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# If m and n are positive integers, what is the units’ digit of

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If m and n are positive integers, what is the units’ digit of  [#permalink]

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27 Aug 2018, 11:12
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If m and n are positive integers, what is the units’ digit of $$7^{m+3+4n}$$ ?

(1) m=7

(2) n=2

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Re: If m and n are positive integers, what is the units’ digit of  [#permalink]

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27 Aug 2018, 11:57
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The cyclicity of 7 is 4 , with last digits 7^1=7, 7^2=9, 7^3=3, 7^4=1
now we need to know the value of m+3+4n to determine the units digit of 7^(m+3+4n)
St1) m=7 i.e 7+3+4n=10+4n
If we divide 10+4n by 4(cyclicity no.) it will always yield remainder 2. So the units digit is same as 7^2 =9
Sufficient
St2) n=2 i.e m+3+8= m+11 . If we divide by 4 , we cannot determine the exact remainder , as different values of m will yield different remainders and hence different unit digits.
Not Sufficient

Ans :A
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Re: If m and n are positive integers, what is the units’ digit of  [#permalink]

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27 Aug 2018, 12:48
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carcass wrote:
If m and n are positive integers, what is the units’ digit of $$7^{m+3+4n}$$ ?

(1) m=7

(2) n=2

Discussed here bro.

https://gmatclub.com/forum/if-m-and-n-a ... fl=similar
Re: If m and n are positive integers, what is the units’ digit of   [#permalink] 27 Aug 2018, 12:48
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