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m = 4n + 9, where n is a positive integer. What is the GCD [#permalink]
 14 Feb 2012, 05:16
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80% (01:08) wrong based on 6 sessions
m = 4n + 9, where n is a positive integer. What is the GCD of m and n? (1) m = 9s, where s is a positive integer. (2) n = 4t, where t is a positive integer.
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Smita04 wrote: m = 4n + 9, where n is a positive integer. What is the GCD of m and n?
(1) m = 9s, where s is a positive integer.
(2) n = 4t, where t is a positive integer. GCD? Do you mean Lowest Common Multiple or Greatest Common Factor?
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I think he means GCF.
A is sufficient because you know M is a multiple of 9. Since 9s is a multiple of 9 regardless of what s. You know N and M is consecutive multiples of 9 because their difference is 9. You know N is a multiple of 9 since if you add 9 to a number the only way it will form a multiple of 9 if it was already a multiple of 9.
Since you know their consecutive multiples of 9, their GCF is also 9.
B) Not enough info. You're not sure what number M is since, 4X+9 could be prime (13,17) or a multiple of 3 (21) or 5(25).
Therefore answer A is sufficient.
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m = 4n + 9, where n is a positive integer. What is the GCD of m and n? (1) m = 9s, where s is a positive integer --> since m is a multiple of 9 and is equal to 4n+ 9, then n must also be a multiple of 9 (in order 4n+ 9 to be a multiple of 9). Hence m and 4n are multiples of 9 and are 9 units apart from each other, which means that the Greatest Common Divisor of m and 4n is 9, obviously the GCD of m and n will also be 9. Sufficient. USEFUL PROPERTY: if a and b are multiples of k and are k units apart from each other then k is greatest common divisor of a and b. For example if a and b are multiples of 7 and a=b+7 then 7 is GCD of a and b. (2) n = 4t, where t is a positive integer. If n=4 then GCD of m and n is 1 (m=9 in this case) but if n=4*9 then GCD of m and n is 9 (m=17*9 in this case). Not sufficient. Answer: A.
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kys123 wrote: I think he means GCF.
A is sufficient because you know M is a multiple of 9. Since 9s is a multiple of 9 regardless of what s. You know N and M is consecutive multiples of 9 because their difference is 9. You know N is a multiple of 9 since if you add 9 to a number the only way it will form a multiple of 9 if it was already a multiple of 9.
Since you know their consecutive multiples of 9, their GCF is also 9.
B) Not enough info. You're not sure what number M is since, 4X+9 could be prime (13,17) or a multiple of 3 (21) or 5(25).
Therefore answer A is sufficient. m cannot be 17 or 21 as in this case n won't be a multiple of 4.
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Bunuel wrote: m = 4n + 9, where n is a positive integer. What is the GCD of m and n?
(1) m = 9s, where s is a positive integer --> since m is a multiple of 9 and is equal to 4n+9, then n must also be a multiple of 9 (in order 4n+9 to be a multiple of 9). Hence m and 4n are multiples of 9 and are 9 units apart from each other, which means that the Greatest Common Divisor of m and 4n is 9, obviously the GCD of m and n will also be 9. Sufficient.
USEFUL PROPERTY:
if a and b are multiples of k and are k units apart from each other then k is greatest common divisor of a and b. For example if a and b are multiples of 7 and a=b+7 then 7 is GCD of a and b.
(2) n = 4t, where t is a positive integer. If n=4 then GCD of m and n is 1 (m=9 in this case) but if n=4*9 then GCD of m and n is 9 (m=17*9 in this case). Not sufficient.
Answer: A. Hi Bunnel, Had the question stem been like this > m=3n+9, then the GCF would hav been 3 right?
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Re: m = 4n + 9, where n is a positive integer. What is the GCD [#permalink]
05 May 2013, 11:12
m = 4n + 9, where n is a positive integer. What is the GCD of m and n?
(1) m = 9s, where s is a positive integer.
(2) n = 4t, where t is a positive integer.
Bunnel : Interesting way of Defining the GCD of two numbers.
My thought process :
1)m=9s but m=4n+9. -> n is definately a multiple of 9. Hence GCD of m and n is 9. Sufficient.
2)n=4t. Doesn't help to establish any relation b/w m and n more than whatever is already mentioned. Insufficient.
Hence A
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Re: m = 4n + 9, where n is a positive integer. What is the GCD
[#permalink]
05 May 2013, 11:12
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