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# What is the units digit of positive integer n?

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Math Expert
Joined: 02 Sep 2009
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What is the units digit of positive integer n?  [#permalink]

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20 Nov 2016, 10:14
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78% (00:55) correct 22% (01:20) wrong based on 124 sessions

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What is the units digit of positive integer n?

(1) When dividing n by 11, the remainder is 3.

(2) When dividing n by 10, the remainder is 6.

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Re: What is the units digit of positive integer n?  [#permalink]

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20 Nov 2016, 11:20
Bunuel wrote:
What is the units digit of positive integer n?

(1) When dividing n by 11, the remainder is 3.

(2) When dividing n by 10, the remainder is 6.

Given n is a positive integer

From statement 1
n=11k+3
i.e., n= 3, 14, 25, 36, 47, 58, 69, 80, 91, 102, 113, 124, 135, 146..
As you can see units digit keeps varying
Hence insufficient

From statement 2
n=10k+6
i.e., n= 6, 16, 26, 36, 46, 56, 66, 76, 86, 96, 106, 116, 126, 136, 146...

Combining we see that
n=36, 146, ....
units digit= 6
Sufficient
Hence C
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What is the units digit of positive integer n?  [#permalink]

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20 Nov 2016, 13:20
Good question! It threw me off for a while.

Statements 1 and 2 are individually insufficient, therefore A, B and D are out of the picture.

If you take both statements together, you get the following expression:
Quote:
10x+6 = 11y+3

which a linear equation with two variables.

Ideally, since this is a single linear equation with two variables, it should not be possible to get a specific answer. However, the units digit will always be 6 for any number multiplied into 10 plus 6!

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Re: What is the units digit of positive integer n?  [#permalink]

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20 Nov 2016, 20:34
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We need to find the units digit of n.
(1) $$n=13k+3$$, then n could be 3, 16, 29, 42,... so the units digit could be 3, 6, 9, 2, ... Insufficient
(2) When dividing n by 10, the remainder is 6.
In fact, finding the units digit of n is finding the remainder when dividing n by 10. So the units digit of n is 6. Sufficient.

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What is the units digit of positive integer n?  [#permalink]

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23 Nov 2016, 14:37
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Bunuel wrote:
What is the units digit of positive integer n?

(1) When dividing n by 11, the remainder is 3.

(2) When dividing n by 10, the remainder is 6.

(1) Insufficient
n = 11q+3
Possible values of n are 3, 14, 25 36, .... We can not eliminate any of these possibilities with the given information.

(2) Sufficient
n=10q+6
Possible values of n are 6, 16, 26, 36, .... No matter the value of n, the units digit will always equal 6.
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Re: What is the units digit of positive integer n?  [#permalink]

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28 Feb 2018, 20:56
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Re: What is the units digit of positive integer n?   [#permalink] 28 Feb 2018, 20:56
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