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Math Expert V
Joined: 02 Sep 2009
Posts: 55228
M01-06  [#permalink]

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Difficulty:   5% (low)

Question Stats: 86% (00:47) correct 14% (00:58) wrong based on 204 sessions

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If $$m$$ and $$n$$ are positive integers is $$\frac{m}{n}$$ an integer?

(1) $$m$$ is a multiple of 14

(2) $$n$$ is a divisor of 14

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Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re M01-06  [#permalink]

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Official Solution:

(1) $$m$$ is a multiple of 14. Not sufficient as no info about $$n$$.

(2) $$n$$ is a divisor of 14. Not sufficient as no info about $$m$$.

(1)+(2) As from (2) $$n$$ is a divisor of 14 then it must be a divisor of every multiple of 14, therefore it's a divisor of $$m$$ too. Sufficient.

Answer: C
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Intern  B
Joined: 03 Jun 2013
Posts: 19
Concentration: Strategy, General Management
GMAT 1: 520 Q38 V32 GMAT 2: 530 Q44 V22 GMAT 3: 670 Q47 V34 WE: Information Technology (Consulting)
Re: M01-06  [#permalink]

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Bunuel wrote:
Official Solution:

(1) $$m$$ is a multiple of 14. Not sufficient as no info about $$n$$.

(2) $$n$$ is a divisor of 14. Not sufficient as no info about $$m$$.

(1)+(2) As from (2) $$n$$ is a divisor of 14 then it must be a divisor of every multiple of 14, therefore it's a divisor of $$m$$ too. Sufficient.

Answer: C

I got E for this question. Followed the below approach.
What if we consider m=14 and n=28 => Not an integer
If m=28, n=28 => integer.

What did i do wrong?
Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re: M01-06  [#permalink]

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1
arunpkumar wrote:
Bunuel wrote:
Official Solution:

(1) $$m$$ is a multiple of 14. Not sufficient as no info about $$n$$.

(2) $$n$$ is a divisor of 14. Not sufficient as no info about $$m$$.

(1)+(2) As from (2) $$n$$ is a divisor of 14 then it must be a divisor of every multiple of 14, therefore it's a divisor of $$m$$ too. Sufficient.

Answer: C

I got E for this question. Followed the below approach.
What if we consider m=14 and n=28 => Not an integer
If m=28, n=28 => integer.

What did i do wrong?

(2) says that n is a divisor of 14 but if n = 28, then it's not a divisor of 14, it's a multiple of 14.
_________________
Intern  B
Joined: 03 Jun 2013
Posts: 19
Concentration: Strategy, General Management
GMAT 1: 520 Q38 V32 GMAT 2: 530 Q44 V22 GMAT 3: 670 Q47 V34 WE: Information Technology (Consulting)
Re: M01-06  [#permalink]

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Bunuel wrote:
arunpkumar wrote:
Bunuel wrote:
Official Solution:

(1) $$m$$ is a multiple of 14. Not sufficient as no info about $$n$$.

(2) $$n$$ is a divisor of 14. Not sufficient as no info about $$m$$.

(1)+(2) As from (2) $$n$$ is a divisor of 14 then it must be a divisor of every multiple of 14, therefore it's a divisor of $$m$$ too. Sufficient.

Answer: C

I got E for this question. Followed the below approach.
What if we consider m=14 and n=28 => Not an integer
If m=28, n=28 => integer.

What did i do wrong?

(2) says that n is a divisor of 14 but if n = 28, then it's not a divisor of 14, it's a multiple of 14.

aah i get it now! thank you
Intern  Joined: 05 Dec 2013
Posts: 29
Re: M01-06  [#permalink]

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Hi Bunuel,
Please confirm if the below is correct...
If it was given : m is not necessarily an integer then the answer would be E ?
My reasoning:
1) m could 14 x integer or
m could be 14 x 2.5

2 ) n = 2 or 7

Then by combining 1 and 2, m/n can still be fraction ( 2.5 in this case) hence E
Intern  B
Joined: 26 Dec 2016
Posts: 19
Re: M01-06  [#permalink]

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I'm quite sure that 2.5 x 14 is no valid multiple of 14
Intern  B
Joined: 24 Feb 2017
Posts: 35
Schools: CBS '20 (S)
GMAT 1: 760 Q50 V42 Re: M01-06  [#permalink]

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I got this question wrong since I didn't think "Divisor" can refer to a "Factor".

From what I knew, a number divided by a divisor, may/may not yield a remainder. Doesn't say anything about the divisor being a factor.

Turns out a divisor and factor are the same Intern  B
Joined: 26 May 2017
Posts: 25
GMAT 1: 620 Q48 V27 M01-06  [#permalink]

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Statement 1:
m = 14k, where k is a positive integer. Can't say if m/n is an integer since 14/3 is not an integer and 14/7 is an integer.

Statement 2:
n is a divisor of 14. This means n can be 1, 2, 7 or 14. But the statement alone does not tell us about m/n. m/n could be 5/7 (is not an integer) or 14/7 (is an integer).

Statements 1+2:

m = 14k and n=1,2,7 or 14. For all the 4 values of n, m/n is an integer. Hence this is sufficient to answer weather m/n is an integer.
Hence answer is C

----- Crave Your Rave -------
Manager  B
Joined: 02 Jan 2017
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Location: Pakistan
Concentration: Finance, Technology
GMAT 1: 650 Q47 V34 GPA: 3.41
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Re M01-06  [#permalink]

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The attempted questions should also show the answer test taker opted for initially when clicked on explanation. After a long test you don't remember what option you chose and it can help you assess your own mindset while making a particular mistake. But this should only be shown when clicked on explanation. otherwise, it needs to be hidden.
Manager  B
Joined: 02 Jan 2017
Posts: 71
Location: Pakistan
Concentration: Finance, Technology
GMAT 1: 650 Q47 V34 GPA: 3.41
WE: Business Development (Accounting)
Re M01-06  [#permalink]

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I think this is a high-quality question and I agree with explanation.
Retired Moderator G
Joined: 11 Aug 2016
Posts: 376
Re: M01-06  [#permalink]

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Bunuel wrote:
Official Solution:

(1) $$m$$ is a multiple of 14. Not sufficient as no info about $$n$$.

(2) $$n$$ is a divisor of 14. Not sufficient as no info about $$m$$.

(1)+(2) As from (2) $$n$$ is a divisor of 14 then it must be a divisor of every multiple of 14, therefore it's a divisor of $$m$$ too. Sufficient.

Answer: C

Please help me clear my confusion:
When statement 2 says that "'n' is a divisor of 14", why did we assume that it is a factor of 14 ?
since it is a divisor, it can or can not completely divide 14 or any of its multiples.

Any help would be appreciated.
Thanks in Advance!! _________________
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Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re: M01-06  [#permalink]

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Rumanshu1990 wrote:
Bunuel wrote:
Official Solution:

(1) $$m$$ is a multiple of 14. Not sufficient as no info about $$n$$.

(2) $$n$$ is a divisor of 14. Not sufficient as no info about $$m$$.

(1)+(2) As from (2) $$n$$ is a divisor of 14 then it must be a divisor of every multiple of 14, therefore it's a divisor of $$m$$ too. Sufficient.

Answer: C

Please help me clear my confusion:
When statement 2 says that "'n' is a divisor of 14", why did we assume that it is a factor of 14 ?
since it is a divisor, it can or can not completely divide 14 or any of its multiples.

Any help would be appreciated.
Thanks in Advance!! A divisor = a factor, it's an integer which divides another integer without a remainder.
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Intern  B
Joined: 20 Dec 2013
Posts: 12
Re: M01-06  [#permalink]

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can n be equal to SQRT(14)?
Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re: M01-06  [#permalink]

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urvi470 wrote:
can n be equal to SQRT(14)?

No, because we are told that n is a positive integer, while $$\sqrt{14}$$ is not.
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Re: M01-06  [#permalink]

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Please help me to understand why m and n cant be the below
m = 28 (multiple of 14)
n = 42 (divisor of 14)

Then m/n will be 2/3
Math Expert V
Joined: 02 Sep 2009
Posts: 55228
Re: M01-06  [#permalink]

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joneyb wrote:
Please help me to understand why m and n cant be the below
m = 28 (multiple of 14)
n = 42 (divisor of 14)

Then m/n will be 2/3

42 is a multiple of 14, not a divisor. 14 is divisor of 42.
_________________ Re: M01-06   [#permalink] 22 Feb 2019, 02:40
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