If k is a positive integer how many unique prime factors does 14k have

Question

If k is a positive integer, how many unique prime factors does 14*k have ?

(1) k^4 is divisible by 100
(2) 50*k has 2 unique prime factors

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Bryan180599 · Accepted Answer

If k is a positive integer, how many unique prime factors does 14*k have?

To know how many factors does 14*k have, we need to know the factors of k

(1) k^4 is divisible by 100
Insufficient. k^4 is divisible by 100 means that k = 2*5*x where x can be whatever we want (3, 5, 7, 11,...). So impossible to know the number of unique factors of 14*k

(2) 50*k has 2 unique prime factors
Insufficient 50*k = 2*5*5*k. The two unique factors are 2 and 5. Therefore k can be for example 5 (then 14*k = 2*7*5 has 3 unique prime factors) or 2 (then 2*7*2 ==> 2 unique factors)

(1) and (2): with (1) we know that k=2*5*x and with (2) we know that k cannot have other factors than 5 and 2. Hence k=2^n * 5^m for n and m greater than 1. ==> Unique factor of 14*k are 2, 7 and 5 ==> 3 unique factors.

Answer C

Deepakjhamb · Answer

Let’s consider option 1 : we need to have 2 and 5 in K but another prime factor can also be there so insufficient

For option 2 : we can have 2 or 5 or 2 and 5 in any proportion so we are not sure about k

By combining k has to include 2 and 5 in any powers but only 2 prime factors so it’s sufficient so answer is c

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mcmoorthy · Answer

Hi Deepak,

Consider statement 2.

50*k has 2 prime factors. 50 has 2 and 5 as prime factors so does k. 
14*k has 3 prime factors 2,5 & 7.

Hence statement 2 is sufficient.

Ans B

Deepakjhamb · Answer

Hi Mac

But in b k can be 2 or 5 or 2 and 5 together also , so insuff

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mcmoorthy · Answer

Got it Deepak.

Thanks.

kovid231 · Answer

1. k^4 will give a large value for most of the digits. on trying you see this statement can only be true for K= 1,2,3. However this is insufficient.

2. 50k will have 2 primes only when k is either 2 or 5 (since 50 already contributes the 2 prime factors in the equation). But 2 values are also insufficient

1+2 shows that only 2 is the value which is true for both conditions. So the value must be 2. - Sufficient.

carouselambra · Answer

Folks, slightly confused here.
Please help.

If k is a positive integer, how many unique prime factors does 14*k have ?

(1) k^4 is divisible by 100
k can be anything from 1,2,3...
Answer will not be unique.
 (A) not sufficient

(2) 50*k has 2 unique prime factors
50 already has 2 unique prime factors.
So, k can have varying proportions of 5s or 2s but ultimately we are restricted to 2 prime factors only - correct?
Where am I wrong?

GCMEMBER · Answer

If k is a positive integer, how many unique prime factors does 14*k have ?

(1) k^4 is divisible by 100
For k = 100, 14*k has 2, 5, and 7 as its prime factors.
For k = 300, 14*k has 2, 3, 5, and 7 as its prime factors.
Not sufficient

(2) 50*k has 2 unique prime factors
For k = 1, 14*k has 2 and 7 as its prime factors.
For k = 5, 14*k has 2, 5, and 7 as its prime factors.
Not sufficient

(1) and (2)
k has to be of the form 2^a*5^b
in which a nad b are positive integers

14*k has 2, 5, and 7 as its prime factors.
Sufficient

Option C

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MHIKER · Answer

(1) If k=10; The prime factors of 14*k will be 14*10= 2,5 & 7 =3 unique prime factors

If =30; The prime factors of 14*k will be 14*30=2,7,3, & 5 = 4 Unique prime factros

Insufficient.

(2) If  k=1 , The prime factors of 14*k will be  14*1=2, \ & \ 7 = 2  Unique prime factros

If  k=10,  The prime factors of 14*k will be  14*10=2,5, & \ 7 = 3  Unique prime factros

Insufficient.

Considering Both:
K can take only 10;  K=10

14*k=14*10  will be  3  unique prime factors  2, 5 \ & \ 5 . Sufficient.

The answer is  C

exc4libur · Answer

uprf(14k)=7,2,k

(1) insufic
uprf(k)=2,5,x

(2) insufic
k = multi any {1,2,5}

(1/2) sufic
k=mult{2,5}
uprf(14k)=7,2,k=7,2,{2,5}=3

(C)

Gmat202023 · Answer

Given : 14k
 Assume k has x factors
 14k = x+2 ( if 2 and 7 are not the actors of k)
 = x+1 ( if either one of 2 and 7 is a factor)
 = x ( ix 2 and 7 are factors of k)

To find : Numbers of factors of 14k

S1 : K^4=2^2 * 5^2 * P^a 
Not sufficient to find x or x+1

S2 : Factors of 50k = 2 and 5 or 2 or 5
Not certain. Therefore not sufficient

S1 + S2: K has 2 factors 2 and 5 as no other factor is possible. 
Therefore x = 2
Therefore no of factors of 14k = 3 ( 2, 5, and 7)

Therefore answer is C.

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If k is a positive integer how many unique prime factors does 14k have

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If k is a positive integer how many unique prime factors does 14k have

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