SOLUTION: a, b, c and d are numbers of different values such that a + b = d a*b*c = 0 Which of the 4 numbers MUST be equal to 0? A) a B) b C) c D) d E) none

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: a, b, c and d are numbers of different values such that a + b = d a*b*c = 0 Which of the 4 numbers MUST be equal to 0? A) a B) b C) c D) d E) none       Log On

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Question 311271: a, b, c and d are numbers of different values such that a + b = d a*b*c = 0
Which of the 4 numbers MUST be equal to 0?
A) a B) b C) c D) d E) none

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Since a%2Ab%2Ac=0, one of them must be equal to zero.
a%2Bb=d, and each number is unique so a,b, and d cannot all be zero.
Since a cannot equal d, then b cannot be zero or else a=d.
Since b cannot equal d, then a cannot be zero or else b=d.
Since a and b cannot be zero, divide them out of the equation,
a%2Ab%2Ac=0
which leaves
c=0
And then c must be zero.