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(1) The lowest common multiple of x and 16 is 48 --> x can be 3, 6, 12, 24, or 48. Not sufficient.
(2) The greatest common factor of x and 16 is 4 --> x can take more than one value, for example, 4, 12, 20, .. (basically any number of the form 4*odd). Not sufficient.
(1)+(2) The most important property of LCM and GCD is: for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\). According to this 16x=48*4 --> x=12. Sufficient.
This question is straightforward as the factors are simple and easy to digest. For more complex questions of the type, it helps to draw table with the prime factors.
4 = 2^2 16 = 2^4 48 = 2^4 * 3
With that in mind consider the following two tables showing the overlaps for GCF and LCM.
Attachment:
image.png [ 15.7 KiB | Viewed 8287 times ]
Statement (1) The prime factors for 16 are clear, they only include 2. So if the LCM is 48, the 3^1 must come from x. However, x could also include some "2"s. If it includes none, then it would be 2^0 for x. Or just one 2. Then it would be 2^1. In both these cases the still LCM would be 48. Statement (1) does not allow to clearly answer what the value of x is. We only know it has a 3 which is not in 16. We don't know what else it has as prime factors.
Statement (2) Looking at the table again, now for GCF, we see the overlap is 2^2. We don't know the value of x. But we are told the GCF of both numbers (x and 16) is 4. But we don't know if x has any other prime factors. X could have many other prime factors that are not part of 16, thus other prime factors than 2. So Statement (2) is not sufficient.
Putting both statements together, we know x includes 2^2 (we know this from the GCF) and we know it has a 3^1 (which is not part of 16 but in the LCM). Thus, x must be = 2^2*3^1.
Again ...this approach is "overdoing it" as the numbers are straightforward. But the moment the numbers get more complicated or there are more than two numbers, it helps to structure your thoughts with such a table.
Originally posted by BabySmurf on 22 Jan 2014, 10:34.
Last edited by BabySmurf on 22 Jan 2014, 10:42, edited 2 times in total.
(1) The lowest common multiple of x and 16 is 48 --> x can be 3, 6, 12, 24, or 48. Not sufficient.
(2) The greatest common factor of x and 16 is 4 --> x can take more than one value, for example, 4, 12, 20, .. (basically any number of the form 4*odd). Not sufficient.
(1)+(2) The most important property of LCM and GCD is: for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\). According to this 16x=48*4 --> x=12. Sufficient.
Answer: C.
this is the best explanation I have heard so far) even my tutor from Veritas prep can't solve it today:( thinking maybe i need to change my tutor?:) btw-it so sad that you don't provide tutoring:(
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Good things come to those who wait… greater things come to those who get off their ass and do anything to make it happen...
(1) The lowest common multiple of x and 16 is 48 --> x can be 3, 6, 12, 24, or 48. Not sufficient.
(2) The greatest common factor of x and 16 is 4 --> x can take more than one value, for example, 4, 12, 20, .. (basically any number of the form 4*odd). Not sufficient.
(1)+(2) The most important property of LCM and GCD is: for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\). According to this 16x=48*4 --> x=12. Sufficient.
Answer: C.
Hello Bunuel,
Could you explain this part in red please? Why 4*odd?
(1) The lowest common multiple of x and 16 is 48 --> x can be 3, 6, 12, 24, or 48. Not sufficient.
(2) The greatest common factor of x and 16 is 4 --> x can take more than one value, for example, 4, 12, 20, .. (basically any number of the form 4*odd). Not sufficient.
(1)+(2) The most important property of LCM and GCD is: for any positive integers \(x\) and \(y\), \(x*y=GCD(x,y)*LCM(x,y)\). According to this 16x=48*4 --> x=12. Sufficient.
Answer: C.
Hello Bunuel,
Could you explain this part in red please? Why 4*odd?
Thank you.
Since the greatest common factor of x and 16 = 2^4 is 4 = 2^2, then x cannot have 2 in higher power than 2, hence 4*odd.
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Excellent Question. Here is what i did in this one --> We need the value of integer x. Statement 1--> LCM(x,16)=48 Hence the possible values of x --> 3 3*2 3*2^2 3*2^3 3*2^4 Hence not sufficient. Statement 2-> GCD(x,16)=4 Hence the general Expression for x will be => x=2^2*k where x is any odd number. Hence not sufficient.
Combing the two statements-> x must be 3*2^2 Hence sufficient.
Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
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70% (01:36) correct 
