If x, p and q are not 0, is p = q? (1) x^p = x^q (2) x is not 1

Question

If x, p and q are not 0, is p = q?

(1)   x^p = x^q 
(2) x is not 1

chetan2u · Answer

If x, p and q are not 0, is p = q?

(1)   x^p = x^q 
If x is 1, then p and q could be anything. 
Insufficient

(2) x is not 1
Nothing about p and q. 
Insufficient

Combined 
Easy to fall for C trap. 
X is not 1, but what if x=-1: p and q could be any even integers 
 (-1)^2=(-1)^4=(-1)^{100} 
Insufficient

E

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  Variables x, p and q are not equal to 0 
 We are asked if p = q or not 
 This is a YES-NO question

Statement 1:     x^p = x^q 
  In the above scenario, we can equate the powers and say   p=q  if and only if  x≠1,0,-1   
 In this question we are sure that  x≠0   
 However, if  x=1 , then   x^p = x^q  for all values of p and q (same or different) 
 And if  x=-1  then   x^p = x^q  for all even values of p and q (same or different) 
 Thus,  statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2:   x is not 1
  We know that  x,p,q≠0  and from this statement. we get that  x≠-1  
 However, from this, we cannot answer if  p=q  or not 
 Thus,  statement 2 alone is not sufficient and we can eliminate options B, C and E

Combining:   
  We already know  x≠0  
 from statement 1, we get   x^p = x^q  
 From statement 2, we get  x≠1  
 However, the  x=-1  scenario (talked about in statement 1) still exists

Hence the right answer is    Option E

If x, p and q are not 0, is p = q? (1) x^p = x^q (2) x is not 1

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