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A two digit number is randomly selected and multiplied by itself x

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A two digit number is randomly selected and multiplied by itself x  [#permalink]

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New post 06 Apr 2018, 02:49
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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
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Joined: 22 Aug 2013
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Re: A two digit number is randomly selected and multiplied by itself x  [#permalink]

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New post 06 Apr 2018, 05:03
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benejo wrote:
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


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
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Re: A two digit number is randomly selected and multiplied by itself x  [#permalink]

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New post 30 Apr 2018, 00:28
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?
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Re: A two digit number is randomly selected and multiplied by itself x  [#permalink]

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New post 30 Apr 2018, 00:33
hellosanthosh2k2 wrote:
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?


Hi

Yes, my reasoning is also same as yours. As it says in the question stem that number is multiplied by itself 'x' times, so saying a number multiplied by itself '0' times doesn't make sense. Hence we reject that possibility. x has to be 1 or more. And both statements mention that its a multiple of 4, so.. D answer
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Re: A two digit number is randomly selected and multiplied by itself x  [#permalink]

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New post 30 Apr 2018, 01:58
amanvermagmat wrote:
hellosanthosh2k2 wrote:
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?


Hi

Yes, my reasoning is also same as yours. As it says in the question stem that number is multiplied by itself 'x' times, so saying a number multiplied by itself '0' times doesn't make sense. Hence we reject that possibility. x has to be 1 or more. And both statements mention that its a multiple of 4, so.. D answer


Thanks amanvermagmat
Re: A two digit number is randomly selected and multiplied by itself x &nbs [#permalink] 30 Apr 2018, 01:58
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