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Senior Manager  G
Joined: 06 Jul 2016
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Q and X are positive integers greater than 1. Is it possible...  [#permalink]

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Difficulty:   95% (hard)

Question Stats: 30% (02:02) correct 70% (02:06) wrong based on 57 sessions

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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

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Joined: 13 Oct 2016
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Re: Q and X are positive integers greater than 1. Is it possible...  [#permalink]

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akshayk 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

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.

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Joined: 24 Sep 2014
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Re: Q and X are positive integers greater than 1. Is it possible...  [#permalink]

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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
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Q and X are positive integers greater than 1. Is it possible...  [#permalink]

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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
Math Expert V
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Posts: 7977
Re: Q and X are positive integers greater than 1. Is it possible to expres  [#permalink]

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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
So X and Q have only one factor other than itself and that is 1, so both Q and X are prime numbers.
All prime numbers >3 are in the form of 6n-1 or 6n+1.
So if Q and X are 2 or 3 Ans is NO, otherwise always YES
Insufficient

(2) Q > X and X is divisible by 5
Say x is 5, yes
X is 15..NO
Insufficient

Combined
Q and X are prime numbers, X=5 and Q>X
So answer is always YES
Sufficient

C
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Re: Q and X are positive integers greater than 1. Is it possible to expres  [#permalink]

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Hi chetan2u ji,

Agree with your explanation. Just one query, in statement 1 , does it not mean that X and Q don't have even 1 as a factor.

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Math Expert V
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Posts: 7977
Q and X are positive integers greater than 1. Is it possible to expres  [#permalink]

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ShankSouljaBoi wrote:
Hi chetan2u ji,

Agree with your explanation. Just one query, in statement 1 , does it not mean that X and Q don't have even 1 as a factor.

Thanks No..
K is >1, so I is not included in the range, 1 could be a factor..
_________________ Q and X are positive integers greater than 1. Is it possible to expres   [#permalink] 10 Oct 2018, 20:45
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