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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]  25 Mar 2018, 03:05
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Question Stats:

73% (00:56) correct 26% (00:40) wrong based on 41 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

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

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]  25 Mar 2018, 10:15
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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
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]  25 Mar 2018, 10:18
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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
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]  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]  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

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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]  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]  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]  23 Nov 2018, 13:56
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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)

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