The integers m and p are such that 2<m<p and m is not a factor of p. If r is the remainder when p is divided by m, is r>1?
(1) The greatest common factor of m and p is 2
(2) The least common factor of m and p is 30
I'm not finding an easy solution to this problem. Can anyone help?
factors and remainders
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p=km+r..where k is any integer
from 1...m=2a and p=2b..where a and b are co-prime
hence 2b=2ka+r or r=2(b-ka)..clearly r is multiple of 2 or r>1..sufficient
from 2
30 is the LCM of the numbers
so the numbers can be 2,15 or 3,30 or 5,6..for each of these reminder is 1....sufficient
And option D
what is OA?
from 1...m=2a and p=2b..where a and b are co-prime
hence 2b=2ka+r or r=2(b-ka)..clearly r is multiple of 2 or r>1..sufficient
from 2
30 is the LCM of the numbers
so the numbers can be 2,15 or 3,30 or 5,6..for each of these reminder is 1....sufficient
And option D
what is OA?
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The answer is (A), Statement 1 alone is sufficient.
Statement 2 says that 30 is least common factor (LCF), not the least common multiple (LCM). The explanation for Statement 1 sounds good, though.
Statement 2 says that 30 is least common factor (LCF), not the least common multiple (LCM). The explanation for Statement 1 sounds good, though.
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hmm...actually i read it as LCM...but now when I think of it..how can two numbers has Least common factor as 30..because if 30 is a multiple 2,3,5,6,10 ..all of these will be factors of that number....am I missing something?aturpening wrote:The answer is (A), Statement 1 alone is sufficient.
Statement 2 says that 30 is least common factor (LCF), not the least common multiple (LCM). The explanation for Statement 1 sounds good, though.
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LR u have missed couple of points in st 2 : they have said m<p. !!liferocks wrote:hmm...actually i read it as LCM...but now when I think of it..how can two numbers has Least common factor as 30..because if 30 is a multiple 2,3,5,6,10 ..all of these will be factors of that number....am I missing something?aturpening wrote:The answer is (A), Statement 1 alone is sufficient.
Statement 2 says that 30 is least common factor (LCF), not the least common multiple (LCM). The explanation for Statement 1 sounds good, though.
and Least Common Factor..( is this same as LCM??)
Ok anyways, let us take m=3,p=10 .m is not a factor od p. actually they are coprimes. Remainder is certainly 1.
one more pair :(5,6) again Remainder is 1.
I think st 2 alone is also sufficient.
So pick D!!
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You also considered that Least common Factor is LCM..but apparently its notgmatmachoman wrote:LR u have missed couple of points in st 2 : they have said m<p. !!liferocks wrote:hmm...actually i read it as LCM...but now when I think of it..how can two numbers has Least common factor as 30..because if 30 is a multiple 2,3,5,6,10 ..all of these will be factors of that number....am I missing something?aturpening wrote:The answer is (A), Statement 1 alone is sufficient.
Statement 2 says that 30 is least common factor (LCF), not the least common multiple (LCM). The explanation for Statement 1 sounds good, though.
and Least Common Factor..( is this same as LCM??)
Ok anyways, let us take m=3,p=10 .m is not a factor od p. actually they are coprimes. Remainder is certainly 1.
one more pair :(5,6) again Remainder is 1.
I think st 2 alone is also sufficient.
So pick D!!
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The least common factor of two numbers m and p is the lowest number than can be divided evenly into either number. For instance, 3 is the least common factor for 9 and 12. the least common multiple of two numbers m and p is the lowest number that has both m and p as factors. For instance, 15 is the least common multiple of 3 and 5.
Therefore, LCM and LCF are not the same thing.
So, reading statement (2), if the least common factor of m and p is 30, then m and p have to larger than 30 considering 30 is a factor of either number.
But I'm not sure how to find out for sure whether statement (2) is sufficient or not.
Therefore, LCM and LCF are not the same thing.
So, reading statement (2), if the least common factor of m and p is 30, then m and p have to larger than 30 considering 30 is a factor of either number.
But I'm not sure how to find out for sure whether statement (2) is sufficient or not.
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I still do not understand how a number has 30 as one of its factor but not 2 or 3.aturpening wrote:The least common factor of two numbers m and p is the lowest number than can be divided evenly into either number. For instance, 3 is the least common factor for 9 and 12. the least common multiple of two numbers m and p is the lowest number that has both m and p as factors. For instance, 15 is the least common multiple of 3 and 5.
Therefore, LCM and LCF are not the same thing.
So, reading statement (2), if the least common factor of m and p is 30, then m and p have to larger than 30 considering 30 is a factor of either number.
But I'm not sure how to find out for sure whether statement (2) is sufficient or not.
as per your explanation of LCF the number is 30k..now 30 is divisible by 2,3,5,6,10 etc..so the number should also be divisible evenly by 2,3,5,6,10 etc ..all of these are less than 30..so 30 cannot be the LCF. Can you please recheck the wordings of the question?
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And aturpening,aturpening wrote:The least common factor of two numbers m and p is the lowest number than can be divided evenly into either number. For instance, 3 is the least common factor for 9 and 12. the least common multiple of two numbers m and p is the lowest number that has both m and p as factors. For instance, 15 is the least common multiple of 3 and 5.
Therefore, LCM and LCF are not the same thing.
So, reading statement (2), if the least common factor of m and p is 30, then m and p have to larger than 30 considering 30 is a factor of either number.
But I'm not sure how to find out for sure whether statement (2) is sufficient or not.
is there any Greatest common factor and Greatest common multiple?
I'm already all mixed up.
Thanks
Silvia