subgeeth wrote:If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of p²t?
1) m has more than 9 positive factors.
2) m is a multiple of p³


I got the answer has E assuming p and t are two different numbers if not B

Can any one confirm which should be correct

prime numbers p and t are the only prime factors of the integer m. so m is a multiple of pt.
1) m has more than 9 positive factors... this does not show that m is a multiple of P^2 or not. it can be of t^n also.......not sufficient
2) m is a multiple of of p^3 that means m is surely a multiple of P^2 . SO m is a multiple of p^2t ......sufficient.


Hence B is the ans,

Hey thanks for the reply...
but I have a doubt still..
if m is a multiple of of p^3 that means m is surely a multiple of P^2

can u give pls me an example for the above

subgeeth wrote:Hey thanks for the reply...
but I have a doubt still..
if m is a multiple of of p^3 that means m is surely a multiple of P^2

can u give pls me an example for the above

yeah subgeeth ... say for example m is a multiple of prime numbers 3 and 5 only
now say m is a multiple of 5^3 = 5x5x5.
so you can clearly say that m is a multiple of 5^2 = 5x5 ..don't u think so..?/

yes u are correct but what about t am not able to get the answer when it is p^2*t

subgeeth wrote:yes u are correct but what about t am not able to get the answer when it is p^2*t

Dude its clearly written that p and t are only prime factors of the integer m i.e. t is also a prime factor of m


If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of p²t?

So u can easily say that m is a multiple of p^2xt.

subgeeth wrote:If the prime numbers p and t are the only prime factors of the integer m, is m a multiple of p²t?
1) m has more than 9 positive factors.
2) m is a multiple of p³


I got the answer has E assuming p and t are two different numbers if not B

Can any one confirm which should be correct

Now, m can be denoted as (p^x)(t^y) = m [since we know that these are the only prime factors]
(1):-m has more than 9 positive factors.[Now,the factors can also be t², t^3 and subsequent powers of t]Hence ,we are not sure if p^2 is there or not. Hence,insufficient.
(2):-m is a multiple of p^3 .
Now,p^3 = p x p²
Hence we see that p² is a multiple of m.
Also,t is one of the prime factor so t would also be a multiple of m.
Hence, m is a multiple of p²t.
So,sufficient.

The OA should be B.

For example:-The two different no.s can be
A:- m = 2 x( 3^7 ) [p=2 and t=3 Hence,not divisible by p²t]
B:- m = (2^3 X 3^5) [p=2 and t=3 Hence,divisible by p²t]


I guess the soln. is clear now subgeeth.

Thanks for the response ............. i understood

subgeeth wrote:Thanks for the response ............. i understood

Well subgeeth thats good u understood the concept behind the problem...

Thanks harsh for giving some real examples... dat was a good idea to make subgeeth understand the thing..