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.