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12 Jun 2008, 08:44
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12 Jun 2008, 11:10
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We know that \(m=p*t*X\), where X is an integer
If (2) is true then we can also write \(m=p^3*Y\), where Y is another integer.
Then \(p*t*X=p^3*Y\) => \(X=(p^2*Y)/t\)
As X is integer \((p^2*Y)/t\) is and since t is prime either t divides p or t divides Y
p is prime too so that if t divides p we can say that p=t, meaning \(p^2*t=p^3\) : original statement is verified
it t doesn't divide p, it divides Y, then we can write \(Y=t*Z\), where Z is another integer : so \(m=p^3*Y=p*p^2*t*Z\) i.e. original statement is verified
(1) is insufficient : p=2, t=3, \(m=p*t*5*7*9*11*13*15*17*19\) has more than 9 factors and is not dividable by \(p^3=8\)
Therefore the answer is (B)
If (2) is true then we can also write \(m=p^3*Y\), where Y is another integer.
Then \(p*t*X=p^3*Y\) => \(X=(p^2*Y)/t\)
As X is integer \((p^2*Y)/t\) is and since t is prime either t divides p or t divides Y
p is prime too so that if t divides p we can say that p=t, meaning \(p^2*t=p^3\) : original statement is verified
it t doesn't divide p, it divides Y, then we can write \(Y=t*Z\), where Z is another integer : so \(m=p^3*Y=p*p^2*t*Z\) i.e. original statement is verified
(1) is insufficient : p=2, t=3, \(m=p*t*5*7*9*11*13*15*17*19\) has more than 9 factors and is not dividable by \(p^3=8\)
Therefore the answer is (B)
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
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