number properties

[abhi332]

If x>1, what is the value of x

1) There are x unique factors of x.
2) The sum of x and any prime number larger than x is odd.

[Ian Stewart]

If x>1, what is the value of x

1) There are x unique factors of x.
2) The sum of x and any prime number larger than x is odd.

I'm sure Statement 1 means to say "There are x distinct positive factors of x." I think it's easiest to see what this means by trying a number for x. If x were, say, 25, then this would say "25 has 25 distinct positive factors". That's clearly absurd; that would mean that 25 was divisible by every single number between 1 and 25. Indeed, x can never be divisible by *every* number between 1 and x if x is greater than 2, since if x > 2, x is never divisible by x-1. So if Statement 1 is true, x can only be 1 or 2, and since we know x > 1, x must be equal to 2.

Statement 2 is not sufficient; since x > 2, then any prime larger than x is odd. So Statement 2 only tells us that x is even.

The answer is A.

[girish3131]

IAN

Ans will be D

because

2 is only number in which if u add any other prime no , summation will be ODD



Thanks.....

[papgust]

IAN

Ans will be D

because

2 is only number in which if u add any other prime no , summation will be ODD



Thanks.....

Nope. Any even integer added with a prime number greater than 2 will be ODD. I guess you stole information from statement I and confused yourself.

[girish3131]

if u take any no ( except 2 ) and then add any prime number ( obviously greater than the number wch u have taken then their sum will be EVEN )

N when u take x= 2 and add any prime no then sum is ODD

this is sufficient to say X IS ONLY 2

hence ans is D

if u still disagree then give ex wch contradict my expalanation....

ta

[firdaus117]

if u take any no ( except 2 ) and then add any prime number ( obviously greater than the number wch u have taken then their sum will be EVEN )

N when u take x= 2 and add any prime no then sum is ODD

this is sufficient to say X IS ONLY 2

hence ans is D

if u still disagree then give ex wch contradict my expalanation....

ta

x=4 prime number greater than 4=5 4+5=9 :An odd number

[girish3131]

hmm .. good

Thanks!