x is a positive integer; what is the value of x?
1) The sum of any two positive factors of x is even
2) x is a prime number and x < 4
what is the value of x
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- eaakbari
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Statement one
This implies x is odd and therefore does not have any even factors. As even + odd = odd and will always be 1 odd multiple.
But this info is not enough.Hence Insuff
Statement two. The number can be 2 or 3.Insuff
Combined
We know from(1) that number should be odd and from 2 that number is 2 or 3
Hence x = 3
Suff
Answer C
This implies x is odd and therefore does not have any even factors. As even + odd = odd and will always be 1 odd multiple.
But this info is not enough.Hence Insuff
Statement two. The number can be 2 or 3.Insuff
Combined
We know from(1) that number should be odd and from 2 that number is 2 or 3
Hence x = 3
Suff
Answer C
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@eaakbari -
Thanks for your reply. Can you explain your below logic in detail -
This implies x is odd and therefore does not have any even factors. As even + odd = odd and will always be 1 odd multiple.
Thanks for your reply. Can you explain your below logic in detail -
This implies x is odd and therefore does not have any even factors. As even + odd = odd and will always be 1 odd multiple.
- eaakbari
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I may have phrased that wrong. I meant the number 1 will always be a factor and hence will always cause any number with all even factors to have the sum of factors as oddjerryragland wrote:@eaakbari -
Thanks for your reply. Can you explain your below logic in detail -
This implies x is odd and therefore does not have any even factors. As even + odd = odd and will always be 1 odd multiple.
8 =2 *2*2*1 ; sum 7
A number with all even factors will be broken down in 2^n and when that is added will give you even result and when its added with 1 , result odd
HTH
statement 1:gmatmachoman wrote:x is a positive integer; what is the value of x?
1) The sum of any two positive factors of x is even
2) x is a prime number and x < 4
sum of any two positive factors is even
1 implies => all the factors are either even or all are odd.
if all the factors are even so that if we pick any 2 of them sum will be even (even+even=even).. but since 1 is a factor so all factors are odd will make sense (odd+odd=even)
so only conclusion from statement 1 is x has all odd factors.
insufficient
statement 2: x is a prime number < 4
it can be 2 or 3
insufficient
statement 1 and 2 combined:
factors of 2: 2, 1
factors of 3: 3, 1 (sum = 4 which is even)
hence x=3
C