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C
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Difficulty:
35%
(medium)
Question Stats:
68% (01:34) correct
32%
(01:41)
wrong
based on 597
sessions
History
Date
Time
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What is the value of integer x?
(1) The lowest common multiple of x and 16 is 48.
(2) The greatest common factor of x and 16 is 4
(1) The lowest common multiple of x and 16 is 48.
(2) The greatest common factor of x and 16 is 4
have no idea why the answer is not E,cause
from (1) i have ...6->12->24
from (2) i have ...4->12->24
thanks for explanation;)
this question from Veritas prep:)
from (1) i have ...6->12->24
from (2) i have ...4->12->24
thanks for explanation;)
this question from Veritas prep:)
21 Jan 2014, 17:48
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What is the value of integer x?
(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.
(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.
General Discussion
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.
image.png [ 15.7 KiB | Viewed 20679 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.
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 20679 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.
