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Is the integer n odd? (1) n is divisible by 3 (2) 2n is

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Is the integer n odd? (1) n is divisible by 3 (2) 2n is [#permalink] New post 20 Aug 2006, 20:16
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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.

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

:?:
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 [#permalink] New post 20 Aug 2006, 23:36
D

(1) no is a multiple of 3 ..so its odd
(2) valid only for odd nos.
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 [#permalink] New post 21 Aug 2006, 06:49
B.

1. number is divisible by 3 - 9 or 6 INSUFF
2. The factors of an odd number are always odd, which means that if the number is mulitplied by 2 there will be double the number of factors
if a number n has 3 odd factors - 1, a and n then 2n will have 1, 2, a, 2a, n ,2n - double the number. an even number on the other hand will have atleast 1 less than the number of factors. SUFF


Or you could plug in a few numbers and get a general trend

so Answer B
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 [#permalink] New post 21 Aug 2006, 08:44
B....

1) insuff - could be 6 which is even

2) Suff - 2(n) set N = 2, compares 2 div by 1 and 2 to 4 div by 4, 2, 1 - only an addition of 1 divisibility. Set N = 3 - suff.
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 [#permalink] New post 21 Aug 2006, 08:46
Concur with (B). Try picking 15 and then break down its prime factors.

15 = 4 factors (1,3,5,15)
30= 8 factors (1,2,3,5,6,10,15,30)

works with other obscure odd numbers as well.
  [#permalink] 21 Aug 2006, 08:46
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