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D. - For 7 is indivisible by 3, then x must be divisible by 3 => x/3 an integer - 14 = 7*2, neither is divisible by 3, then x must be divisible by 3 => x/3 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.

(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.

Oh yeah..integer trap thing..it took me weeks to get over that. Still got me sometimes ! Here's another good integer trap with excellent explanation from HRH Bunuel http://gmatclub.com/forum/odd-even-95982.html

(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.

Hats off !! Not a single thought about x values , considered about x/3 only .

gmatclubot

Re: Is x/3 an integer?
[#permalink]
24 Dec 2015, 07:35

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