integer is x even

[uptowngirl92]

If x is an integer is x even?
1. x is equal to the difference between two consecutive prime nos.
2. x is greater than 1.

I have a doubt with stmt 1. is'nt it a bit vague?Two consecutive prime nos...only one such set exists i.e 2,3.right?So why is my answer A wrong?

[rahulmehra13]

IMO C

Prime nos: 2,3,5,7,11,13,17,19 ..


1. x is equal to the difference between two consecutive prime nos

NS

Note: By two consecutive prime nos they mean : 2-3, 3-5, 5-7 ....

now the diff b/w 2 n 3 is '1' which is 'odd'

for rest of the consecutive prime nos it will be some 'even' no 2,4,6 ( 5-3 =2, 17-13 =4, 29-23 =6)

so we can't say whether x is odd or even.

2. x is greater than 1

Alone NS

Both together:

x is odd only when it is = 1 (for prime nos 2,3) for rest of the consec prime no.s it will be some even no. as the difference will always be even.

By Stmnt 2 x>1 i.e. we rule out x=1

Hence x will always be even.