is always odd, and the denominator even, so it'll never reduce by any even number. And 6x + 2 can never be a multiple of 3, because 6x is a multiple of 3 and you're adding 2 to it.

Is there something more interesting that one should extrapolate from this? If so, I don't know what it is! : )

-t

lime777 wrote:Is there a positive integer x such that the fraction (8x+3)/(6x+2) is not in lowest terms? Why or why not?

Let us assume that the fraction is not in lowest term, i.e. (8x + 3) is a multiple of (6x + 2) or (8x + 3) = k*(6x + 2), where k is some positive integer definitely greater than 1.

So, (8x + 3) = (6kx + 2k)
--> x = (2k - 3)/(8 - 6k)

As k > 1, (2k - 3) > 0 but (8 - 6k) < 0
This indicates x cannot be positive --> A contradiction

Hence, our initial assumption is definitely not true, i.e. the fraction is in fact in lowest term.