It's easier to step through this and test numbers.
We are asked whether the GCF between (a+b) and c is greater than 1.
Theory: if the GCF between (a+b) and c = 1 then (a+b) and c are consecutive integers
4,5 = GCF 1
5,6 = GCF 1 and so on...
Statement (1) a, b, c are all different primes
Firstly, take note of statement 2 as it gives us a reason for us to suspect that when c=2 different outcomes occur, so lets test c= 2 first
a= 3
b=5
c= 2
GCF (3+5), 2
GCF 8,2 = 2
is the GCF > 1? Yes
Now, lets test either a=2 or b=2
a= 2
b=3
c=5
GCF (a+b), c
= GCF (2+3), 5
= GCF 5,5 = 5 --- another Yes
What about
a=2
b=5
c=3
GCF(a+b),c
GCF(7,3) = 1
GCF > 1? NO
Therefore A is insufficient
Statement (2)
Just tells us that C is not equal to 2. There are heaps of possibilities for a, b and c, including repetitions since we don't have the restrictions of statement 1
Combined we know that when c is not equal 2 and a, b, and c are all different primes, then the two scenarios from above can occur:
GCF(7,3) = 1
OR
GCF (5,5) = 5
Producing NO and Yes answers respectively. Therefore E -->combined insufficient.
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