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Director  Joined: 07 Jun 2004
Posts: 555
Location: PA
If the greatest common factor of two integers, m and n, is  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 40% (02:02) correct 60% (02:34) 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.
Director  Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 654
Re: Number Prop DS  [#permalink]

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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  Joined: 01 Feb 2011
Posts: 546
Re: Number Prop DS  [#permalink]

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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

Hence answer is B.
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Location: United States (IN)
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Re: Number Prop DS  [#permalink]

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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

So answer is B
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Manager  Joined: 05 Jan 2011
Posts: 101
Re: Number Prop DS  [#permalink]

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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
Manager  Joined: 20 Jul 2011
Posts: 93
GMAT Date: 10-21-2011
Re: Number Prop DS  [#permalink]

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2
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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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
Manager  Joined: 04 Oct 2013
Posts: 68
Location: Brazil
GMAT 1: 660 Q45 V35 GMAT 2: 710 Q49 V38 Re: Number Prop DS  [#permalink]

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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  Joined: 29 Mar 2015
Posts: 11
Re: If the greatest common factor of two integers, m and n, is  [#permalink]

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1
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.
SVP  B
Joined: 06 Nov 2014
Posts: 1873
Re: what is the sum of the m and n?  [#permalink]

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1
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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Re: If the greatest common factor of two integers, m and n, is  [#permalink]

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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?
Intern  Joined: 29 Mar 2015
Posts: 11
Re: If the greatest common factor of two integers, m and n, is  [#permalink]

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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.
Non-Human User Joined: 09 Sep 2013
Posts: 13244
Re: If the greatest common factor of two integers, m and n, is  [#permalink]

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_________________ Re: If the greatest common factor of two integers, m and n, is   [#permalink] 11 Jul 2019, 09:53
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