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Moderator  Joined: 18 Apr 2015
Posts: 5888
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Kudos [?]: 1154 , given: 5471

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

Question Stats: 53% (00:49) correct 46% (00:41) wrong based on 15 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

_________________
Manager Joined: 25 Nov 2017
Posts: 51
Followers: 0

Kudos [?]: 41 , 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 ?
Moderator  Joined: 18 Apr 2015
Posts: 5888
Followers: 96

Kudos [?]: 1154 , given: 5471

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.

B is the answer
_________________ Manager Joined: 29 Nov 2017
Posts: 190
Location: United States
GRE 1: Q142 V146 WE: Information Technology (Computer Software)
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Kudos [?]: 78  , given: 99

Re: If x is a positive integer such that the units digit of x^3 [#permalink]
1
KUDOS
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. Re: If x is a positive integer such that the units digit of x^3   [#permalink] 10 May 2018, 10:38
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