sampath wrote:Set S consists of numbers 2, 3, 6, 48 and 164. Number K is computed by multiplying one random
number from set S by one of the first 10 non-negative integers, also selected at random. If Z = 6^k, what is the probability that 678463 is not a multiple of Z?
Ans:[spoiler]9/10[/spoiler]
Hi! This is a truly bizarre question - what's the source?
In any case, it can be solved fairly quickly if you can actually decipher it and understand a few underlying concepts.
First, we note that 6^k will be even for all positive values of k. Since 678463 is odd, if k is positive then 678463 will NOT be a multiple of 6^k.
Second, we note that "non-negative" does NOT mean "positive"; "non-negative" includes 0. So, the first 10 non-negative integers are:
{0, 1, 2, 3, ... , 9}.
Third, we note that any positive number to the exponent 0 equals 1, which is a factor of 678463.
Putting it all together:
there's a 1/10 chance that we're multiplying a number from set S by 0; so, there's a 1/10 chance that k=0. Consequently, there's a 9/10 chance that k is positive. Accordingly, the answer is 9/10.
The question is interesting, but unlike anything I've seen on the GMAT or from a reliable source - for those who read it and shook your heads, I wouldn't worry about it too much.
