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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If 1 < p < 3, then which of the following could be true? (I)  Question banks Downloads My Bookmarks Reviews Important topics
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Founder  Joined: 18 Apr 2015
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If 1 < p < 3, then which of the following could be true? (I) [#permalink]
Expert's post 00:00

Question Stats: 72% (00:55) correct 27% (00:40) wrong based on 40 sessions
If $$1 < p < 3$$, then which of the following could be true?

(I) $$p^2 < 2p$$

(II) $$p^2 = 2p$$

(III) $$p^2 > 2p$$

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
[Reveal] Spoiler: OA

_________________
Intern Joined: 20 Dec 2017
Posts: 30
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Kudos [?]: 17 , given: 9

Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
Carcass wrote:
If $$1 < p < 3$$, then which of the following could be true?

(I) $$p^2 < 2p$$

(II) $$p^2 = 2p$$

(III) $$p^2 > 2p$$

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III

Please, SOS
When we have "could be true" - we don't have to try to find contrargument do we? We just need a prove, that in some scenario an argument is working. Am I right? Founder  Joined: 18 Apr 2015
Posts: 6607
Followers: 107

Kudos [?]: 1264  , given: 5990

Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
1
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Expert's post
Actually, in this kind of question, the wrong answer is that is impossible or ALWAYS NOT true.

The other options that could be true are right, even though NOT always are true.

The best strategy here is to pick numbers, positive, between 1 and 3 such as an integer and a fraction: $$2$$ and $$\frac{3}{2}$$.

Hope this helps
_________________ Intern Joined: 20 Dec 2017
Posts: 30
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Kudos [?]: 17  , given: 9

Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
1
This post received
KUDOS
Carcass wrote:
Actually, in this kind of question, the wrong answer is that is impossible or ALWAYS NOT true.

The other options that could be true are right, even though NOT always are true.

The best strategy here is to pick numbers, positive, between 1 and 3 such as an integer and a fraction: $$2$$ and $$\frac{3}{2}$$.

Hope this helps

Thank you  Intern Joined: 15 May 2018
Posts: 38
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
answer is E.All three are possible
Intern Joined: 15 May 2018
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Kudos [?]: 5 , given: 1

Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
Carcass wrote:
If $$1 < p < 3$$, then which of the following could be true?

(I) $$p^2 < 2p$$

(II) $$p^2 = 2p$$

(III) $$p^2 > 2p$$

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III

My Answer is E
Intern Joined: 04 Jun 2018
Posts: 8
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Kudos [?]: 3 , given: 0

Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
The answer is E, just input numbers from the range
Director Joined: 09 Nov 2018
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
E Intern Joined: 07 Aug 2016
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Kudos [?]: 15  , given: 0

Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
1
This post received
KUDOS
Carcass wrote:
If $$1 < p < 3$$, then which of the following could be true?

(I) $$p^2 < 2p$$

(II) $$p^2 = 2p$$

(III) $$p^2 > 2p$$

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III

Algebraically.

Given that p is positive from 1 < p < 3

p^2 < 2p

p^2 - 2p < 0
p (p - 2) < 0 possible if p is less than 2.

Also p < 2 which is already given from the statement.

p^2 = 2p

p^2 - 2p = 0
p (p-2) = 0

Either p = 0 or 2, we know that p cannot be 0 so it must be 2

p = 2 (possible)

The last option as p^2 > 2p

p^2 - 2p > 0
p (p-2) > 0 possible if p > 2

Or p > 2 (true according to the stem)

Answer choice E.
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
it was intersting question thanks Re: If 1 < p < 3, then which of the following could be true? (I)   [#permalink] 27 Nov 2018, 06:51
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