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 multiple of m and p is 30
gprep ds remainder problem
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IMO A
1)The greatest common factor of m and p is 2 .
both m and p are even. if m is not a factor of p, remainder will always be atleast 2.
ex, 4,6
4,10
8,20
20,22
20,98
Sufficient
2)The least common multiple of m and p is 30.
m=5,p=6, r=1
m=6,p=15,r=3
not sufficient
1)The greatest common factor of m and p is 2 .
both m and p are even. if m is not a factor of p, remainder will always be atleast 2.
ex, 4,6
4,10
8,20
20,22
20,98
Sufficient
2)The least common multiple of m and p is 30.
m=5,p=6, r=1
m=6,p=15,r=3
not sufficient
The powers of two are bloody impolite!!
- cubicle_bound_misfit
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what the question is asking ?
1. m and p both greater than 2
now as p is not a factor of m then
p%m can have values like 1, 2, .... m-1
so only case where p%m will have a value of 1 is when m and p are consecutive integers , i.e 4,5 ... 6,7.... 9,10 etc and their GCF is 1. and LCM is = m*p
stmt 1 says
GCF is 2 therefore remainder is always >1. SUFF
stmt 2 says LCM is 30 , it can have multiple possibilities ie m = 5 , p =6 remainder is 1
but m =3 and p =10 remainder is >1. Hence Insufficient.
Hope that helps.
1. m and p both greater than 2
now as p is not a factor of m then
p%m can have values like 1, 2, .... m-1
so only case where p%m will have a value of 1 is when m and p are consecutive integers , i.e 4,5 ... 6,7.... 9,10 etc and their GCF is 1. and LCM is = m*p
stmt 1 says
GCF is 2 therefore remainder is always >1. SUFF
stmt 2 says LCM is 30 , it can have multiple possibilities ie m = 5 , p =6 remainder is 1
but m =3 and p =10 remainder is >1. Hence Insufficient.
Hope that helps.
Cubicle Bound Misfit
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Thanks a lot guys.
OA - A
I made a mistake in choosing D. For statement 2 I took a couple of number pairs and always go a remainder of 1. I had not taken 6 and 15 !
OA - A
I made a mistake in choosing D. For statement 2 I took a couple of number pairs and always go a remainder of 1. I had not taken 6 and 15 !