Data Sufficiency

I came across this question while trying the GMAT prep
Question: What is the remainder when a positive integer n is divided by 6?
(1)n is a multiple of 5
(2)n is a multiple of 12

Answer: B

Can somebody pls explain how the answer is derived?

My understanding of the question is if we can atleast narrow it down to a range of numbers which satisfy the condition of being divisible by 6 it is sufficient to answer the question, need not specifically find the remainder.

The first statement tells n is a multiple of 5, thus the range could be 5,10,15,20,25,30,35,40,45,50,55,60....Of this range, checking 10 for divisibility with 6, the remainder is 4.Similarly for 15, it is 3 and so on. Thus I am able to tell what the remainder is.

The second statement tells n is a multiple of 12, thus the range could be 12,24,36,48,60....Of this range, checking 12 for divisbilty with 6, the remainder is 0,Similarly for 24, again remainder is 0 and so on. Thus again I am able to tell what the remainder is.

So according to me the answer should be D (Each statement alone is sufficient).
But the answer given is B.
Had the question been what is the value of n , then B would have been the right answer.

Please help me in understanding what is wrong in my logic. Btw this type of question falls in which range like 300-500/600-700??

sbhawal wrote:I came across this question while trying the GMAT prep
Question: What is the remainder when a positive integer n is divided by 6?
(1)n is a multiple of 5
(2)n is a multiple of 12

The question stem asks for a SPECIFIC VALUE (the remainder when n is divided by 6).
One way to evaluate the statements is to test cases.
If the value is THE SAME in every case. then the statement is SUFFICIENT.
If the value is NOT THE SAME in every case, then the statement is INSUFFICIENT.

Statement 1:
Options for n = 5, 10, 15, 20...
When 10 is divided by 6, the remainder is 4.
When 15 is divided by 6, the remainder is 3.
Since the remainder can be different values, INSUFFICIENT.

Statement 2:
Options for n = 12, 24, 36, 48...
When 12 is divided by 6, the remainder is 0.
When 24 is divided by 6, the remainder is 0.
When 36 is divided by 6, the remainder is is 0.
Since the remainder is the same in every case, SUFFICIENT.

The correct answer is B.

Hi Sbhawal

My understanding of the question is if we can atleast narrow it down to a range of numbers which satisfy the condition of being divisible by 6 it is sufficient to answer the question, need not specifically find the remainder.

The first statement tells n is a multiple of 5, thus the range could be 5,10,15,20,25,30,35,40,45,50,55,60....Of this range, checking 10 for divisibility with 6, the remainder is 4.Similarly for 15, it is 3 and so on. Thus I am able to tell what the remainder is.

What you did is correct,
But, Thing you have to note is,
You got remainder 4 when you divide 10 by 6
and remainder 3 divide 15 by 6
Since remainder is changing.
Statement 1 is Insufficient.

Hope it helps you.

Regards,
Uva.

Ohk! Now I get it, the trick is about getting same value every time!!

Thanks!

Uva@90 wrote:Hi Sbhawal

My understanding of the question is if we can atleast narrow it down to a range of numbers which satisfy the condition of being divisible by 6 it is sufficient to answer the question, need not specifically find the remainder.

The first statement tells n is a multiple of 5, thus the range could be 5,10,15,20,25,30,35,40,45,50,55,60....Of this range, checking 10 for divisibility with 6, the remainder is 4.Similarly for 15, it is 3 and so on. Thus I am able to tell what the remainder is.

What you did is correct,
But, Thing you have to note is,
You got remainder 4 when you divide 10 by 6
and remainder 3 divide 15 by 6
Since remainder is changing.
Statement 1 is Insufficient.

Hope it helps you.

Regards,
Uva.