If 1/3

Question

If 1/3 < z < 2/3, then what is the value of z?

(1) When positive integer x is divided by 2, the result is z. 
(2) When positive even integer y is divided by 12, the result is z.

Bunuel · Accepted Answer

If 1/3 < z <2/3 , then what is the value of z?

(1) When positive integer x is divided by 2, the result is z --> \(z=\frac{x}{2}\) --> \(\frac{1}{3}<\frac{x}{2}<\frac{2}{3}\) --> \(\frac{2}{3}<x<\frac{4}{3}\) --> since \(x\) is an integer then \(x=1\) (the only integer in that range) --> \(z=\frac{x}{2}=\frac{1}{2}\). Sufficient.

(2) When positive even integer y is divided by 12, the result is z --> \(z=\frac{y}{12}\) --> \(\frac{1}{3}<\frac{y}{12}<\frac{2}{3}\) --> \(4<y<8\) --> since \(y\) is an even integer then \(y=6\) (the only even integer in that range) --> \(z=\frac{y}{12}=\frac{1}{2}\). Sufficient.

Answer: D.

Bunuel · Answer

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SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  We are given  \frac{1}{3} < z < \frac{2}{3}  
 We are asked the value of z which is in between  \frac{1}{3}=0.33  and  \frac{2}{3}=0.66

Statement 1:   When positive integer x is divided by 2, the result is z 
  According to this statement  z=\frac{x}{2}  where x is a positive integer like 1, 2, 3, 4 and so on... 
 Thus, we can write  \frac{1}{3} < \frac{x}{2} < \frac{2}{3}  which is  only satisfied when  x=1  because when  x\ge 2 , then  z=\frac{x}{2}  will no longer be between 0.33 and 0.66
   Thus,  statement 1 alone is sufficient and we can eliminate options B, C and E

Statement 2:   When positive even integer y is divided by 12, the result is z 
  According to this statement  z=\frac{y}{12}  where y is a positive even integer like 2, 4, 6 and so on... 
 Thus, we can write  \frac{1}{3} < \frac{y}{12} < \frac{2}{3}  which is  only satisfied when  y=6  because when  y \le 4  or  y\ge 8 , then  z=\frac{y}{12}  will no longer be between 0.33 and 0.66
   Thus,  statement 2 alone is also sufficient

Hence the right answer is    Option D

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If 1/3 < z < 2/3, then what is the value of z?

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