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If x is an integer, is x even?

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If x is an integer, is x even? [#permalink]

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New post 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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New post 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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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 = odd-even = 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

3-2 = 1, odd, ignored as statement 2 mentions that x>1
5-3 = 2, even
11-7 = 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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New post 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 = odd-even = 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 5-3 = 2 or 7-5 = 2 or 13-11 = 2

3-2 =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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New post 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 = odd-even = 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 5-3 = 2 or 7-5 = 2 or 13-11 = 2

3-2 =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 two-prime-numbers-are-considered-consecutive-if-no-other-prime-lies-be-205124.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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New post 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 odd-odd 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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New post 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?   [#permalink] 28 Dec 2017, 06:54
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