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

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Senior Manager
Joined: 02 Jan 2017
Posts: 307
If 1 < p < 3, then which of the following could be true?  [#permalink]

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03 Mar 2017, 02:33
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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
Senior Manager
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Posts: 274
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GMAT 2: 640 Q49 V28
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Re: If 1 < p < 3, then which of the following could be true?  [#permalink]

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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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Senior Manager
Joined: 15 Jan 2017
Posts: 351
Re: If 1 < p < 3, then which of the following could be true?  [#permalink]

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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)

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

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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.

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

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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
Re: If 1 < p < 3, then which of the following could be true?   [#permalink] 07 Jul 2017, 11:25
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