p and q are integers

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uptowngirl92: Master | Next Rank: 500 Posts; Posts: 447; Joined: Sun Apr 19, 2009 9:08 pm; Location: Kolkata,India; Thanked: 7 times; GMAT Score:670

p and q are integers

by uptowngirl92 » Mon Jul 20, 2009 7:54 am

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!

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Source: Beat The GMAT — Data Sufficiency | Mon Jul 20, 2009 7:54 am

real2008: Legendary Member; Posts: 527; Joined: Thu May 01, 2008 12:06 am; Thanked: 7 times

Re: p and q are integers

by real2008 » Mon Jul 20, 2009 9:12 am

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!

(sorry, I have modified my post)

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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raghavsarathy: Master | Next Rank: 500 Posts; Posts: 166; Joined: Sat Apr 18, 2009 10:41 pm; Thanked: 9 times; GMAT Score:770

by raghavsarathy » Mon Jul 20, 2009 9:19 am

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

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shibal: Master | Next Rank: 500 Posts; Posts: 345; Joined: Wed Mar 18, 2009 6:53 pm; Location: Sao Paulo-Brazil; Thanked: 12 times; GMAT Score:660