krishna19 wrote:
Q and X are positive integers greater than 1. Is it possible to express Q and X in the form of 6n-1 or 6n+1, where n is a positive integer?
(1) Q and X do not have a factor K such that 1< K < X, Q
(2) Q > X and X is divisible by 5
s1: says Q and X are prime numbers. prob statement says Q and X can be a set of {5,11,17,23,29,....} or {7,13,19,25,31,.....}. If we take Q or X = 25, then s1 is violated, and if we take Q or X = 11, then s1 is true. Hence not sufficient
s2: X is divisible by 5, then X={5,10,15,20....} and Q can be any set {7,13,19} which is > X. However, we can't express set X by 6n-1 or 6n+1, hence it is not possible to express both Q and X by 6n-1 or 6n+1, hence this info is sufficient.
ans: B
Hi
X=5, 10, 15 ....
n=1 ----> 6*1 - 1 = 5. If X=5 (prime) we can express it in the form 6n - 1. If it's multiple of 5 > 5 then no.
Same with Q, if it's prime > 3 say 7, 11, 13 ...
7 = 6*1 + 1
11 = 6*2 - 1
13 = 6*2 + 1 .... Yes.
If Q is not prime - then no. Satement 2 is not sufficient.
Important thing to remember:
"Every prime number > 3 can be expressed in the form 6n +/-1, but that's not always true in other direction. Not every integer which can be expressed as 6n +/- 1 is prime."Hope this helps.
Regards