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If [p] is defined as the smallest integer greater than or equal to -p,  [#permalink]

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Difficulty:   65% (hard)

Question Stats: 49% (01:45) correct 51% (01:27) wrong based on 51 sessions

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If [p] is defined as the smallest integer greater than or equal to -p, is [p] < 0?

(1) p ≥ 0

(2) p ≤ 1

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Re: If [p] is defined as the smallest integer greater than or equal to -p,  [#permalink]

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If [p] is defined as the smallest integer greater than or equal to -p, is [p] < 0?

(1) p ≥ 0

(2) p ≤ 1

$$\left[ p \right] = \min \left\{ {n\,\,\operatorname{int} \,\,\,:\,\,n \geqslant - p} \right\}$$

$$\left[ p \right]\mathop < \limits^? 0$$

$$\left( {1 + 2} \right)\,\,\,\,0 \leqslant p \leqslant 1\,\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,p = 0\,\,\,\, \Rightarrow \,\,\,\,\,\,\left[ p \right] = 0\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\, \hfill \\ \,{\text{Take}}\,\,p = 1\,\,\,\, \Rightarrow \,\,\,\,\,\,\left[ p \right] = - 1\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\, \hfill \\ \end{gathered} \right.$$

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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Re: If [p] is defined as the smallest integer greater than or equal to -p,  [#permalink]

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Lets discuss for statement 1 only :
For any Value of P>= 0, [P] will be negative..
I will go for A.
GMATH Teacher P
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Re: If [p] is defined as the smallest integer greater than or equal to -p,  [#permalink]

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6697 wrote:
Lets discuss for statement 1 only :
For any Value of P>= 0, [P] will be negative..
I will go for A.

Hi, 6697!

Please pay attention to the definition of [p], mathematically explained as I presented:

$$\left[ p \right] = \min \left\{ {n\,\,\operatorname{int} \,\,\,:\,\,n \geqslant - p} \right\}$$

If p=1, for instance, we look for the minimum value of $$\left\{ {n\,\,\operatorname{int} \,\,\,:\,\,n \geqslant - 1} \right\}$$ ...

The minimum value will be -1, hence [p] will be negative.

On the other hand, when p=0, we look for the minimum value of $$\left\{ {n\,\,\operatorname{int} \,\,\,:\,\,n \geqslant -0=0} \right\}$$ ...

In this case, [p] will be zero, therefore nonnegative.

(Check that [-2] equals 2, and that [-2.5] equals 3, to verify you understood the definition of [p] without any doubt!)

I hope the definition of [p] is now clear.

Regards,
Fabio.
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If [p] is defined as the smallest integer greater than or equal to -p,  [#permalink]

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Question: If [p] is defined as the smallest integer greater than or equal to -p, is [p] < 0?

(1) p ≥ 0

No, sufficient. However...

(2) p ≤ 1

2 alone is not sufficient as it could be 1, which is >0 , nil if 0 or negative if < 0.

Combining both we assume that p could be 0 or 1, which is not < 0. I would go for C...
Retired Moderator V
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Posts: 1261
Location: India
Concentration: International Business, General Management
GPA: 3.64
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If [p] is defined as the smallest integer greater than or equal to -p,  [#permalink]

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1
Hi iamzyw

Combining Statement 1 & 2, as you derived correctly p could be 0 or 1,

Now if p = 0, -p= 0. hence [p] =0

If p =1, -p = -1. hence [p] = -1

Hence even after combing statement 1 & 2 , it is insufficient to say whether [p] <0

Hence Answer = E

iamzyw wrote:
Question: If [p] is defined as the smallest integer greater than or equal to -p, is [p] < 0?

(1) p ≥ 0

No, sufficient. However...

(2) p ≤ 1

2 alone is not sufficient as it could be 1, which is >0 , nil if 0 or negative if < 0.

Combining both we assume that p could be 0 or 1, which is not < 0. I would go for C...

_________________
Retired Moderator V
Joined: 27 Oct 2017
Posts: 1261
Location: India
Concentration: International Business, General Management
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If [p] is defined as the smallest integer greater than or equal to -p,  [#permalink]

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Hi6697

If p = 0.2, -p = -0.2 , hence [p] = 0
If p =1, -p = -1, hence [p] = -1
hence Statement 1 is NOT SUFFICIENT to say whether [p] < 0.

6697 wrote:
Lets discuss for statement 1 only :
For any Value of P>= 0, [P] will be negative..
I will go for A.

_________________ Re: If [p] is defined as the smallest integer greater than or equal to -p,   [#permalink] 18 Sep 2018, 10:18
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