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What is the units digit of positive integer n?

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

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New post 20 Nov 2016, 09:14
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

75% (00:54) correct 25% (01:21) wrong based on 111 sessions

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

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New post 20 Nov 2016, 10:20
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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New post 20 Nov 2016, 12:20
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!

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

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New post 20 Nov 2016, 19:34
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.

The answer is B.
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What is the units digit of positive integer n?  [#permalink]

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New post 23 Nov 2016, 13:37
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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New post 28 Feb 2018, 19:56
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Re: What is the units digit of positive integer n? &nbs [#permalink] 28 Feb 2018, 19:56
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