number properties

[shilpi84]

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

[tohellandback]

repost the question correctly. it is very confusing. Is there a full stop after 5n or what??

[tohellandback]

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

[sudi760mba]

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.

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