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

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Is the integer n odd? (1) n is divisible by 3 (2) 2 n is [#permalink]  26 Dec 2005, 17:18
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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
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Re: DS: Is the integer N odd? [#permalink]  26 Dec 2005, 17:46
TeHCM wrote:
Is the integer n odd?

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

B.
suppose n = 2, factors are 1 and 2. no of dividers = 2
2n = 4, factors are 1 2, and 4. no of dividers = 3

if n = 1, divider =1
2n = 2, factors 1 and 2 so dividers =2.
the same applies to all primes other than 2.
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B

When n is even

n = 6 then divisors are 1, 2, 3, 6 (Total 4)
n = 12 then divisors are 1, 2, 3, 4, 6, 12 (Total 6)

When n is odd

n = 9 then divisors are 1, 3, 9 (Total 3)
n = 18 then divisors are 1, 2, 3, 6, 9, 18 (Total 6) <- twice as many positive integers
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Re: DS: Is the integer N odd? [#permalink]  26 Dec 2005, 23:37
TeHCM wrote:
Is the integer n odd?

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

Stmt 1: Let n =6 divisible by 3 but even. Let n = 9 odd and divisible by 3. So insuff.

Stmt2: Let n = 7 (a prime number) factors 1,7. 2n = 14 factors = 1,2,7,14 = There are twice as many factors as n.
Let n = 9 (odd number but not prime) factors = 1,3,9. 2n = 18 factors = 1,2,3,6,9,18 (There are twice as many factors)
Let n = 4 factors = 1,2,4 2n= 8 factors = 1,2,4,8 (Thre are no twice as many factors)

So stmt 2 is suff.
Hence B
Re: DS: Is the integer N odd?   [#permalink] 26 Dec 2005, 23:37
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