What is the value of the prime number k?

Question

What is the value of the prime number k? 
(1) 2k has 2 odd factors. 
(2) 3^k + 2 is a two-digit prime number.

chetan2u · Answer

What is the value of the prime number k? 
(1) 2k has 2 odd factors. 
It will be true for all odd prime numbers, as two odd factors will be 1 and k. 
Insufficient

(2) 3^k + 2 is a two-digit prime number.
So 0< 3^k+2 <100 or  -2<3^k<98 
So, k can take values 1, 2, 3 and 4. 
Insufficient

Combined 
As k is odd prime, only value 3 fits in in statement II. 
Sufficient

C

SaquibHGMATWhiz · Answer

Solution:      
  Pre Analysis:  
  We are asked the value of prime number k

Statement 1:   2k has 2 odd factors
  For this to happen  k can be any odd prime  like 5, 7 etc 
 Thus,  statement 1 alone is not sufficient and we can eliminate options A and D

Statement 2:    3^k + 2  is a two-digit prime number
   3^k + 2  is a two-digit prime number only when  k=2  or  k=3  
 After that  k=5 ,  3^k=3^5  will not even be a two digit integer 
 Thus,  statement 2 alone is also not sufficient

Combining:   
  From statement 1,  k is any odd prime  
 From statement 2,  k=2  or  k=3  
 After combining we can be sure that  k=3

Hence the right answer is    Option C

mpattersonmusic · Answer

While it doesn’t change the answer, isn’t it true that k cannot be 4 in the second condition because in the original condition we know that k is a prime number?

Posted from my mobile device

bumpbot · Answer

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What is the value of the prime number k?

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