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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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GRE 1: Q160 V160 Followers: 305

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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: 77% (00:50) correct 22% (00:51) wrong based on 71 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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Intern Joined: 20 Dec 2017
Posts: 30
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Kudos [?]: 19 , 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

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: 13720
GRE 1: Q160 V160 Followers: 305

Kudos [?]: 3553  , given: 12681

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

- Do you want all the GRE Prep Club resources at a glance (sort of ) ?? Look at GRE Prep Club Official LinkTree page
- Do you want all the GRE Prep Club FREE resources in one spot ?? Look at Free GRE Materials - Where to get it!! (2020)
- Do you want all the FREE GRE tests on earth ?? Look at FREE GRE Practice Tests [Collection] - New Edition (2021)
- Do you want to know the GRE score in the Top 25 BS in 7 continents ?? Look at here The GRE average score at Top 25 Business Schools 2020 Ed.
- Need Practice 20 Free GRE Quant Tests available for free with 20 Kudos
- GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Intern Joined: 20 Dec 2017
Posts: 30
Followers: 0

Kudos [?]: 19  , given: 9

Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
1
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
Followers: 0

Kudos [?]: 6 , given: 1

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
Posts: 38
Followers: 0

Kudos [?]: 6 , 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

Intern Joined: 04 Jun 2018
Posts: 8
Followers: 0

Kudos [?]: 6 , 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
Posts: 505
Followers: 0

Kudos [?]: 56 , given: 1

Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
E Manager Joined: 07 Aug 2016
Posts: 59
GRE 1: Q166 V156 Followers: 0

Kudos [?]: 43  , given: 3

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

Manager Joined: 23 Oct 2018
Posts: 57
Followers: 0

Kudos [?]: 0 , given: 0

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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