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# Is |p|^2<|p| ?

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18 Apr 2013, 13:32
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36% (01:54) correct 64% (00:49) wrong based on 223 sessions

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Is $$|p|^2<|p|$$ ?

1.$$p^2\leq{1}$$

2.$$p^2-1\neq{0}$$

Hi guys! I created this DS, if you want give it a try!

This is my first creation, I appreciate any feedback
Scroll down for OE.
[Reveal] Spoiler: OA

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Last edited by Zarrolou on 18 Apr 2013, 15:51, edited 1 time in total.
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18 Apr 2013, 15:48
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Official Explanation

Is $$|p|^2<|p|$$ ?

Splitting the equation into two scenarios $$p>0$$ and $$p<0$$

I)$$p>0$$
$$p^2-p>0$$
$$0<p<1$$
II)$$p<{}0$$
$$(-p)^2+p<0$$
$$-1<p<0$$

We can rewrite the question as: is $$-1<p<1$$ and $$p\neq{0}$$?

1.$$p^2\leq{1}$$
$$-1\leq{}p\leq{}1$$
We cannot say if given this interval p will have one of those values: $$-1<p<1$$ and $$p\neq{0}$$
Not Sufficient

2.$$p^2-1\neq{0}$$
$$p\neq{}+,-1$$
Clearly not Sufficient

1+2. Using both 1 and 2 we can conclude that $$-1<p<1$$ but p could equal 0. Not Sufficient

OA:
[Reveal] Spoiler: OA
E

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19 Apr 2013, 11:54
2
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Hi manishuol,

lets see if I can remove your doubts. The graph will help a lot, scroll down it's $$|p|^2-|p|<0$$ we have to look where it is negative!

$$|p|^2<|p|$$, remember that both |p| and |p|^2 don't have to be positive, they can also equal 0.

"So, we have to find if |p| is a proper fraction or not. okay." Not correct, we must find out if p is in the interval $$-1<p<1$$ AND $$\neq{0}$$.

"this means that P can be equal to +1, -1 or p can be equal to any proper fraction" AND 0 I would add, p ranges in the interval $$-1\leq{p}\leq{1}$$
"however this is insufficient because of multiple possibilities." Correct

"Now statement 2 is clearly insufficient" Correct

Question: is p $$-1<p<1$$ AND $$\neq{0}$$?
Statement 1: $$-1\leq{p}\leq{1}$$
Statement 2 $$p\neq{-,+1}$$

1+2 $$-1<p<1$$ But no one says anything about $$p=0$$

The point is all here: p could still equal 0, and both statement don't give us info about this possibility.
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_________________

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18 Apr 2013, 14:29
1
KUDOS
Zarrolou wrote:
Is $$|p|^2<|p|$$ ?

1.$$p^2\leq{1}$$
2.$$p^2-1\neq{0}$$

Hi guys! I created this DS, if you want give it a try!

I'll post the solution after some discussion
This is my first creation, I appreciate any feedback

E it is ... my bad

Last edited by yezz on 18 Apr 2013, 16:31, edited 1 time in total.
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18 Apr 2013, 15:34
1
KUDOS
Zarrolou wrote:
Is $$|p|^2<|p|$$ ?

1.$$p^2\leq{1}$$
2.$$p^2-1\neq{0}$$

Hi guys! I created this DS, if you want give it a try!

I'll post the solution after some discussion
This is my first creation, I appreciate any feedback

From F.S 1, for p=0, we have a NO. For p=-1/2, we have a YES. Insufficient.

From F.S 2, Just as above. Insufficient.

Both together, for p=0, a NO. For p=-1/2, a YES. Insufficient.

E.
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18 Apr 2013, 15:52
1
KUDOS
/p/(/p/-1)<0 we cannot divide the inequality with /p/ since we don't know if /p/=0.
from statement 1 ,we have that -1<=p<=1 insuff
from statement 2, p<>+-1. insuff

combined p lies in(-1 U +1). p=0.5 ,we have YES,p=0 we have NO. insuff
IMO E
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19 Apr 2013, 11:36
1
KUDOS
Zarrolou wrote:
Official Explanation

Is $$|p|^2<|p|$$ ?

Splitting the equation into two scenarios $$p>0$$ and $$p<0$$

I)$$p>0$$
$$p^2-p>0$$
$$0<p<1$$
II)$$p<{}0$$
$$(-p)^2+p<0$$
$$-1<p<0$$

We can rewrite the question as: is $$-1<p<1$$ and $$p\neq{0}$$?

1.$$p^2\leq{1}$$
$$-1\leq{}p\leq{}1$$
We cannot say if given this interval p will have one of those values: $$-1<p<1$$ and $$p\neq{0}$$
Not Sufficient

2.$$p^2-1\neq{0}$$
$$p\neq{}+,-1$$
Clearly not Sufficient

1+2. Using both 1 and 2 we can conclude that $$-1<p<1$$ but p could equal 0. Not Sufficient

OA:
[Reveal] Spoiler: OA
E

----------------------------------------------------------------

Hey, Good Q ..... I'm bit confused ... Correct me if I'm wrong ....

Is |p|^2<|p| ? , one must always keep in mind that Is |p| is always positive, no matter the sign of P ..Okay & second thing that p^2 will always remain +ve. Now, |p|^2<|p| will only be possible if |p| must be a proper fraction okay. So, we have to find if |p|
is a proper fraction or not. okay.

now statement 1 says .......... p^2 =<1 ...... this means that P can be equal to +1, -1 or p can be equal to any proper fraction as P^2 must always be less than 1 only if P is a proper fraction. so from this we have three values of P... 1, -1 & any proper fraction... however this is insufficient because of multiple possibilities.

Now statement 2 says ....... p^2-1 is not equal to Zero. that means that p is not equal to +,-1 , therefore it is clearly insufficient. .....

Now, 1+2 ........ as statement 1 says that p can be 1 or -1 or any proper fraction & statement 2 says that P is not equal to +,-1 , therefore we can conclude that p = Proper fraction & if P is a Proper fraction whether +ve Proper fraction or -ve Proper fraction, ..... |p|^2<|p| will always remain true. Hence , C.

Please correct me if I'm wrong. Pls......
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19 Apr 2013, 12:06
Zarrolou wrote:
Hi manishuol,

lets see if I can remove your doubts. The graph will help a lot, scroll down it's $$|p|^2-|p|<0$$ we have to look where it is negative!

$$|p|^2<|p|$$, remember that both |p| and |p|^2 don't have to be positive, they can also equal 0.

"So, we have to find if |p| is a proper fraction or not. okay." Not correct, we must find out if p is in the interval $$-1<p<1$$ AND $$\neq{0}$$.

"this means that P can be equal to +1, -1 or p can be equal to any proper fraction" AND 0 I would add, p ranges in the interval $$-1\leq{p}\leq{1}$$
"however this is insufficient because of multiple possibilities." Correct

"Now statement 2 is clearly insufficient" Correct

Question: is p $$-1<p<1$$ AND $$\neq{0}$$?
Statement 1: $$-1\leq{p}\leq{1}$$
Statement 2 $$p\neq{-,+1}$$

1+2 $$-1<p<1$$ But no one says anything about $$p=0$$

The point is all here: p could still equal 0, and both statement don't give us info about this possibility.

-----------------------------------

Yeah You're certainly right. I missed out 0 as one of the possibility. .......I really appreciate your quick help.Thanks !! Brother !!
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25 Jun 2013, 16:59
Is |p|^2<|p| ?

1.p^2≤1

2.p^2-1≠0

Is |p|^2<|p|? ==> is -1<p<1

1.) insufficient as p could be 1 or -1 meaning p|^2 could equal |p| or p|^2 could be less than |p| Insufficient.

2.) p^2-1≠0 insufficient. p could = 1/2 which when squared = 1/4 which doesn't = 0 and p^2 would be less than P. On the other hand P could = 10 and 10^2-1 > 10.

1+2) we know that -1<p<1 and that p^2-1≠0 so the range of values to test is between -1 and 1. Fine. For ALL values of p except -1, 0 and 1 is |p|^2<|p|. However, while -1^2 - 1 and 1^2 - 1 = 0 (which rules out p being -1 or 1) p could be 0 In which case p^2 = p or it could be a fraction in which p^2 is less than p!

Great question Zarrolou!
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24 Jul 2014, 05:16
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Re: Is |p|^2<|p| ?   [#permalink] 25 Jun 2016, 22:09
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