Question

${a}^{6 } + {2b}^{6} = {4c}^{6}$
a,b,c are integers what is the value of a+b+c=​

Answer 1

Hi All,

This is a great 'concept' question, and it doesn't require much math to solve it.

We're told that A, B and C are all integers. We're asked for the value of A.

1) (A - 7)(B - 7)(C - 7) = 0

With this Fact, we know that AT LEAST one of the variables MUST equal 7, while the other two variables could be ANY integer. Thus, A could be 7, but it could also be any other integer.

Fact 1 is INSUFFICIENT

2) BC = 18

This Fact tells us NOTHING about the value of A.

Fact 2 is INSUFFICIENT

Combined, we know...

(A - 7)(B - 7)(C - 7) = 0

BC = 18

From the second Fact (AND that the variables are all INTEGERS), neither B nor C can equal 7. If either of those variables was 7, then the other variable would have to be 18/7, which is NOT an option). Since those 2 variables CANNOT be 7, the variable A MUST be 7 (to satisfy the first Fact).

Combined, SUFFICIENT