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

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fozzzy
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If n is a positive integer, what is the units digit of n? [#permalink] New post   Updated on: 16 Jun 2013, 00:10
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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

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C

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.
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Re: If n is a positive integer, what is the units digit of n? [#permalink] New post   16 Jun 2013, 00:13
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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

Show Spoiler
Any other alternative solution


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Re: if n is a positive integer, what is the units digit of n? [#permalink] New post   15 Jun 2013, 23:18
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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, 23:27
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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   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 :lol: :lol: :lol: :lol:
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Re: If n is a positive integer, what is the units digit of n? [#permalink] New post   14 Oct 2019, 23:23
Unit digit of n: 0 1 2 3 4 5 6 7 8 9
Statement 1:
Unit digit of n+4: 4 5 6 7 8 9 0 1 2 3
Unit digit of(n+4)^2: 6 5 6 9 4 1 0 1 4 9
Thus, unit digit can be 4 or 8, insufficient

Statement 2:
Unit digit of n+3: 3 4 5 6 7 8 9 0 1 2
Unit digit of(n+3)^2: 9 6 5 6 9 4 1 0 1 4
Thus, unit digit can be 6 or 8, insufficient

Statement 1 & 2: unit digit is 8, sufficient.
Choose C.
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Re: If n is a positive integer, what is the units digit of n? [#permalink] New post   27 May 2023, 14:47
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Re: If n is a positive integer, what is the units digit of n? [#permalink]
27 May 2023, 14:47
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