Number Properties

[raja11010]

Could some one post me the explanation for this (yes/no type) question..

If 80 is a factor of r,is 15 a factor of r?

regards
Raja.

[manpsingh87]

Could some one post me the explanation for this (yes/no type) question..

If 80 is a factor of r,is 15 a factor of r?

regards
Raja.

as 80 is a factor therefore r can be written as 80k; where k is an integer 1,2,3..

if 15 is a factor of r; than r/15 should give 0 remainder; also we know that r=80k;
80k/15; 16k/3 if k=1 than 16k/3 will not be divisible by 3; hence 15 is not a factor of r;
but if k=3 than 16k/3 will be divisible by 3; now we have 15 as a factor of r;
as we have seen,, different scenarios are possible for different values of k; hence we need some more additional information.. to answer the question..!!!

[pemdas]

this question is looking for lowest common multiple (lcm), I guess
we would perform prime factorization of 80 and 15
80 (2) 40
40 (2) 20
20 (2) 10
10 (2) 5
5 (5) 1
80=2^4*5^1
15=3^1*5^1
the number can have factors 80 and 15 if it can be factored to 2^4, 5^1 and 3^1. If the number can be factored to the listed values then our answer is Yes, if not then we must answer No. I agree with manpsingh87 here, we need some data about the number itself-if it contains the factor 3^1

Could some one post me the explanation for this (yes/no type) question..

If 80 is a factor of r,is 15 a factor of r?

regards
Raja.

[Brent@GMATPrepNow]

Could some one post me the explanation for this (yes/no type) question..

If 80 is a factor of r,is 15 a factor of r?

regards
Raja.

When it comes to factors/divisors, I find it useful to relate information to the prime factorization of a number.

For example, if we know that 5 is a divisor of 70, we can say that 5 is "hiding" in the prime factorization of 70.
Prime factorization of 70: 70 = (2)(5)(7)

Similarly, if 6 is a divisor of 210, we can say that 6 is "hiding" in the prime factorization of 120.
Prime factorization of 120: 120 = (2)(3)(5)(7) [here, the 6 is in the form (2)(3)]

If we are told that 15 is a factor of M, then we know that 15 will be "hiding" in the prime factorization of M. In other words, (3)(5) will be "hiding" in the prime factorization of M
So, we know that M = (3)(5)(?)(?)(?)(?) where the ?'s represent other possible prime numbers in the prime factorization of M

To answer your question, if 80 is a factor of r then we know that 80 is "hiding" in the prime factorization of r.
Since 80 is also known as (2)(2)(2)(2)(5), we know that prime factorization of r looks like this:
r = (2)(2)(2)(2)(5)(?)(?)(?)(?) where the ?'s represent other possible prime numbers in the prime factorization of r

For 15 to be a factor of r, it must be true that 15 is hiding in the PF of r. In other words (3)(5) must be hiding in the PF of r.

At the moment, all we know is that r =(2)(2)(2)(2)(5)(?)(?)(?)(?)
So, we know for certain that a (5) is hiding in the PF of r, but we can't say for certain that a (3) is hiding in the PF of r.

As such, we can't determine with any certainty whether or not 15 is a factor of r.

[MAAJ]

Does r has 3 and 5 in its prime factors?

r has 2,2,2,2,5,...? in its prime factors (...? because it could have more prime factors)

For example if r = 240, then both 80 and 15 could be factors of r. So it's insufficient to answer yes or no here.

[raja11010]

Well, firstly I am pleased with the response from manpsingh87,pemdas,Brent@GMATPrepNow,MAAJ...
Thank you so very much friends!!

Specifically @Brent: U made my day.. Thanks a lott man!!..

regards
Raja