If K is a positive integer, how many different prime numbers are factors of the expression K^2?
(1) Three different prime numbers are factors of 4K^4
(2) Three different prime numbers are factors of 4K
OA: E
Source: Knewton
i was stunned after reading the statements. i didn't know how to approach them. how do i simplify the statements? what's the approach?
prime factorization
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- ajith
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K, K^2, K^4, K^n where n is an integer, all have equal no of prime factors.rahul.s wrote:If K is a positive integer, how many different prime numbers are factors of the expression K^2?
(1) Three different prime numbers are factors of 4K^4
(2) Three different prime numbers are factors of 4K
OA: E
Source: Knewton
i was stunned after reading the statements. i didn't know how to approach them. how do i simplify the statements? what's the approach?
1) Three prime factors are there for 4K^4
Insufficient to determine how many prime factors are there for K^4 since 2 may or may not be a prime factor of K^4
thus K^4 and thus K will have either 2 or 3 prime numbers as factors
2) Same is the case, we do not know whether 2 is a factor of K, Insufficient
Combined also insufficient, E
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2 could be a factor of K as it is for 4 , Good catch.....ajith wrote:K, K^2, K^4, K^n where n is an integer, all have equal no of prime factors.rahul.s wrote:If K is a positive integer, how many different prime numbers are factors of the expression K^2?
(1) Three different prime numbers are factors of 4K^4
(2) Three different prime numbers are factors of 4K
OA: E
Source: Knewton
i was stunned after reading the statements. i didn't know how to approach them. how do i simplify the statements? what's the approach?
1-You mean equal number of distinct prime factors, right ?
2- how hard you guys rate this question?
Thanks
- ajith
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1. Yes I do mean distinct prime factorsPedros wrote: 2 could be a factor of K as it is for 4 , Good catch.....
1-You mean equal number of distinct prime factors, right ?
2- how hard you guys rate this question?
Thanks
2. It is a question which is not very difficult when you know the concept. Yet, it is a bit tricky
Always borrow money from a pessimist, he doesn't expect to be paid back.