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factors and remainders

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factors and remainders

by aturpening » Mon May 10, 2010 7:04 pm
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?
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by liferocks » Mon May 10, 2010 7:36 pm
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
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by aturpening » Mon May 10, 2010 8:06 pm
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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by liferocks » Mon May 10, 2010 9:04 pm
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.
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?
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by gmatmachoman » Mon May 10, 2010 11:23 pm
liferocks wrote:
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.
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?
LR u have missed couple of points in st 2 : they have said m<p. !!

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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by liferocks » Mon May 10, 2010 11:34 pm
gmatmachoman wrote:
liferocks wrote:
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.
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?
LR u have missed couple of points in st 2 : they have said m<p. !!

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!!
You also considered that Least common Factor is LCM..but apparently its not :( as per aturpening.
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by aturpening » Tue May 11, 2010 7:45 pm
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.
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by liferocks » Tue May 11, 2010 8:21 pm
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.
I still do not understand how a number has 30 as one of its factor but not 2 or 3.
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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by ssuarezo » Wed May 12, 2010 11:49 am
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.
And aturpening,
is there any Greatest common factor and Greatest common multiple?
I'm already all mixed up.
Thanks
Silvia
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