# Thread: Is the integer n odd ?

1. Good post? |

## Is the integer n odd ?

(1) n is divisible by 3
(2) 2n is divisible by twice as many positive integers as n

I need more explanations on (2) especially.

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

To me it looks like statement 2 is alone sufficient to answer the question but not 1

(1) a number divisible by 3 may be even
(2) let suppose the number n is divisible by m positive integers [1 ...... n ]
now if n is odd it will have [ 1 . ...... n] positive integers or have it in powers of prime
2^03^b5^c.......
now the number 2n will have twice integers divisible as we already have 2^0[3^a.5^b....]
numbers now we will also have 2^1[3^a.5^b....] so the total numbers would be exactly
double
2^0[3^a5^b....] & the set consisting of 2^1[3^a.5^b....]
however in case of even n this wont happen as we won get new number on doubling n
( think of it as we already have a combination of atleast 2^0.3^a... and 2^1.3^b... so on multiplying former by 2 would result in the latter that is already present in our set).

do write if there is any better solution or any correction needed to this ...

regards
sason

3. Good post? |
we can do it by putting number too:

1. 1,3,6, : 6 is not
2. 3 and 6

for 3: 1,3
6: 1,2,3,6

try for 4 and 8....

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