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17 Sep 2008, 04:17
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If \(x\) is a perfect square and \(x=(p^a)(q^b)(r^c)(s^d)\), are prime numbers \(p\), \(q\), \(r\), and \(s\) distinct?
(1) 18 is a factor of \(ab\) and \(cd\)
(2) 4 is not a factor of \(ab\) and \(cd\)
Please explain your answer.
Thanks
(1) 18 is a factor of \(ab\) and \(cd\)
(2) 4 is not a factor of \(ab\) and \(cd\)
Please explain your answer.
Thanks
17 Sep 2008, 07:01
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tarek99
1)
when a=2k b=2l c=2m d=2n ..
if all a , b, c, d are multiple of 2 then clearly.. p,q,r,s can be distinct or not.
ab=18*i = say i=2
ab=cd= 2*k 2*l = 18*2 =
insuffcient
2)
when a=2k b=l c=2m d=n ..
here b and n not multiple of 2..
So.. q, s must be same to make l+n= multiple of 2.
They are not distinct.
B
