Dicey DS question

[shivrakesh65]

Hi Ron,

This was one of the questions that i encountered in one of the Manhattan GMAT's CATs recently.

If n is a positive integer, is n/18 an integer?

(1) 5n/18 is an integer.

(2) 3n/18 is an integer.



Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient

The official answer is Option A, which was posted by Manhattan on this.

Although i do not agree with this.

My line of reasoning as below

Consider statement 5n/18 is an integer, which means 5n is a multiple of 18, so 5n could equal 18, 36, 54, 74, 90 etc..

Only in the 5th, 10th 15th and so on and so forth, multiple of 18, will n actually be an integer & multiple of 18, so n would be 18, 36, 54, 72 . In every other casein statement it will be a decimal. So a decimal divided by an integer can never be an integer.

Statement 2 also has multiple scenarios where n is either an integer & a multiple of 18 or just an integer but not a multiple of 18.

Combining both you would have commonalities between 18, 36, 54, 72 etc which would make n an integer and a multiple of 18, answering the question, whether n/18 is an integer or not.

Hence Option C is the right answer

Could you please explain where i have faltered in my reasoning?

Best Regards,

Rakeshh

[RonPurewal]

you're forgetting that n itself is an integer. so, the majority of the cases you listed are not actually valid cases.
for instance, the first case you listed is 5n = 18, which would mean n = 18/5... but that's not an integer, so that case isn't valid. (the same goes for most of the cases you listed.)

try the problem again, this time realizing that n itself has to be a whole number, and you'll see why statement 1 is sufficient.

statement 2 isn't sufficient because it reduces to "n/6 is an integer".
this just means n is a multiple of 6, not necessarily a multiple of 18.

[shivrakesh65]

Brilliant reasoning Ron!

A very simple , yet the most effective reasoning for a 700 level GMAT question....

Now why didn't I think of that?!

Rakeshh

[RonPurewal]

Brilliant reasoning Ron!

A very simple , yet the most effective reasoning for a 700 level GMAT question....

Now why didn't I think of that?!

Rakeshh

^^ did you mean to post this response on a different thread?

(it doesn't really make sense in response to what I posted here)