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# Is p^3 < p? (1) p < 1 (2) p is an integer

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Math Expert
Joined: 02 Sep 2009
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Is p^3 < p? (1) p < 1 (2) p is an integer  [#permalink]

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06 Apr 2018, 05:06
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Difficulty:

35% (medium)

Question Stats:

72% (01:07) correct 28% (00:55) wrong based on 62 sessions

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Is p^3 < p?

(1) p < 1

(2) p is an integer

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Is p^3 < p? (1) p < 1 (2) p is an integer  [#permalink]

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06 Apr 2018, 05:19
Bunuel wrote:
Is p^3 < p?

(1) p < 1

(2) p is an integer

Statement 1:
If p = 0, then both p and p^3 are equal so the answer is NO.
But if p = -2, then p^3 = -8 which is less than -2, so the answer is YES.
thus this statement in itself is not sufficient.

Statement 2:
If p=0 Or if p = 1, then both p and p^3 are equal so the answer is NO.
If p is a negative integer (except -1) than p^3 will be less than p so the answer will be YES.
If p is a positive integer > 1, then p^3 will be greater than p so the answer will be NO again.
thus this statement also is not sufficient.

Combining the statements, p is an integer < 1.
If p=0 or -1, then the answer is NO.
If p=-2 or -3, then the answer is YES. Again not sufficient. Hence E answer
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Re: Is p^3 < p? (1) p < 1 (2) p is an integer  [#permalink]

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06 Apr 2018, 08:25
1
It can also be done by wavy curve method a s explained in the sketch attached.

See this
https://gmatclub.com/forum/inequalities ... l#p1582891
Attachments

Screenshot001.jpg [ 64.41 KiB | Viewed 904 times ]

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Re: Is p^3 < p? (1) p < 1 (2) p is an integer  [#permalink]

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06 Apr 2018, 10:04
Bunuel wrote:
Is p^3 < p?

(1) p < 1

(2) p is an integer

we are looking whetherp^3 is less than p or not.

statement 1: it states that p<1. thus, p could be 0 , -2, - 100, -1/2. If we just consider p=0, p^3 and p will be same. Thus, statement 1 is not sufficient.

statement 2: p is and integer.
o is also an integer. in that case p^3 and p will be same. Integer can be negative or positive. thus answer will vary.

statement 1+2: still not sufficient. statement 1 tells us the range and statement 2 tells us that p is an integer. because of 0, we won't get the perfect answer.

thus , the correct answer is E.
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Re: Is p^3 < p? (1) p < 1 (2) p is an integer  [#permalink]

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08 Apr 2018, 16:12
question becomes -

is P^3 -P <1

or is (p-0)(p-1)(p- (-1)) < 0

drawing number line says this is true only when P is b/n 0 and 1 (not inclusive) and P is <-1 (non inclusive)

1) P < 1 clearly NS ( as the equation is > 0 b/n -1 and 0 and -ve b/n 0 and 1)
2) P is an integer again NS

(1) + (2) -
equation doesn't hold true If P is -1 ( equation is > 0) .
equation holds true for integers to left of -1 i.e. P(p-1)(p+1) is < 0

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Re: Is p^3 < p? (1) p < 1 (2) p is an integer  [#permalink]

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08 Apr 2018, 17:31
Bunuel wrote:
Is p^3 < p?

(1) p < 1

(2) p is an integer

(1) p < 1

Let p = 0................Answer is No

Let p = -2...............Answer is Yes

Insufficient

(2) p is an integer

Let p = 0................Answer is No

Let p = -2...............Answer is Yes

Insufficient

Combine 1 & 2

Same examples lead to no clear cut

Re: Is p^3 < p? (1) p < 1 (2) p is an integer   [#permalink] 08 Apr 2018, 17:31
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