Does it terminate?

[chan.juan]

If 0 < x < 1, is it possible to write x as a terminating decimal?

(1) 24x is an integer.

(2) 28x is an integer.

The Manhattanprep official answer is "Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient." However, I believe "EACH statement ALONE is sufficient." Manhattanprep's explained its answer by giving the example: if x is 1/2, 24x = 12, and the decimal terminates (0.5). If, however, x = 1/3, 24x = 8, but the decimal does not terminate (0.3333….).

This example actually makes statement (1) sufficient, as now we know that it is "possible to write x as a terminating decimal". With statement (2), we can also know that it is possible to write x as a terminating decimal, just as proofed by Manhattenprep's example, when 28x=14, x will equal to 0.5, which is a terminating decimal. Hence, knowing that 28x is an integer, we can be sure that it is possible to write x as a terminating decimal.

If the question were changed to "If 0 < x < 1, is x a terminating decimal?", with the same premises (statements), then the official answer "both statement TOGETHER are sufficient,..." would be the correct answer.

[RonPurewal]

the answer to "is it possible to write x as...?" is not yes unless it's possible for EVERY value of x that fits the statement.

there's no way to write this question without "can", "possible", or some other equivalent of those--because we're talking about only one possible representation of a number.
"Can 1/2 be written as a terminating decimal?" yes, it's 0.5.
it would be nonsense to ask "Is 1/2 written as a terminating decimal?"

[RonPurewal]

If 0 < x < 1, is it possible to write x as a terminating decimal?

(1) 24x is an integer.

(2) 28x is an integer.

The Manhattanprep official answer is "Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient." However, I believe "EACH statement ALONE is sufficient." Manhattanprep's explained its answer by giving the example: if x is 1/2, 24x = 12, and the decimal terminates (0.5). If, however, x = 1/3, 24x = 8, but the decimal does not terminate (0.3333….).

This example actually makes statement (1) sufficient, as now we know that it is "possible to write x as a terminating decimal". With statement (2), we can also know that it is possible to write x as a terminating decimal, just as proofed by Manhattenprep's example, when 28x=14, x will equal to 0.5, which is a terminating decimal. Hence, knowing that 28x is an integer, we can be sure that it is possible to write x as a terminating decimal.

If the question were changed to "If 0 < x < 1, is x a terminating decimal?", with the same premises (statements), then the official answer "both statement TOGETHER are sufficient,..." would be the correct answer.

^^ by the way, according to your interpretation here, you wouldn't even have to think about the problem!
if this were the correct interpretation, then "not sufficient" would be absolutely impossible under any circumstances whatsoever. that observation alone should convince you that it's the wrong interpretation.

[RonPurewal]

finally, and most importantly, remember that there are NEVER any "trick questions" on this exam.

if your answer to a question changes because of some "tricky" interpretation of the words ... don't go there. that's not how this test works.