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Founder  Joined: 18 Apr 2015
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If x is a positive integer such that the units digit of x^3 [#permalink]
Expert's post 00:00

Question Stats: 66% (00:55) correct 33% (00:48) wrong based on 39 sessions
If x is a positive integer such that the units digit of $$x^3$$ is 3, what is the units digit of $$x^{15}$$ ?

A. 1
B. 3
C. 5
D. 7
E. 9
[Reveal] Spoiler: OA

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Manager Joined: 25 Nov 2017
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Kudos [?]: 48 , given: 5

Re: If x is a positive integer such that the units digit of x^3 [#permalink]
If x^3 has 3 as unit digit, it must be 7^3 since it equals 343.
The 7 has the following pattern
7 ^1 7
7^2 9
7^3 3
7^4 1
7^5 7 and so one
So 7^15 has a 3 as unit digits. Since I did it quickly, I am pretty sure that it is false. Any help ?
Founder  Joined: 18 Apr 2015
Posts: 13432
Followers: 292

Kudos [?]: 3418 , given: 12318

Re: If x is a positive integer such that the units digit of x^3 [#permalink]
Expert's post
Explenation

$$X^3$$ for ending in 3 must be $$7^3= 343$$

Seeing a repeating pattern for 7 every four numbers 7 starts over again.

A cycle of 14 end in 9. So, the next number must be ending in 3.

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GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Manager Joined: 29 Nov 2017
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Re: If x is a positive integer such that the units digit of x^3 [#permalink]
1
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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. Intern Joined: 26 Apr 2019
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Re: If x is a positive integer such that the units digit of x^3 [#permalink]
1
KUDOS
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 Intern Joined: 27 Apr 2019
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Kudos [?]: 3  , given: 0

Re: If x is a positive integer such that the units digit of x^3 [#permalink]
2
KUDOS
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!
Intern Joined: 21 May 2020
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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! Re: If x is a positive integer such that the units digit of x^3   [#permalink] 17 Jun 2020, 16:07
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