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If 1 < p < 3, then which of the following could be true? (I)

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If 1 < p < 3, then which of the following could be true? (I) [#permalink] New post 25 Mar 2018, 03:05
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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

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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink] New post 25 Mar 2018, 10:11
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?
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink] New post 25 Mar 2018, 10:15
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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
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink] New post 25 Mar 2018, 10:18
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 :) :beat
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink] New post 18 May 2018, 16:04
answer is E.All three are possible
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink] New post 09 Jul 2018, 18:38
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
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink] New post 10 Jul 2018, 19:35
The answer is E, just input numbers from the range
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink] New post 18 Nov 2018, 21:04
E
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink] New post 23 Nov 2018, 13:56
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] New post 27 Nov 2018, 06:51
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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If 1 < p < 3, then which of the following could be true? (I)

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