Carcass wrote:
\(ab > 0\)
\(|c| > |a+b|
\)
Quantity A |
Quantity B |
\(|a+b-c|\) |
\( |a|+|b|-|c|\) |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
General Information.We don't know the signs for any of the variables, however, a&b have the same sign because two positive numbers multiplied by each other will give a positive number. The exact same situation happens for 2 negative numbers, their multiplication results in a positive number.
Quantity A Evaluationa+b-c will give a non-zero positive or negative value since |c| > |a+b|. The sign of a and b do not matter because as long as the absolute value of their sum is not equal to c, the result will be a non-zero value irrespective of the sign.
The absolute value of the result is then positive.
Hence Quantity A, |a+b-c| is positiveQuantity B EvaluationBecause a and b have the same sign and |c| > |a+b|, hence |c| > |a| + |b|
The sum each of the absolute values of a and b will still be less than the absolute value of c,
so |a|+|b|-|c| will give a non-zero negative value.
Hence Quantity B, |a+b-c| is negativeAnswer hence is A and Quantity A is bigger.