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# If n is a positive integer, what is the units digit of n?

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Director
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If n is a positive integer, what is the units digit of n?  [#permalink]

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Updated on: 16 Jun 2013, 00:10
8
00:00

Difficulty:

45% (medium)

Question Stats:

70% (01:38) correct 30% (01:32) wrong based on 264 sessions

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If n is a positive integer, what is the units digit of n?

(1) the units digit of $$(n+4)^2$$ is 4
(2) the units digit of $$(n+3)^2$$ is 1

Any other alternative solution

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Originally posted by fozzzy on 15 Jun 2013, 23:14.
Last edited by Bunuel on 16 Jun 2013, 00:10, edited 1 time in total.
Edited the question.
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Re: If n is a positive integer, what is the units digit of n?  [#permalink]

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16 Jun 2013, 00:13
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##### General Discussion
Director
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Re: if n is a positive integer, what is the units digit of n?  [#permalink]

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15 Jun 2013, 23:18
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1
From statement 1 we get 2 values for n 4,8

$$(4+4)^2$$ = 4

$$(8+4)^2$$ = 4

From staement 2 we get 6,8

$$(6+3)^2$$ =1

$$(8+3)^2$$= 1

so combined from 4,8 and 6,8

we get 8
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Re: if n is a positive integer, what is the units digit of n?  [#permalink]

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15 Jun 2013, 23:27
3
if n is a positive integer, what is the units digit of n?

1) the units digit of $$(n+4)^2$$ is 4
2) the units digit of $$(n+3)^2$$ is 1

Given that alone they are not sufficient, combining them we get that:
because $$(n+4)^2$$ has a 4 as unit digit, $$n+4$$ or is 8 or is a two digit integer ending with a 2
because $$(n+3)^2$$ has a 1 as unit digit, $$n+3$$ or is 9 or is a two digit integer ending with a 1

Because the question asks for the unit digit of n, we can conclude that n will have a 8 as unit digit:
X8+4=K2
X8+3=K1
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Re: If n is a positive integer, what is the units digit of n?  [#permalink]

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02 Jan 2015, 03:38
Statement #1 ) : the unit digit of (n+4 ) ^ 2 is 4 : we know that the unit digit of 8^2 is 4 and also the unit digit of 12^2 . so n+4 could be 8 and 12

so n+4 = 8 and here n =4 OR n+4= 12 and Here n=8 so Two different integer and two different result . so Data # 1 Is insufficient.

Statement#2) : the unit digit of (n+3)^2 is 1 : we know that 9^2 has 1 in its unit digit and also 11^2 has 1 unit digit so n+3 = 9 OR 11 and n could be 6 OR 8 this Data

has 2 possible value and is ruled out too....

Combined info : we get 8 from 2 info in common so sufficient ... Answer is C
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Re: If n is a positive integer, what is the units digit of n?  [#permalink]

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08 Jun 2018, 17:39
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Re: If n is a positive integer, what is the units digit of n? &nbs [#permalink] 08 Jun 2018, 17:39
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