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

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If n is a positive integer, what is the units digit of n? [#permalink] New post 15 Jun 2013, 22:14
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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

[Reveal] Spoiler:
Any other alternative solution
[Reveal] Spoiler: OA

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Last edited by Bunuel on 15 Jun 2013, 23:10, edited 1 time in total.
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Re: if n is a positive integer, what is the units digit of n? [#permalink] New post 15 Jun 2013, 22:18
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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] New post 15 Jun 2013, 22:27
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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

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] New post 15 Jun 2013, 23:13
Expert's post
fozzzy wrote:
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

[Reveal] Spoiler:
Any other alternative solution


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Re: If n is a positive integer, what is the units digit of n?   [#permalink] 15 Jun 2013, 23:13
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