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What is the value of p?

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Bunuel
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What is the value of p? [#permalink] New post   11 Nov 2019, 03:48
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What is the value of p?

(1) \((\frac{p}{2}) ^ {(\frac{p}{2})} = \frac{p}{2}\)


(2) \((\frac{2}{p}) ^ {(\frac{2}{p})} = \frac{2}{p}\)


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Re: What is the value of p? [#permalink] New post   02 Jan 2020, 02:36
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+2 and -2 both satisfy both the statements. Hence, E
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Re: What is the value of p? [#permalink] New post   11 Nov 2019, 04:55
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itoyj wrote:
Bunuel
Can u please help with option B
It is not understandable

Posted from my mobile device


(2) says that 2/p in the power of 2/p equals to 2/p.
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Re: What is the value of p? [#permalink] New post   11 Nov 2019, 06:30
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assume P/2=X , then P=2X then option 1 can be converted to
x^x=x
x=1
then p=2
Do the same thing with option 2
Which will again give P=2.
Ans. D
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What is the value of p? [#permalink] New post   Updated on: 12 Nov 2019, 06:57
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Bunuel wrote:
What is the value of p?

(1) \((\frac{p}{2}) ^ {(\frac{p}{2})} = \frac{p}{2}\)


(2) \((\frac{2}{p}) ^ {(\frac{2}{p})} = \frac{2}{p}\)




statement 1: As p is in numerator P can be 0 or a definite value =2 if we equate the bases so insufficient
statement 2: P is in the denominator so p not equal 0 and therefore we get a unique value on equating the bases : sufficient

therefore B

Originally posted by OC2910 on 11 Nov 2019, 06:57.
Last edited by OC2910 on 12 Nov 2019, 06:57, edited 2 times in total.
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Re: What is the value of p? [#permalink] New post   12 Nov 2019, 21:30
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I am not sure but for option B (-2) also satisfies the value
I think it should b E
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Re: What is the value of p? [#permalink] New post   11 Nov 2019, 04:52
Bunuel
Can u please help with option B
It is not understandable

Posted from my mobile device
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Re: What is the value of p? [#permalink] New post   11 Nov 2019, 05:49
case 1: assume p/2 = a
then a^a = a => a=1
--> p/2 =1 or p=2 (sufficient)

case 2: assume 2/p = a
then a^a =a => a=1
--> 2/p = 1 or p=2 (sufficient)

Ans D
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What is the value of p? [#permalink] New post   Updated on: 13 Nov 2019, 01:51
StrugglingGmat2910 wrote:
Bunuel wrote:
What is the value of p?

(1) \((\frac{p}{2}) ^ {(\frac{p}{2})} = \frac{p}{2}\)


(2) \((\frac{2}{p}) ^ {(\frac{2}{p})} = \frac{2}{p}\)




statement 1: As p is in numerator P can be 0 or a definite value =2 if we equate the bases so insufficient
statement 2: P is in the denominator so p not equal 0 and therefore we get a unique value on equating the bases : sufficient

therefore B





0^0 is not defined if it is defined as in most cases 0^0 =1

Originally posted by Prateeksansanwal on 12 Nov 2019, 01:34.
Last edited by Prateeksansanwal on 13 Nov 2019, 01:51, edited 1 time in total.
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Re: What is the value of p? [#permalink] New post   02 Jan 2020, 09:43
0 and 2 satisfies both the statements.
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What is the value of p? [#permalink] New post   17 Feb 2020, 22:28
Given statements essentially say a^a=a
Only possible for values of 1 or -1.
St 1 - P can be 2 or -2
St 2 - P can be 2 or -2

Hence, Insufficient information given.
IMO E
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Re: What is the value of p? [#permalink] New post   21 Oct 2021, 20:28
Bunuel wrote:
What is the value of p?

(1) \((\frac{p}{2}) ^ {(\frac{p}{2})} = \frac{p}{2}\)


(2) \((\frac{2}{p}) ^ {(\frac{2}{p})} = \frac{2}{p}\)


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(1) \((\frac{p}{2}) ^ {(\frac{p}{2})} = \frac{p}{2}\)
Squaring both sides
(p/2)^p = (p/2)^2
p^(p-2) = 2^(p-2) - Eq 1

Here, we need to be careful with EVEN powers.
Eq 1 satisfies both +2, -2 as a solution.

(2) \((\frac{2}{p}) ^ {(\frac{2}{p})} = \frac{2}{p}\)
Just like (1)
2^(2-p) = p^(2-p)
Here as well, +2, -2 both satisfies.

Hence, can't be determined by both. (E)
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Re: What is the value of p? [#permalink]
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