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Re: If x is a positive integer such that the units digit of x^3 [#permalink]
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How about we divide 15/3 as it goes completely in 15.. the 15 power will have its unit digit ending as 3.. hence the option is B.
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Re: If x is a positive integer such that the units digit of x^3 [#permalink]
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First of all, we can find out that when we multiply the same unit digit, they are following the same law
eg. 23*23=529, 63*63=3969 the unit digit remain the same

When x3' unit digit is 3, and x15=x3*x3*x3*x3*x3
3*3=9, 3*3*3=27, 3*3*3*3=81, 3*3*3*3*3=243,
so the unit digit is 3
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Re: If x is a positive integer such that the units digit of x^3 [#permalink]
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Given : Units digit of x^3 is 3
To find : Units digit of x^15

Steps to solve:
1. x^15 can be written as (x^3)^5
2. W.K.T, x^3 is 3
3. Now , simplifying step 1 we get, i.e. 3^5 = 243

observe, the units digit here is 3

Hence, the option is B.

P.S. To solve 3^5 quickly, wk.t, 3^2=9
so, 3^5 it boils down to (3^2) (3^2) 3 =9*9*3=81*3=243

Hope, this helps!
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Re: If x is a positive integer such that the units digit of x^3 [#permalink]
curiouscat wrote:
Given : Units digit of x^3 is 3
To find : Units digit of x^15

Steps to solve:
1. x^15 can be written as (x^3)^5
2. W.K.T, x^3 is 3
3. Now , simplifying step 1 we get, i.e. 3^5 = 243

observe, the units digit here is 3

Hence, the option is B.

P.S. To solve 3^5 quickly, wk.t, 3^2=9
so, 3^5 it boils down to (3^2) (3^2) 3 =9*9*3=81*3=243

Hope, this helps!


I read it the same way as you and solved it the same way too. Thanks for re-assuring this method is the quickest!
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Re: If x is a positive integer such that the units digit of x^3 [#permalink]
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