If in the equation m = 1/2^x, x is an integer, x 0, and m is express

Question

If in the equation m = 1/2^x, x is an integer, x > 0, and m is expressed as a decimal, what is the value of the tenths digit of m?

(1) x < 5

(2) x > 3

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SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  We are given  m=\frac{1}{2^x}  where x is a positive integer 
 When  x=1 , then  m=\frac{1}{2^x}=\frac{1}{2}=0.5 . The tenth digit is 5  
 When  x=2 , then  m=\frac{1}{2^x}=\frac{1}{2^2}=0.25 . The tenth digit is 2  
 When  x=3 , then  m=\frac{1}{2^x}=\frac{1}{2^3}=0.125 . The tenth digit is 1  
 When  x=4 , then  m=\frac{1}{2^x}=\frac{1}{2^4}=0.0625 . The tenth digit is 0 
 For x = 4 and beyond i.e.,  when  x>3 , the tenth digit of  m=\frac{1}{2^x}  will always be 0

Statement 1:    x<5 
  When x = 4, tenth digit is 0   When x = 3, the tenth digit is 1 
 Thus,  statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2:    x>3 
  We have already discussed this in the pre-analysis step that  when  x>3 , the tenth digit of  m=\frac{1}{2^x}  will always be 0  
 Thus,  statement 2 alone is sufficient

Hence the right answer is    Option B

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If in the equation m = 1/2^x, x is an integer, x > 0, and m is express

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