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# If the greatest common factor of two integers, m and n, is

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Director
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If the greatest common factor of two integers, m and n, is [#permalink]

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20 Mar 2011, 09:52
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Question Stats:

41% (02:23) correct 59% (01:59) wrong based on 160 sessions

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If the greatest common factor of two integers, m and n, is 56 and the least common multiple is 840, what is the sum of the m and n?

(1) m is not divisible by 15.
(2) n is divisible by 15.
[Reveal] Spoiler: OA

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Director
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20 Mar 2011, 10:02
s1 insufficient
Consider m=56*3 and n=56*5
consider m = 56 and n=56*15

s2 sufficient
m=56 and n=56*15

Hence B

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Director
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20 Mar 2011, 11:22
1 not sufficient
as there more than one possible combination for m and n

m = (2^3)7(3) n = (2^3)7(5)

m = (2^3)7 n = (2^3)7(15)

2. Sufficient

only possible combination for m and n here is m = (2^3)7 n = (2^3)15

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20 Mar 2011, 20:12
56 = 2^3 * 7

So m and n have 2^3 * 7 as factor

840 = 7 * 120 = 7 * 5 * 24 = 7 * 5 * 3 * 2^3

(1), m is m is not divisible by 15, so m does not have 5 and 3 as factor

So m = 2^3 * 7 * k (where k is an intger other than 3 or 5)

Now m*n = 56 * 840

So n = 56/56k * 840 = 840/k , which is not sufficient as n could be 840, or 840/56 = 15

(2) n is divisible by 15, so n has 3 and 5 as factor

So n = 3*5* 2^3 * 7*p, where p is an integer

=> m = 56*840/15*56p = 56*56/56p, so m can be 56/p, now m has to be minimum 56, so p = 1, hence m = 56 and n = 840

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Manager
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21 Mar 2011, 22:10
Product of M & N= LCM *GCD
==>56*840
==>7^2*2^6*5*3

Stmt 1 m could be 7*2^3*5 or 7*2^3*3..
Stmt 2
Since GCD is 56 both m and n should have 7 *2^3
n =>7 *2^3 *3*5 (n is divisible by 15 so it should have 3 and 5 as a factor).. Sufficient

B
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05 Sep 2011, 12:21
1
KUDOS
Quote:
If the greatest common factor of two integers, m and n, is 56 and the least common multiple is 840, what is the sum of the m and n?

(1) m is not divisible by 15.
(2) n is divisible by 15.

prime factors of 56: 7, 2, 2, 2
prime factors of 840: 7, 2, 2, 2, 3, 5

From Statement 1
m = 56*3 or m=56
Insufficient

From Statement 2

m=56; n=840
sufficient

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Re: If the greatest common factor of two integers, m and n, is [#permalink]

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15 Oct 2013, 17:27
It is given GCF = 56 = 7 x 2 x 2 x 2
and LCM = 840 = 56 (GCF) x 15
For more fundamental elaboration:-
GCF and LCM
----------
7 |m , n
2 |m1, n1
2 |m2, n2
2 |m3, n3
--- 1 , 15
or
--- 3 , 5
From Statement 1 informs "m" is not divisible by 15, so in above illustration, we can have either 1 or 3 under "m", which makes the statement insufficient to identify the value of m,

From Statement 2 informs "n" is divisible by 15, so in above graphic illustration, we can establish that we will have 1 under "m" and 15 under "n", which is sufficient to derive both the value of n and m

The value of m = 1 x 2 x 2 x 2 x 7 = 56
The value of n = 15 x 2 x 2 x 2 x 7 = 840
m + n = 896
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16 Nov 2013, 15:00
gmatopoeia wrote:
Quote:

From Statement 1
m = 56*3 or m=56
Insufficient
[u]

For the sake of my comprehension, should m=56*5 be a possibility as well?
Intern
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Kudos [?]: -14 [2] , given: 15

Re: If the greatest common factor of two integers, m and n, is [#permalink]

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14 May 2015, 23:26
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In such questions with a common GCD, I find it convenient to take the numbers as:

m=56*x
n=56*y

Also we know that the LCM is 840:
so we can write

56*x*a=840 => x*a=15
56*y*b=840 => y*b=15

Where a & b are two integers.

We get the four options for the two pairs and solve as has been shown above.

Hope it helps.
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what is the sum of the m and n? [#permalink]

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14 Sep 2015, 15:58
If the greatest common factor of two integers, m and n, is 56 and the least common multiple is 840, what is the sum of the m and n?

(1) m is not divisible by 15.
(2) n is divisible by 15
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Kudos [?]: 355 [0], given: 21

Re: what is the sum of the m and n? [#permalink]

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14 Sep 2015, 20:34
To solve this, first we need to find the prime factors of 56 and 840

prime factors of 56 = 2, 2, 2, 7
prime factors of 840 = 2, 2, 2, 3, 5, 7

Statement 1
m = 56*3, n = 56*5 or m=56, n = 56*3*5
Insufficient

Statement 2
m=56; n=56*3*5
Sufficient

The correct answer choice is B
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Kudos [?]: 14 [0], given: 651

Re: If the greatest common factor of two integers, m and n, is [#permalink]

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16 Sep 2015, 00:04
The answer of this question is apparently B but if the statement 2 change to "n is not divisible by 15", will the answer be C?
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Re: If the greatest common factor of two integers, m and n, is [#permalink]

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16 Sep 2015, 03:07
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Yes in that case, combining the two equations will lead to a unique solution i.e. 56*(5+3)=56*8=448 & the answer would be C.
Re: If the greatest common factor of two integers, m and n, is   [#permalink] 16 Sep 2015, 03:07
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