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Factor + Probability

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Factor + Probability

by Anindya Madhudor » Fri Dec 14, 2012 10:32 am
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?

a. 1/10
b. 3/10
c. 5/10
d. 7/10
e. 9/10

OA: E
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by puneetkhurana2000 » Fri Dec 14, 2012 11:01 am
678463 is not a multiple of either 2,3 so definitely not of 6, only possibility is 6^0 =1

So for 678463 to be multiple of Z = 6^k, k needs to be 0 as 6^0 = 1.

So, total ways = 5*10 = 50 (picking all integers from 0 to 9 -- 5 times)

Favorable ways = 45 (picking all integers from 0 to 9 but 0 -- 5 times)

P = 45/50 = [spoiler]9/10[/spoiler].
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