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If x is an integer, is x even? [#permalink]
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10 Sep 2015, 23:38
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If x is an integer, is x even? (1) x is equal to the difference between two consecutive prime numbers (2) x is greater than 1
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Re: If x is an integer, is x even? [#permalink]
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10 Sep 2015, 23:41
The question I have here is
(1) x is equal to the difference between two consecutive prime numbers
> As far as i understand only consecutive prime numbers are 2 and 3.
Are 3 and 5 or 5 and 7 consecutive prime number?



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If x is an integer, is x even? [#permalink]
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Updated on: 11 Sep 2015, 02:42
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kuttingchai wrote: The question I have here is
(1) x is equal to the difference between two consecutive prime numbers
> As far as i understand only consecutive prime numbers are 2 and 3.
Are 3 and 5 or 5 and 7 consecutive prime number? "Consecutive" prime numbers are prime numbers that have no other prime numbers between them. So the list is : 2,3 3,5 5,7 7,11 11,13 etc As for your question, is x = even? Statement 1, x = p1  p2, where p1 and p2 are consecutive prime numbers. Now, if the 2 prime numbers are 2 and 3, you get x = oddeven = ODD, "no" to the question but if you choose any other set of consecutive prime numbers, you get x = odd  odd = even , "yes" to the question. This statement is thus not sufficient. Statement 2, x>1, again not helpful. Statement NOT sufficient. Combining the statements you see that the possible values are 32 = 1, odd, ignored as statement 2 mentions that x>1 53 = 2, even 117 = 4, even etc Thus, the only possible set of values for x are {2,4,...} and all of these are even. Thus x = even. C is the correct answer.
Originally posted by ENGRTOMBA2018 on 11 Sep 2015, 01:41.
Last edited by ENGRTOMBA2018 on 11 Sep 2015, 02:42, edited 1 time in total.
Updated the solution



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Re: If x is an integer, is x even? [#permalink]
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11 Sep 2015, 02:31
Engr2012 wrote: kuttingchai wrote: The question I have here is
(1) x is equal to the difference between two consecutive prime numbers
> As far as i understand only consecutive prime numbers are 2 and 3.
Are 3 and 5 or 5 and 7 consecutive prime number? "Consecutive" prime numbers are prime numbers that have no other prime numbers between them. So the list is : 2,3 3,5 5,7 7,11 11,13 etc As for your question, is x = even? Statement 1, x = p1  p2, where p1 and p2 are consecutive prime numbers. Now, if the 2 prime numbers are 2 and 3, you get x = oddeven = ODD, "no" to the question but if you choose any other set of consecutive prime numbers, you get x = odd  odd = even , "yes" to the question. This statement is thus not sufficient. Statement 2, x>1, again not helpful. Statement NOT sufficient. Combining you see that statements do not provide any extra information and hence E should be the correct answer. kuttingchai Please check the OA. Had statement 2 been x>2, then you would have C as the correct answer. OA is correct  C Combined statement 1 and 2 we will have 53 = 2 or 75 = 2 or 1311 = 2 32 =1 will not be considered as per statement 2. C will be correct answer only when we say {3,2} {5,3} {7,5} are considered as consecutive prime numbers. but, while reading on prime number in one of the reference book  I saw {3,2} is only consecutive prime numbers and {5,3} or {7,5} is not considered consecutive prime numbers.  This is the reason i got confused. we don't consider {17,13} as consecutive prime numbers



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If x is an integer, is x even? [#permalink]
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11 Sep 2015, 02:38
kuttingchai wrote: Engr2012 wrote: kuttingchai wrote: The question I have here is
(1) x is equal to the difference between two consecutive prime numbers
> As far as i understand only consecutive prime numbers are 2 and 3.
Are 3 and 5 or 5 and 7 consecutive prime number? "Consecutive" prime numbers are prime numbers that have no other prime numbers between them. So the list is : 2,3 3,5 5,7 7,11 11,13 etc As for your question, is x = even? Statement 1, x = p1  p2, where p1 and p2 are consecutive prime numbers. Now, if the 2 prime numbers are 2 and 3, you get x = oddeven = ODD, "no" to the question but if you choose any other set of consecutive prime numbers, you get x = odd  odd = even , "yes" to the question. This statement is thus not sufficient. Statement 2, x>1, again not helpful. Statement NOT sufficient. Combining you see that statements do not provide any extra information and hence E should be the correct answer. kuttingchai Please check the OA. Had statement 2 been x>2, then you would have C as the correct answer. OA is correct  C Combined statement 1 and 2 we will have 53 = 2 or 75 = 2 or 1311 = 2 32 =1 will not be considered as per statement 2. C will be correct answer only when we say {3,2} {5,3} {7,5} are considered as consecutive prime numbers. but, while reading on prime number in one of the reference book  I saw {3,2} is only consecutive prime numbers and {5,3} or {7,5} is not considered consecutive prime numbers.  This is the reason i got confused. we don't consider {17,13} as consecutive prime numbers Your definition of consecutive prime numbers is not correct. 2 prime numbers are considered consecutive if there are no prime numbers between them. 13 and 17 are consecutive prime numbers as there is no prime number between them. This is from wikipedia: https://en.wikipedia.org/wiki/List_of_prime_numbers , in particular look at the table "The first 500 prime numbers" Also, look at the question statement twoprimenumbersareconsideredconsecutiveifnootherprimeliesbe205124.html especially the definition of "consecutive prime". Additionally, knowing what do you mean by "consecutive prime numbers" is not required for answering this question. Look at my solution above.



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Re: If x is an integer, is x even? [#permalink]
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21 Nov 2016, 00:48
Great Question Here x is an integer . WE need to check if x is even or not Lets look at statements Statement 1 Consecutive primes aren't just 2,3 Infact they can be 2,3 or 5,7 or 97,101 etc Hence Insufficient Statement 2 Here x>1 so x can be even or odd Hence insufficient Combining the two statements we can say that x>1 so 2,3 are out of the equation and rest primes are all odd(2 is the only even prime) Hence x must be form oddodd which is always even hence sufficient to say that x must be always even Hence C
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Re: If x is an integer, is x even? [#permalink]
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28 Dec 2017, 06:54
Given x is an integer. From Statement 1) Diff btw 2,3 is 1. But since all other prime numbers are Odd, diff between 2 consecutive primes will always be Even and always >=2. Insufficient. Statement 2) X is greater than 1. Insufficient Combining 1 and 2 we can definitely say x will always be even.
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Re: If x is an integer, is x even?
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