(1) n = 9 (ODD), and n = 12 (EVEN). Both of them are divisible by 3, so no definite answer.atulmangal wrote:Is the integer n odd?
(1) n is divisible by 3.
(2) 2n is divisible by twice as many positive integers as n.
Hi Anurag,Anurag@Gurome wrote:(1) n = 9 (ODD), and n = 12 (EVEN). Both of them are divisible by 3, so no definite answer.atulmangal wrote:Is the integer n odd?
(1) n is divisible by 3.
(2) 2n is divisible by twice as many positive integers as n.
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 Atul!atulmangal wrote: 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 ???
n has 4 while 2n has 6 factors.sourabh33 wrote: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.
Hi Sourabh!sourabh33 wrote: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
