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perfect square

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perfect square

by pappueshwar » Mon Mar 12, 2012 9:55 am
p^a * q^b * r^c * s^d = x, where x is a perfect square. If p, q, r, and s are prime integers, are they distinct?

(1) 18 is a factor of ab and cd
(2) 4 is not a factor of ab and cd

OA IS B

how to solve this ?
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by Neo Anderson » Mon Mar 12, 2012 10:09 am
if p,q,r and s are to be distinct, then a,b,c, and d need to be even (because when a perfect square is expressed in terms of prime factors, they all should have even powers)
thus question rephrased, are a,b,c,and d even?

statement 1. 18 is factor of ab and cd. not sufficient as this does not tell us about individually a and b & c and d being even or not.

statement 2. 4 is not a factor of ab and cd. that means either of a , b & either of c , d is not even thus sufficient to answer the question posed above!

hence the answer B
Last edited by Neo Anderson on Mon Mar 12, 2012 10:25 am, edited 1 time in total.
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by pappueshwar » Mon Mar 12, 2012 10:22 am
hi anderson,

can u explain stmtn 2 with an example using numbers?
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by Neo Anderson » Mon Mar 12, 2012 10:30 am
minor correction!! re read the statement 2!

only means that: if 4 is not a factor of ab, both a and b together can not be even. say a=2 and b=3 4 is not a factor of 6. but if a=2x (even) and b= 2y(even) =>4 has to be factor of ab.
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