dimitri92 wrote:

Is x/3 an integer?

(1) 7x/3 = Positive integer

(2) 14x/3 = Positive integer

Is \(\frac{x}{3}=integer\)?

Note that we are not told that x is an integer.

(1) \(\frac{7}{3}x\) = Positive integer --> x is of a type \(x=\frac{3k}{7}\), where \(k\) is an integer \(>{0}\). Hence x may be multiple of 3 (3, 6, ...) in this case \(\frac{x}{3}=integer\) OR x can be reduced fraction (3/7, 6/7, ...) in this case \(\frac{x}{3}\neq{integer}\). Not sufficient.

(2) \(\frac{14}{3}x\) = Positive integer --> x is of a type \(x=\frac{3n}{14}\), where \(n\) is an integer \(>{0}\). Hence x may be multiple of 3 (3, 6, ...) in this case \(\frac{x}{3}=integer\) OR x can be reduced fraction (3/14, 6/14=3/7, ...) in this case \(\frac{x}{3}\neq{integer}\). Not sufficient.

(1)+(2) No new info. If \(x=3\), answer is YES but if \(x=\frac{3}{7}\), answer is NO. Not sufficient.

Answer: E.