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20 k is divisible

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20 k is divisible

by sanju09 » Wed Apr 08, 2009 4:10 am
If k is a positive integer, then 20 k is divisible by how many different positive integers?

(1) k is prime.

(2) k = 7.



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by sacx » Wed Apr 08, 2009 7:29 am
Stmt I

k is prime

if k = 11, then 20k has 3 different prime numbers (2,5 and 11)

if k = 2 or 5 then 20k has only 2 different prime numbers ( 2 and 5)

Insuff

Stmt II

k = 7

20 k has 3 different prime numbers (2,5,7)

[spoiler]Suff

B[/spoiler]
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by cubicle_bound_misfit » Wed Apr 08, 2009 9:06 pm
stmt 1 is insufficient coz

if k is prime it can be 2 also.
if it is 2 then total number of intergers dividing 20k does not change.
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by gmat740 » Wed Apr 08, 2009 9:22 pm
stmt 1 is insufficient coz

if k is prime it can be 2 also.
if it is 2 then total number of intergers dividing 20k does not change.
Even I missed this point actually

Thanks a lot

by the way there can be a twist to this problem:

if k was an integer>2

ie: k>2

so answer would be D

I know that we are only suppose to discuss the questions which are posted rather than to bring our input, but what's the harm in knowing the variety of ways one particular question can be framed

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by mehravikas » Thu Sep 24, 2009 1:34 pm
@@Karan,

Sorry to open an old thread. I don't think that the answer to this problem would be 'D' if it was given that k > 2

The question is asking for "different positive integers" not "different positive prime factors"

Please correct if I am wrong.

Thanks,
Vikas
gmat740 wrote:
stmt 1 is insufficient coz

if k is prime it can be 2 also.
if it is 2 then total number of intergers dividing 20k does not change.
Even I missed this point actually

Thanks a lot

by the way there can be a twist to this problem:

if k was an integer>2

ie: k>2

so answer would be D

I know that we are only suppose to discuss the questions which are posted rather than to bring our input, but what's the harm in knowing the variety of ways one particular question can be framed

Karan
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by sanju09 » Fri Sep 25, 2009 2:35 am
Please note:

If X is a positive composite integer such that X = A^α × B^β × C^γ × D^δ......, where A, B, C, D... are distinct primes and α, β, γ, δ... are positive integers, then the total number of positive divisors of X will be given by

(α + 1) (β + 1) (γ + 1)(δ + 1)...
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by woo » Fri Sep 25, 2009 2:35 am
Yep I agree with mehravikas..
Answer is D if condition 1 says k is a prime greater than 5.
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by sanju09 » Fri Sep 25, 2009 2:40 am
In X = A^α × B^β × C^γ × D^δ......, read '×' as 'multiplied by'.
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