Does the integer k have at least four different prime factors?

Question

(1) k/14 is an integer
(2) k/30 is an integer

nipunjain14 · Answer

St 1: K /14 is integer means k is a multiple of 14
multiple 210 has 4 prime factors, whereas, 28 has 2 prime factors
Insufficient

St2:k /30 is an integer means k is multiple of 30
multiple 30 will have 3 prime factors whereas multiple 210 will have 4 prime factors
Insufficient

St1 + St2:

LCM of 14, 30 = 210
this will have atleast 4 factors

Ans; c

marvas8581 · Answer

A. K is divisible by 7 and 2 - 2 Prime factors - Not Sufficient
B. K is divisible by 3, 5, 2 - 3 Prime factors - Not sufficient

From a and b, k has latest 4 prime factors,

Hence C

stonecold · Answer

here is my approach=>
statement 1 => Prime factors ≥2 => not sufficient
statement 2 => prime factors ≥3 not sufficient
combing them prime factors ≥4 (as 2,5,3,7 must be the Primes of K)

sarathgopinath · Answer

Hi
Could someone check if this question is right?
If k=0, both the conditions are satisfied and the answer will be no.

Bunuel · Answer

0 is a multiple of every positive integer, so it has infinitely many factors.

akshayk · Answer

Is k = a*b*c*d*n ?
Where a,b,c,d are different prime factors.

1) k = 14n
14 = 2*7
=> if k = 14, then it's prime factors are 2 and 7 => No.
=> if k = 14*15, then it's prime factors are 2,3,5 and 7 => Yes.
2 different answers. Insufficient.

2) k = 30m
30 = 2*3*5
=> if k = 30, then it's prime factors are 2,3 and 5 => No.
=> if k = 210, then it's prime factors are 2,3,5 and 7 => Yes.
2 different answers. Insufficient.

1+2)
k is divisible by 14 and 30 => k's prime factors are 2,3,5 and 7 at least.
Sufficient. Answer is C.

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Does the integer k have at least four different prime factors?

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Does the integer k have at least four different prime factors?

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