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number properties

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number properties

by shilpi84 » Fri Jun 12, 2009 2:10 am
If n is a positive integer less than 200 and 5n/42
is an integer, then n
has how many di¤erent positive prime factors?
(A) Two
(B) Three
(C) Four
(D) Five
(E) Seven

OA B

if n = 42 then OA is fine but if n=210 then OA should be C.
210 = 2*3*7*5
Last edited by shilpi84 on Fri Jun 12, 2009 2:50 am, edited 1 time in total.
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by tohellandback » Fri Jun 12, 2009 2:20 am
repost the question correctly. it is very confusing. Is there a full stop after 5n or what??
The powers of two are bloody impolite!!
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by tohellandback » Fri Jun 12, 2009 2:26 am
if it is 5n/42
then answer is B
explanation
5n/42 is an integer.
5n divisible by 42
i.e. divisible by 2,3, and 7
5 is not divisible by any of these so n must be divisible by 2,3,7
2,3,7 are the prime factors. if you take any other prime number
say 5
2*3*5*7=210>200
thats why total three prime factors
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Re: number properties

by sudi760mba » Fri Jul 03, 2009 12:08 am
n<200
42 in the denominator should be broken down into it's prime factors
(2)(3)(7)

5(n)/(2)(3)(7). At a minimum, since 42 does not contain 5 as a prime factor, n must have (2)(3)(7) as it's prime factors otherwise 5n would not be divisible by 42. There are therefore 3 prime factors - 2,3,7

5(2)(3)(7)
----------
(2)(3)(7) = 5

Take a look at #249 in OG 11 PS for a similar example.

shilpi84 wrote:If n is a positive integer less than 200 and 5n/42
is an integer, then n
has how many di¤erent positive prime factors?
(A) Two
(B) Three
(C) Four
(D) Five
(E) Seven

OA B

if n = 42 then OA is fine but if n=210 then OA should be C.
210 = 2*3*7*5
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