If p=(x^a+b)/(x^b), what is the value of positive integer p?

Question

If  p=\frac{x^{a+b}}{x^b} , what is the value of positive integer p?

(1)  x = 5 
(2)  a = 0

sashiim20 · Answer

p=\frac{x^{a+b}}{x^b}

Reducing the above equation;

p=\frac{x^a*x^b}{x^b}

Cancelling out  x^b , we get;

p=x^a

(1)  x = 5

Statement I can give multiple values for  p .

If  a = 0

p=5^0 = 1

If  a = 1

p=5^1 = 5

If  a = 2

p=5^2 = 25

Hence Statement I is insufficient.

(2)  a = 0

Any non- zero integer with exponent  0  will give value  1 .

Hence value of  p = 1

Statement II is sufficient.

Answer B

DavidTutorexamPAL · Answer

The answer is B. 
1) is insufficient - p is 5 taken to some power, but we don't know which. 
2) if a=0, p=x^b/x^b=1. sufficient!

u1983 · Answer

p=\frac{x^{a+b}}{x^b}  =  x^{a+b-b}  =  x^a

(1)  NS -  as we donot know the value of  a .
(2)   Suff   ... as the index value is  0 , whatever is the base  x , the expression  x^a  yields a fixed result ......  thus Ans B

nkshmalik1 · Answer

Given, P=x^(a+b) /x^b, 
p= x^a

A) x= 5, 
P=5^a, not sufficient.

B) a=0
P= x^0=1,sufficient

Hence, b.

Posted from my mobile device

GMATWhizTeam · Answer

Solution 
 Step 1: Analyse Question Stem 
 •  p = \frac{x^{(a+b)}}{x^b} 
•  p = x^{(a+b-b)} 
•  p= x^a  
We need to find the value of p.
 • The value of p depends upon the value of x and a. 
 Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE 
 Statement 1:   x = 5. 
 •  p= 5^a 
 o However, we don’t know the value of a.
o Thus, we cannot find the value of p.  
Hence, statement 1 is not sufficient, we can eliminate answer options A and B.
 Statement 2:  a = 0.
 •  p = x^0 
 o Now, irrespective of the value of x,  x^0  will be 1 only.
o Therefore,  p= x^0 = 1 .  
Hence, statement 2 is sufficient, the correct answer is  Option B .
 Note that in this question many of the students will mark the answer as option C, this is the C-trap.

SpartanX · Answer

Hi Bunuel Why is the answer B? Nothing is mentioned about the possibility of x not being 0. How can statement 2 alone be sufficient? I read in the below article that https://gmatclub.com/forum/exponents-an ... 74993.html

Bunuel · Answer

We are given that p is a positive integer, while if x = 0, it won't be so. Hence x cannot be 0.

If p=(x^a+b)/(x^b), what is the value of positive integer p?

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If p=(x^a+b)/(x^b), what is the value of positive integer p?

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