What is the value of p?

Question

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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itoyj · Answer

Bunuel 
Can u please help with option B 
It is not understandable

Posted from my mobile device

Bunuel · Answer

(2) says that 2/p in the power of 2/p equals to 2/p.

navaneethmmb · Answer

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

TAC470 · Answer

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

OC2910 · Answer

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

Prateeksansanwal · Answer

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

globaldesi · Answer

I am not sure but for option B (-2) also satisfies the value
I think it should b E

ShankSouljaBoi · Answer

+2 and -2 both satisfy both the statements. Hence, E

hero_with_1000_faces · Answer

0 and 2 satisfies both the statements.

sreddy07 · Answer

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

happypuppy · Answer

(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)

What is the value of p?

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