If p and q are integers and neither p nor q is equal to 0, is p/q > q/p?
1. p^2 > q^2
2.p^3 > q^3
Allright. Simplifying the main equation,
p/q > q/p
= p^2 > q^2.
Is'nt this what the first stmt. is clearly stating?So I answered A and clearly it is wrong.Shed some light guys!
p and q are integers
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(sorry, I have modified my post)uptowngirl92 wrote:If p and q are integers and neither p nor q is equal to 0, is p/q > q/p?
1. p^2 > q^2
2.p^3 > q^3
Allright. Simplifying the main equation,
p/q > q/p
= p^2 > q^2.
Is'nt this what the first stmt. is clearly stating?So I answered A and clearly it is wrong.Shed some light guys!
1. p^2 > q^2
=> (p^2/q^2)>1 [since q^2 >0]
=> (p/q)^2>1
=> (p/q)>1 or (p/q)<-1
now if (p/q)>1, then p/q > q/p
but if p/q<-1 then p/q < q/p
hence not sufficient
2. p^3 > q^3
i) p/q>1 if q>0
so p/q>q/p
ii) but if p>0, q<0 and |p|=|q|
then p/q = q/p
hence not sufficient
Taking both the statements together,
p^3>q^3 & p^2>q^2
case1) if p>q & (p & q>0)
or p/q>q/p
case2) if p>|q| & (p>1 and q<-1 )
p/q<q/p
Hence E
Last edited by real2008 on Mon Jul 20, 2009 10:26 am, edited 1 time in total.
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I think we need to solve this question without simplifying the main statement.
For statement 1.
Take p= -3 and q= 2 p^2 > q^2 but the main statement is not satisfied.
Take p =3 and q= 2 p^2 > q^2 and the main statement is satisfied.
Hence A is not sufficient.
For statement 2
p^3 > q^3.
Take both p nad q as positive. p> q to satisfy the eqn
The main statement not becomens p/q > q/p
Take p positive and q negative
p = 2 , q= -1
In this case p/q < q/p
Hence B is insufficient
Taking both statements together
Take p =2 , q= 1 p^2 > q^2 and p^3 > q^3
We also get p/q > q/p
Take the example of p =2 and q= -1 used above.
We get p/q < q/p
Hence both statements are not sufficient
E
For statement 1.
Take p= -3 and q= 2 p^2 > q^2 but the main statement is not satisfied.
Take p =3 and q= 2 p^2 > q^2 and the main statement is satisfied.
Hence A is not sufficient.
For statement 2
p^3 > q^3.
Take both p nad q as positive. p> q to satisfy the eqn
The main statement not becomens p/q > q/p
Take p positive and q negative
p = 2 , q= -1
In this case p/q < q/p
Hence B is insufficient
Taking both statements together
Take p =2 , q= 1 p^2 > q^2 and p^3 > q^3
We also get p/q > q/p
Take the example of p =2 and q= -1 used above.
We get p/q < q/p
Hence both statements are not sufficient
E