Fishing lures

abhirup1711 wrote:Bill owns a large collection of fishing lures consisting of tiny, small, medium and large lures that weigh 1,3,w and 5 grams each. The medium lures weigh more than the small but less than the large. If the product of the lure weights Bill sold was 216000 grams, how many medium lures did he sell?
6
5
4
3
2

This question would be much better if we just said that w (the weight of a medium lure) is an integer.
For example, the eighth root of 216,000 [i.e., 216,000^ (1/8)] is approximately 4.6] so it's possible that Bill has 8 lures that weigh this amount.
Using a similar technique, we could make all of the answer choices work.

That said, here's the conventional solution (that assumes the medium lures weight 4 grams each) . . .

First find the prime factorization of 216,000
216,000 = (2)(2)(2)(2)(2)(2)(3)(3)(3)(5)(5)(5)
So, for example, since there are three 5's in the factorization, then Bill must own three of the large (5-gram) lures.

Since there are no lures that weigh 2 grams each, we'll have to pair up the six 2's to get three 4's instead:
216,000 = (4)(4)(4)(3)(3)(3)(5)(5)(5)
If medium lures weigh 4 grams each, we can see that Bill owns three of them.

Answer = D

Cheers,
Brent