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# If m is a positive integer with k nonzero digits and no other digits.

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Math Expert
Joined: 02 Sep 2009
Posts: 49231
If m is a positive integer with k nonzero digits and no other digits.  [#permalink]

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20 Jan 2017, 07:39
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Difficulty:

75% (hard)

Question Stats:

45% (01:17) correct 55% (01:15) wrong based on 107 sessions

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If m is a positive integer with k nonzero digits and no other digits. Which digits appear in the number m?

(1) The sum of the digits is k
(2) k = 3

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Joined: 28 Dec 2016
Posts: 7
Re: If m is a positive integer with k nonzero digits and no other digits.  [#permalink]

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20 Jan 2017, 10:07
Ans is C.

Consider question stem
K non zero digits are there in m.it can be any random integer without zeroes.

With st1 we have that the sum of digits is K. The no has to be all 1's. Like 11,111,1111 etc. No unique soln.
With st2 we have k=3. Here the integer can be any 3 digit integer without zeroes. No unique soln.

Considering both statements we get 111 as the unique soln.
Therefore ans is C.

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Joined: 21 May 2013
Posts: 649
Re: If m is a positive integer with k nonzero digits and no other digits.  [#permalink]

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11 Feb 2017, 09:59
Bunuel wrote:
If m is a positive integer with k nonzero digits and no other digits. Which digits appear in the number m?

(1) The sum of the digits is k
(2) k = 3

Bunuel,

Statement 1: The sum of the digits is k: if k=2, meaning k has 2 digits, m can be 20,11 and if k=3, m can be 111:So not sufficient
Statement 2: k=3:Even in this case , if k=3, m can be 111, 123 and so on.Insufficient
Using both, m can be 111,102,201 and so on.

Math Expert
Joined: 02 Sep 2009
Posts: 49231
Re: If m is a positive integer with k nonzero digits and no other digits.  [#permalink]

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11 Feb 2017, 11:53
1
KS15 wrote:
Bunuel wrote:
If m is a positive integer with k nonzero digits and no other digits. Which digits appear in the number m?

(1) The sum of the digits is k
(2) k = 3

Bunuel,

Statement 1: The sum of the digits is k: if k=2, meaning k has 2 digits, m can be 20, 11 and if k=3, m can be 111:So not sufficient
Statement 2: k=3:Even in this case , if k=3, m can be 111, 123 and so on.Insufficient
Using both, m can be 111,102,201 and so on.

Check the highlighted part.
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Re: If m is a positive integer with k nonzero digits and no other digits.  [#permalink]

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13 Feb 2017, 05:02
The question asks for "Which digits appear in the number m"

Referring to the first option
(1) The sum of the digits is k --> only way the sum of K nonzero digits can be equal to sum of 'K' is when all the digits are 1.
If k=3 then 3 nonzero digits and sum of 3.... each digit should be 1. Likewise, If k=4 then 4 nonzero digits and sum of 4.... again each digit should be 1.
Hence A is sufficient

(2) k = 3
This doesn't help much as it gives only number of digits in m, but no hint on what digits appear

Bunuel,
Please let me know if my understanding is right.
Intern
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Posts: 15
Re: If m is a positive integer with k nonzero digits and no other digits.  [#permalink]

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25 May 2017, 19:23
If m is a positive integer with k nonzero digits and no other digits. Which digits appear in the number m?

(1) The sum of the digits is k
(2) k = 3

St 1: Sum of digits = number of digits
This is only possible in two scenarios- 1) Either some of the digits are zero (but all digits must be nonzero as per the statement) Hence reject.
2) Or all digits = 1 ( This is the right answer)
Sufficient

St 2:
K=3
digits can be 111, 123, 212 ... and so on
Not sufficient,

Senior Manager
Joined: 15 Jan 2017
Posts: 367
Re: If m is a positive integer with k nonzero digits and no other digits.  [#permalink]

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23 Sep 2017, 07:17
I have a query as below:

If m is a positive integer with k nonzero digits and no other digits. Which digits appear in the number m?

(1) The sum of the digits is k --> How do we know that K is 3? It could 11,111,1111,11111 - this way number of digits equal to sum of digits. So how is M a fixed value?
(2) k = 3

Thus C; by combing K = 3; gives a limit to number of digits and sum of digits.
Request experts to help me with my reasoning.
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Joined: 25 Feb 2013
Posts: 1213
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Re: If m is a positive integer with k nonzero digits and no other digits.  [#permalink]

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23 Sep 2017, 07:40
1
I have a query as below:

If m is a positive integer with k nonzero digits and no other digits. Which digits appear in the number m?

(1) The sum of the digits is k --> How do we know that K is 3? It could 11,111,1111,11111 - this way number of digits equal to sum of digits. So how is M a fixed value?
(2) k = 3

Thus C; by combing K = 3; gives a limit to number of digits and sum of digits.
Request experts to help me with my reasoning.

The question is not asking to find the value of "$$m$$" but to find the digit/s that appear/s in "$$m$$"

as You have rightly mentioned from Statement 1 we know that m has only one digit $$1$$. Hence Sufficient
Re: If m is a positive integer with k nonzero digits and no other digits. &nbs [#permalink] 23 Sep 2017, 07:40
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