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M01-06

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M01-06 [#permalink]

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New post 16 Sep 2014, 00:14
2
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Difficulty:

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Question Stats:

82% (00:31) correct 18% (00:38) wrong based on 160 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
Spoiler: OA

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Re M01-06 [#permalink]

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New post 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.


Answer: C
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Re: M01-06 [#permalink]

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New post 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.


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?
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Re: M01-06 [#permalink]

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New post 24 Nov 2014, 01:55
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.


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.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: M01-06 [#permalink]

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New post 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.


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
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Re: M01-06 [#permalink]

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New post 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
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Re: M01-06 [#permalink]

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New post 24 Jan 2017, 02:15
I'm quite sure that 2.5 x 14 is no valid multiple of 14
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Re: M01-06 [#permalink]

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New post 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 :)
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M01-06 [#permalink]

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New post 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.
Hence answer is C


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Re M01-06 [#permalink]

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New post 23 Dec 2017, 15:49
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.
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Re M01-06 [#permalink]

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New post 23 Dec 2017, 15:50
I think this is a high-quality question and I agree with explanation.
Re M01-06   [#permalink] 23 Dec 2017, 15:50
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