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.
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