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06 Apr 2018, 02:49
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D
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A two digit number is randomly selected and multiplied by itself x times. What is the probability that the unit's digit of the resulting number is 1?
(1) x = 12
(2) x is a multiple of 4
Source: ExpertsGlobal
(1) x = 12
(2) x is a multiple of 4
Source: ExpertsGlobal
06 Apr 2018, 05:03
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benejo
We should know that every 4th power of odd numbers (except 5) always ends in '1'. So basically if N is an odd number ending in 1 or 3 or 7 or 9, then every fourth power of N (N^4 or N^8 or N^12 or N^16...) will end in '1'. 5 is excluded because every positive integral power of 5 ends in 5 only, and all even numbers are also excluded because integral powers of even numbers end in even, cannot end in 1.
So if a two digit number ends in 1 or 3 or 7 or 9 and if it is multiplied by itself 4 times or 8 times or 12 times or 16 times.. it will end in '1'. And in this case the probability will become 4/10; because out of 10 possibilities for last digit (0,1,2,3,4,5,6,7,8,9) - in four cases (1,3,7,9) will fourth power end in '1'.
In each of the two statements, x is a multiple of 4(12 is also a multiple of 4), so in either case - probability of it ending in '1' will be 4/10. So each statement alone is sufficient.
Hence D answer
General Discussion
30 Apr 2018, 00:28
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Hi amanvermagmat
Question is Probability(unit digit of (two digit number)^x = 1) ?
Statement 1: is clearly sufficient
I have one question for statement 2.
I thought, x can be 0(as 0 also multiple of 4), in which case, whatever double digit number maybe, unit digit will be always one. and probability = 1
But the question clearly mentions as the number is mulitplied itself by 'x' times, so x can't be zero, it has to be some positive integer value, which is multiple of 4(as per statement2).
So statement 2 is also sufficient.
Is my understanding correct?
Question is Probability(unit digit of (two digit number)^x = 1) ?
Statement 1: is clearly sufficient
I have one question for statement 2.
I thought, x can be 0(as 0 also multiple of 4), in which case, whatever double digit number maybe, unit digit will be always one. and probability = 1
But the question clearly mentions as the number is mulitplied itself by 'x' times, so x can't be zero, it has to be some positive integer value, which is multiple of 4(as per statement2).
So statement 2 is also sufficient.
Is my understanding correct?
