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29 Mar 2017, 05:50
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C
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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
(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
29 Mar 2017, 07:47
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akshayk
Hi
Every prime number greater than 3 can be expressed in the form 6n + 1 or 6n - 1. So in orer to unswer this question we need to know weather the number is prime and is it >3.
(1) Q and X do not have a factor K such that 1< K < X, Q
It tells us that number is prime, but it also could be 2 or 3, which cannot be expressed in 6n +/- 1. Insufficient.
(2) Q > X and X is divisible by 5
X can be 5 - prime, 5 = 6*1 - 1 or any multiple of 5 and we don't have any precise information about Q, except that it's > X. Insufficient.
(1)&(2) Now the numbers are prime ----> X=5 and Q prime > 5. Sufficient.
Answer C.
29 Mar 2017, 07:56
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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
(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
