Hi jeph86,

To start, there's a minor typo in your post. The equation should read:

S= (2/n)/(1/x + 2/3x)

We're told that XN is not equal to 0 (so neither of those variables can be 0). We're asked for the value of S. This question can be solved by TESTing VALUES.

1) x = 2n

IF....
n = 1
x = 2
(2/1)/(1/2 + 2/6) = 2/(1/2 + 1/3) = 2/(5/6) = 12/5

IF....
n = 2
x = 4
(2/2)/(1/4 + 2/12) = 1/(1/4 + 1/6) = 1/(5/12) = 12/5

IF...
n = -3
x = -6
(2/-3)/(-1/6 - 2/18) = (-2/3)(-1/6 - 1/9) = (-2/3)/(-5/18) = +36/15 = 12/5

The answer to the question is ALWAYS 12/5.
Fact 1 is SUFFICIENT

2) n = 1/2

This Fact tells us NOTHING about the value of x. As x changes, the value of S will change.
Fact 2 is INSUFFICIENT

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Hi jeph86,

In Fact 1, we're given the extra information that x=2n, so you CANNOT use n=1, x=4 as a TEST case. You have to use values that fit the equation x=2n. Any pair of values that fit THAT equation will also produce the result 12/5 in the original question.

GMAT assassins aren't born, they're made,
Rich

Here is some general advice about DS problems like this one: if it feels too obvious that using both statements together will give you an answer, then it's probably not C. This is what we call a C-Trap.

In this case, if you knew that n = 1/2, you could clearly plug it into x = 2n, and clearly x = 1. We have all of the values we need, but we haven't done any conceptual thinking! That's our signal to be skeptical: could either statement be sufficient on its own? If we rephrase properly, we see that statement (1) is enough, so we don't need to put the 2 statements together. The answer must be A.

For more on how to avoid C-Traps, read these articles:
https://www.manhattanprep.com/gmat/blog ... fficiency/
https://www.manhattanprep.com/gmat/blog ... ncy-traps/