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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
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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 :) :beat
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
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]
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]
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]
E
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
1
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]
it was intersting question thanks
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
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Re: If 1 < p < 3, then which of the following could be true? (I) [#permalink]
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