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# M01-06

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Math Expert
Joined: 02 Sep 2009
Posts: 42247

Kudos [?]: 132677 [0], given: 12331

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16 Sep 2014, 00:14
Expert's post
2
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Difficulty:

5% (low)

Question Stats:

80% (00:32) correct 20% (00:43) wrong based on 149 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
[Reveal] Spoiler: OA

_________________

Kudos [?]: 132677 [0], given: 12331

Math Expert
Joined: 02 Sep 2009
Posts: 42247

Kudos [?]: 132677 [0], given: 12331

### Show Tags

16 Sep 2014, 00:14
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.

_________________

Kudos [?]: 132677 [0], given: 12331

Current Student
Joined: 03 Jun 2013
Posts: 22

Kudos [?]: 3 [0], given: 71

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, 10:59
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?

Kudos [?]: 3 [0], given: 71

Math Expert
Joined: 02 Sep 2009
Posts: 42247

Kudos [?]: 132677 [1], given: 12331

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24 Nov 2014, 01:55
1
KUDOS
Expert's post
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.
_________________

Kudos [?]: 132677 [1], given: 12331

Current Student
Joined: 03 Jun 2013
Posts: 22

Kudos [?]: 3 [0], given: 71

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, 12:33
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

Kudos [?]: 3 [0], given: 71

Intern
Joined: 05 Dec 2013
Posts: 30

Kudos [?]: 9 [0], given: 2

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27 Apr 2015, 16:19
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

Kudos [?]: 9 [0], given: 2

Intern
Joined: 26 Dec 2016
Posts: 20

Kudos [?]: 3 [0], given: 13

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24 Jan 2017, 02:15
I'm quite sure that 2.5 x 14 is no valid multiple of 14

Kudos [?]: 3 [0], given: 13

Intern
Joined: 24 Feb 2017
Posts: 38

Kudos [?]: 11 [0], given: 38

Schools: CBS '20 (S)
GMAT 1: 760 Q50 V42

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24 Feb 2017, 13:37
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

Kudos [?]: 11 [0], given: 38

Intern
Joined: 26 May 2017
Posts: 27

Kudos [?]: 7 [0], given: 22

GMAT 1: 620 Q48 V27

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15 Sep 2017, 04:49
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.

Kudos [?]: 7 [0], given: 22

M01-06   [#permalink] 15 Sep 2017, 04:49
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# M01-06

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