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Set S consists of numbers 2, 3, 6, 48, and 164. Number K is [#permalink]
 28 Mar 2008, 02:32
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66% (01:37) wrong based on 1 sessions
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 678,463 is not a multiple of Z? a. 10% b. 25% c. 50% d. 90% e. 100%
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sondenso 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 678,463 is not a multiple of Z? I first looked at 678,463. The number is not a multiple of 2,3,7 or 9. Then I looked at Z. Z = 6*6*6* ...*6 (k times). If 678,463 has to be a multiple of Z, it has to be a multiple of 6. Another case is that the integer we pick is 0. Probability of picking 0 as integer is 1/10. If integer is 0, Z becomes 1 and 678,463 becomes a multiple of Z. Hence answer is D 90%. What is the answer?
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I think the answer is 90%, because the probablity of choosing 0 from 0-9 is 10%.
If 0 is chosen than only we have 678463 is multiple of 6^0 (= 1).
If any other number is chosen, then 678463 is not multiple of 6 (because 6^k)
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Are the exact numbers in the set irrelevant to finding the answer? Would any positive integers have worked in lieu of 2, 3, 6, 48, and 164?
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I was not able to understand the solution here.
Bunuel, do you mind explaining the approach to such problems?
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sondenso 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 678,463 is not a multiple of Z?
a. 10%
b. 25%
c. 50%
d. 90%
e. 100% S=\{2,3,6,48,164\} and set of first 10 non-negative integers, say T=\{0,1,2,3,4,5,6,7,8,9\}. K=s*t, where s and t are random numbers from respective sets. 678,463 is an odd number. The only case when 6^k IS a factor of 678,463 is when k equals to 0 (in this case 6^k=6^0=1 and 1 is a factor of every integer). Because if k>0, then 6^k=even and even number can not be a factor of odd number 678,463. Hence 6^k NOT to be a factor of 678,463 we should pick any number from S and pick any number but 0 from T: P=1*\frac{9}{10}=\frac{9}{10}. Answer: D.
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Bunuel, I agree that 463 is an odd number but 678 is not odd but an even number. What am I missing here... 
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