Number System -Value of x

[Gmat09_5ALL]

When 15n, where n is a positive integer, is divided by 6, the remainder is x. What is the value of x?
(1) When n is divided by 2, the remainder is 0.
(2) When n is divided by 3, the remainder is 0.

[viju9162]

Is the answer "A" ?

From (1) : n is a multiple of 2 ...and the set will look like this:

15 * 2 / 6 = 0 (Reminder)
15 * 4 / 6 = 0 (Reminder)
15 * 6 / 6 = 0 (Reminder)
15 * 8 / 6 = 0 (Reminder)
15 * 10 / 6 = 0 (Reminder)

From (2): n is a multiple of 3 ..and the set will look like this:

15 * 3 / 6 = 1 ( reminder)
15 * 6/6 = 0 ( reminder)
15 * 12/6 = 0 ( reminder)

We get different reminders from statement (2) ...

[Gmat09_5ALL]

Thanks viju9162, OA is A
is there any other way except from plugging value to tackle such question ?

[viju9162]

Hi Gmat09_5ALL,

Thank you. I am not sure solving without plugging values. Maybe, experts can help us here.

Regards,
Viju

[getso]

We can take this approach.

15n can be expressed as 3*5*n.

Question is Is 3*5*n/2*3=5*n/2 ( 3 gets cancelled)
Thus if number is divisible by 2 then it is divisible by 6 here.


A says 3*5*n is completely divisible by 2.
Thus n will be 2 or multiples of 2.
From this it is clear that for 3*5*n/2 is divisible by 2.

Thus Statement 1 is sufficient.

Statement 2 says that number is divisible by 3. It does not address whether number is divisible by 2 or not.
Hence not sufficient.

So A is the correct answer