Is the integer n odd?

[atulmangal]

Is the integer n odd?
(1) n is divisible by 3.
(2) 2n is divisible by twice as many positive integers as n.

[Anurag@Gurome]

Is the integer n odd?
(1) n is divisible by 3.
(2) 2n is divisible by twice as many positive integers as n.

(1) n = 9 (ODD), and n = 12 (EVEN). Both of them are divisible by 3, so no definite answer.
So, (1) is NOT SUFFICIENT.

(2) If n = 2 (EVEN), then 2n = 4, which is divisible by 1, 2, and 4. 2 is divisible by 1 and 2. Here 2n does not have twice as many divisors as n.
If n = 3 (ODD), then 2n = 6, which is divisible by 1, 2, 3, and 6. 3 is divisible by 1 and 3. Here, 2n has twice as many divisors as n.
If n = 9 (ODD), then 2n = 18, which is divisible by 1, 2, 3, 6, 9 and 18. 3 is divisible by 1, 3, and 9. Here, 2n has twice as many divisors as n.
So, if n is ODD, then 2n will have twice as many divisors as n.
Hence, (2) is SUFFICIENT.

The correct answer is B.

[atulmangal]

Is the integer n odd?
(1) n is divisible by 3.
(2) 2n is divisible by twice as many positive integers as n.

(1) n = 9 (ODD), and n = 12 (EVEN). Both of them are divisible by 3, so no definite answer.
So, (1) is NOT SUFFICIENT.

(2) If n = 2 (EVEN), then 2n = 4, which is divisible by 1, 2, and 4. 2 is divisible by 1 and 2. Here 2n does not have twice as many divisors as n.
If n = 3 (ODD), then 2n = 6, which is divisible by 1, 2, 3, and 6. 3 is divisible by 1 and 3. Here, 2n has twice as many divisors as n.
If n = 9 (ODD), then 2n = 18, which is divisible by 1, 2, 3, 6, 9 and 18. 3 is divisible by 1, 3, and 9. Here, 2n has twice as many divisors as n.
So, if n is ODD, then 2n will have twice as many divisors as n.
Hence, (2) is SUFFICIENT.

The correct answer is B.

Hi Anurag,

Thanks a lot but i have one doubt...in this question don't u think, Op B interpret something else than what u interpret...actually this is why i was not able to solve this question..

Op B: 2n is divisible by twice as many positive integers as n

i interpret it as "2n" is divisible by "2n" numbers---> this is nonsensical but this is what the language of Op B suggest...m i wrong ???

[Anurag@Gurome]

Hi Anurag,

Thanks a lot but i have one doubt...in this question don't u think, Op B interpret something else than what u interpret...actually this is why i was not able to solve this question..

Op B: 2n is divisible by twice as many positive integers as n

i interpret it as "2n" is divisible by "2n" numbers---> this is nonsensical but this is what the language of Op B suggest...m i wrong ???

Hi Atul!

I think you are getting a little bit confused by the language of statement (2).
2n is divisible by twice as many positive integers as n is divisible by, which means 2n has twice as many factors as that of n.

[sourabh33]

Hi Anurag

A small clarification to be made

If n = 6 (Even), then 2n = 12; n is divisible by 1,2,3 & 6....while 2n is divisible by 1,2,3,4,6 and 12. Here, 2n has twice as many divisors as n, so even statement B should be insufficient.

Now, taking 1&2 together, if we choose 3 and 6 as test numbers both qualify in statements 1 & 2. So the answer should be E




In addition, if we consider Atul's interpretation to be correct (although I do not agree with that)
then for statement 2 to be true, n has to be 1.

If n = 1 (odd), then 2n = 2; n is divisible by only 1....while 2n is divisible by 1 and 2. Here, 2n has twice as many divisors as n, so only in this case B could be sufficient.

Please clarify



Best Regards
Sourabh

[Subeg Gill]

Hi Anurag

A small clarification to be made

If n = 6 (Even), then 2n = 12; n is divisible by 1,2,3 & 6....while 2n is divisible by 1,2,3,4,6 and 12. Here, 2n has twice as many divisors as n, so even statement B should be insufficient.

n has 4 while 2n has 6 factors.
B is sufficient.

[Anurag@Gurome]

Hi Anurag

A small clarification to be made

If n = 6 (Even), then 2n = 12; n is divisible by 1,2,3 & 6....while 2n is divisible by 1,2,3,4,6 and 12. Here, 2n has twice as many divisors as n, so even statement B should be insufficient.

Now, taking 1&2 together, if we choose 3 and 6 as test numbers both qualify in statements 1 & 2. So the answer should be E




In addition, if we consider Atul's interpretation to be correct (although I do not agree with that)
then for statement 2 to be true, n has to be 1.

If n = 1 (odd), then 2n = 2; n is divisible by only 1....while 2n is divisible by 1 and 2. Here, 2n has twice as many divisors as n, so only in this case B could be sufficient.

Please clarify

Best Regards
Sourabh

Hi Sourabh!

I think your query is already being answered by Subeg. If there is still any query, please let me know.