Is nonnegative integer x odd? (1) x! = |x - 1|! (2) x! = (x + 1)!

Question

Is nonnegative integer x odd?

(1) x! = |x - 1|!
(2) x! = (x + 1)!

attari92 · Answer

the trick is to not forget considering '0'. 0! =1 option =>b

nkin · Answer

IMO Option B.

(1) x can be 0 or 1. 0! = 1! = 1
If x = 0 then 0! = |0-1|! = |-1|! = 1! = 1
If x = 1, then 1! = |1-1|! = 0! = 1

Hence insufficient to say if x is odd or even since if x is 0, it is neither odd nor even.

(2) Only value (nonnegative integer) to satisfy the equation is x = 0. Hence sufficient to answer Yes/No type question stem.

Hence Option B.

attari92 · Answer

i stand corrected perhaps mistakenly typed 'd' instead of 'b'

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  x is a non-negative integer  
 We are asked if x is odd or not  
 This is a YES-NO question

Statement 1:   x! = |x - 1|!
  According to this statement, the value of x can be both 0 or 1
  When  x=0 ,  x! = |x - 1|!⇒0!=|0-1|!⇒1=|-1|!⇒1=1!⇒1=1  
 When  x=1 ,  x! = |x - 1|!⇒1!=|1-1|!⇒1=|0|!⇒1=0!⇒1=1    
 Thus,  statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2:   x! = (x + 1)!
  According to this statement, the value of x has to be 0 
 When  x=0 ,  x! = (x + 1)!⇒0!=(0+1)!⇒1=1!⇒1=1  
 Thus,  statement 2 alone is sufficient

Hence the right answer is    Option B

Is nonnegative integer x odd? (1) x! = |x - 1|! (2) x! = (x + 1)!

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