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# M01-06

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Math Expert
Joined: 02 Sep 2009
Posts: 51072

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15 Sep 2014, 23:14
00:00

Difficulty:

5% (low)

Question Stats:

85% (00:29) correct 15% (00:38) wrong based on 184 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
Joined: 02 Sep 2009
Posts: 51072

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15 Sep 2014, 23:14
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.

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Joined: 03 Jun 2013
Posts: 20
Concentration: Strategy, General Management
GMAT 1: 520 Q38 V32
GMAT 2: 530 Q44 V22
GMAT 3: 670 Q47 V34
WE: Information Technology (Consulting)

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23 Nov 2014, 09:59
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.

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
Joined: 02 Sep 2009
Posts: 51072

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24 Nov 2014, 00:55
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.

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.
_________________
Current Student
Joined: 03 Jun 2013
Posts: 20
Concentration: Strategy, General Management
GMAT 1: 520 Q38 V32
GMAT 2: 530 Q44 V22
GMAT 3: 670 Q47 V34
WE: Information Technology (Consulting)

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24 Nov 2014, 11:33
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.

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

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27 Apr 2015, 15:19
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
Joined: 26 Dec 2016
Posts: 20

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24 Jan 2017, 01:15
I'm quite sure that 2.5 x 14 is no valid multiple of 14
Intern
Joined: 24 Feb 2017
Posts: 37
Schools: CBS '20 (S)
GMAT 1: 760 Q50 V42

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24 Feb 2017, 12:37
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
Joined: 25 May 2017
Posts: 25
GMAT 1: 620 Q48 V27

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15 Sep 2017, 03:49
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.

Manager
Joined: 02 Jan 2017
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Location: Pakistan
Concentration: Finance, Technology
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23 Dec 2017, 14:49
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
Joined: 02 Jan 2017
Posts: 73
Location: Pakistan
Concentration: Finance, Technology
GMAT 1: 650 Q47 V34
GPA: 3.41

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23 Dec 2017, 14:50
I think this is a high-quality question and I agree with explanation.
ISB, NUS, NTU Moderator
Joined: 11 Aug 2016
Posts: 343

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17 Jul 2018, 22:00
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.

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.
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Math Expert
Joined: 02 Sep 2009
Posts: 51072

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17 Jul 2018, 22:03
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.

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.

A divisor = a factor, it's an integer which divides another integer without a remainder.
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Joined: 20 Dec 2013
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08 Aug 2018, 09:36
can n be equal to SQRT(14)?
Math Expert
Joined: 02 Sep 2009
Posts: 51072

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10 Aug 2018, 00:56
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 &nbs [#permalink] 10 Aug 2018, 00:56
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