STATEMENT 1 IS NOT SUFFICIENT AT ALL IF U TAKE AN ODD VALUE AND A EVEN VALUE YOU WILL GET IT,ITS YES OR NO

SATEMENT 2: FOR ANY RANGE IF YOU WILL CHECK YOU WILL ALWAYS HAVE N IS NOT ODD ie "NO ALWAYS "
SO B IS SUFFICIENT

Thank You all u guyzzz for a wonderful explanation... Honestly i got stunned seeing this explanation..
it did not click to me honestly...
well done guyzz!!

The number of factors of any no is given by the product of sum of all individual prime factors upto their max power. Example 40 = 2^3*5 No of factors = (2^0+2^1+2^2+2^3)*(5^0+5^1) = 15 * 6 = 90

S1: Not sufficient
S2: 2 times the number has twice as many factors as the number itself => 2 must be a factor => Not odd
Sufficient

(B) is answer.

I got stumped with the word translation of this one.....but anyway got it now

IMO B

Got by plugging in values !

Even :

2 - 1 2
4 - 1 2 4

Odd:

3 - 1 3
6 - 1 3 6 2 => Every 2n of an odd number has an extra factor of 2

Hence, 2n of an odd no. has twice as many positive integers as n !

Let it B.

Nice problem!

Is the integer n odd?

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

IMO: B
1. n may be 3, 6, 9, 12, and so on. Not sufficient
2. let n be 3, so 2n = 6
factors of 3: 1,3
factors of 6: 1,2,3,6
if n = 5
factors of 5: 1,5
factors of 10: 1,2,5,10
n=9
factors of 9: 1,3,9
factors of 18:1,2,3,6,9,18 Sufficient

Good one,Just take example of some even & odd numbers it will help to solve.

Answer B.

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Is the integer n odd?

(1) n is divisible by 3.

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

in the original condition we have 1 variable (n) and in order to match the number of variables and equations we need 1 equation. Since there is 1 each in 1) and 2), D is likely the answer.

In case of 1), the answer is yes for n=3, but no for n=6 no. Therefore it is NOT sufficient
In case of 2), if the number of factors for 2n is twice the number of factors of n, then n must be an odd number. This is because if n is an odd number, the multiple of indices + 1 is the number of factors (since 2 is an even number) and thus becomes (1+1)(number of factors of n). Since this is sufficient, the answer is B.


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statement 2 - if n is odd lets say 3

then factors are 1 & 3

factors of 2n - 6 are 1,2,3,6

so n is Odd.
statement 2 is sufficient
Answer is B

I believe that the correct answer to this problem is choice B.

Let's try to break statement (1): n is divisible by 3

Suppose n odd that is 9: it is divisible by 3.
Suppose n is 12: it is also divisible by 3.
Hence, statement (1) provides us with more than one answer, so it is insufficient.

Let's try to break statement (2): 2n is divisible by twice as many positive integers as n
Suppose n is odd that is 9: 1, 3, 9. It has three divisors.
Hence, 2n i.e. 2 x 9 = 18; 1, 2, 3, 6, 9, 18. It has six divisors.
Suppose n is even that is 12: 1, 2, 3, 4, 6, 12. It has six divisors.
Hence 2n i.e. 2 x 12 = 24; 1, 2, 3, 4, 6, 8, 12, 24. It has eight divisors.

Therefore statement (2) maintains the condition for the n to be odd, it is sufficient to prove that n is an odd integer.

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GMAT Assassin