Is x – 1/16 greater than 5/8?

(1) Four times the value of x is less than three.

(2) One third of two is less than the value of x.


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This problem can be tackled algebraically. The trick is make sure you work neatly and stop to reflect before deciding sufficiency.

X-1/16 > 5/8?
Or x>11/16?

Goal: Prove (yes/no) that x is in fact greater than 11/16 (or, conversely, that it is equal to or less than 11/16).

Statement 1: 4x<3 or x<3/4. Use the cross multiplication method to compare fractions (3*16 and 4*11). 48>44, so then 3/4 is greater than 11/16. But we know that x is less than 3/4 so it could be less than 11/16 or more than 11/16 because we do not know the relationship between x and 11/16. So this answer is not sufficient because YES or NO is possible.

Statement 2: For this one, we are told that 2/3<x. We can quickly realize that 2/3<11/16. But once again, we cannot state if x is greater than or less than 11/16 because x > 2/3, so it could be between 2/3 and 11/16 or it could be greater than 11/16. Not sufficient.

Combined: Here we know that 2/3 < x < 3/4, but since 11/16 falls in this range, we cannot state whether 11/16 is greater than x definitively.

It's x – 1/16 NOT (x – 1)/16. So, It's \(x – \frac{1}{16}\) NOT \(\frac{x – 1}{16}\).
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