If z is an integer, is z prime?

1. The greatest common divisor of z and 140 is 7.
2. The sum of the distinct factors of z is less than 10.

1)
Let's simulate the greatest common divisor method
140= 2.2.5.7
z=..............

Greatest common divisor is 7, so the only factor which is in both list of 140 and z is 7
If z has 4, 6 or 8 as a factor, we would not have only 7 as greatest common factor but 2*14 or something like that so 4,6,8 are not factors of z.
We could therefore write z=3^x * 7^k
And z could be 7 a prime number or 21 not a prime number so 1) is insufficient.

2)
6=3*2*1 so 3+2+1=6<10 and 6 is not prime
7=1*7 so 1+7=8<10 and 7 is prime
So 2 is insufficient.

1)and2)
The sum of 7+3=10 so it is impossiblez=7*3 due to 2)
It is possible z=3 or z=7 which are prime numbers
so the answer may be C

Hope I'm clear but I don't think so.

The answer is correct and the explanation is makes sense thanks

pepeprepa wrote:If z is an integer, is z prime?

1. The greatest common divisor of z and 140 is 7.
2. The sum of the distinct factors of z is less than 10.

1)
Let's simulate the greatest common divisor method
140= 2.2.5.7
z=..............

Greatest common divisor is 7, so the only factor which is in both list of 140 and z is 7
If z has 4, 6 or 8 as a factor, we would not have only 7 as greatest common factor but 2*14 or something like that so 4,6,8 are not factors of z.
We could therefore write z=3^x * 7^k
And z could be 7 a prime number or 21 not a prime number so 1) is insufficient.

2)
6=3*2*1 so 3+2+1=6<10 and 6 is not prime
7=1*7 so 1+7=8<10 and 7 is prime
So 2 is insufficient.

1)and2)
The sum of 7+3=10 so it is impossiblez=7*3 due to 2)
It is possible z=3 or z=7 which are prime numbers
so the answer may be C

Hope I'm clear but I don't think so.