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

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Senior Manager
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If 1 < p < 3, then which of the following could be true?  [#permalink]

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New post 03 Mar 2017, 02:33
3
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:18) correct 26% (01:24) wrong based on 128 sessions

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

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New post 03 Mar 2017, 03:47
1
vikasp99 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


Since Question says "could be true"
(I) p^2 < 2p ------ True for p=3/2
(II) p^2 = 2p ------ True for p=2
(III) p^2 > 2p ------ True for p=5/2

Hence option E is correct
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Re: If 1 < p < 3, then which of the following could be true?  [#permalink]

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New post 07 Jul 2017, 07:01
One way to think about it, for questions like these
1. p square < 2p => p<2 (approaching 1 but NOT 1, like 1.2, 1.5, 1.66, 1.999)
2. P sq = 2p => p = 2 (most obvious one, a trap i fell for)
3. p sq > 2p implying p > 2 (approaching 3 NOT 3, and more than 2, like 2.2, 2.3...2.9999)

Is this a correct way to think about problems like these? Thank you for your reply
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If 1 < p < 3, then which of the following could be true?  [#permalink]

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New post 07 Jul 2017, 10:14
4
vikasp99 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


\(1 < p < 3\)

From above expression, we can conclude \(p\) is positive. \(p\) could be positive integer or positive fraction.

(I) \(p^2 < 2p\)

\(p * p < 2*p\)

\(p < 2\) ------------- (Could be true)

\(p\) is positive fraction greater than \(1\) and less than \(2\).

(II) \(p^2 = 2p\)

\(p*p = 2p\)

\(p = 2\) --------------- (Could be true)

(III) \(p^2 > 2p\)

\(p*p >2p\)

\(p>2\) --------------- (Could be true)

\(p\) is positive fraction greater than \(2\) and less than \(3\).

I, II, and III could be true.

Answer (E)...

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

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New post 07 Jul 2017, 11:25
we can also do it by solving equations.

I) p^2 < 2p. This means p^2 - 2p < 0 or p(p-2) < 0.. this will be true for 0<p<2. Since this range is within our given range (1<p<3), this statement COULD be true. Eg for p=1

II) p^2 = 2p. This means p^2 - 2p = 0 or p(p-2) = 0.. this will be true for p=0 and p=2. Since p=2 lies within the given range (1<p<3), this statement COULD be true. for p=2

III) p^2 > 2p. This means p^2 - 2p > 0 or p(p-2) > 0.. this will be true for p>2 or p<0. Since p>2 is possible within our given range (1<p<3), this statement COULD be true. Eg for p=2.5

Since all three statements could be true, answer is E
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Re: If 1 < p < 3, then which of the following could be true?   [#permalink] 07 Jul 2017, 11:25
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If 1 < p < 3, then which of the following could be true?

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