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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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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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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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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.



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Re: Number Prop DS [#permalink]
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05 Sep 2011, 12:21
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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 1m = 56*3 or m=56 Insufficient From Statement 2m=56; n=840 sufficient Answer: B
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Re: Number Prop DS [#permalink]
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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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Re: Number Prop DS [#permalink]
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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
Hence answer is B.



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Re: Number Prop DS [#permalink]
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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 So answer is B
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Re: Number Prop DS [#permalink]
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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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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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Re: Number Prop DS [#permalink]
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16 Nov 2013, 15:00
gmatopoeia wrote: Quote: From Statement 1 m = 56*3 or m=56 Insufficient [u]
Answer: B
For the sake of my comprehension, should m=56*5 be a possibility as well?



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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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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 1m = 56*3, n = 56*5 or m=56, n = 56*3*5 Insufficient Statement 2m=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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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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