If `a+b gt 0` and `c+d gt 0`, which of the following must be true ?

Options

A. `a+b+c gt 0`
B. `ac+bd gt 0`
C. `a^(2)+b^(2)gt 0`
D. `d(a+b)gt 0`

Answer

C

Explanation

The best way to go about this one is to check out each answer choice, trying to think of a case where that choice is not true. The correct answer is the one that has no counterexample. That `a+b gt 0` and `c+d gt 0` would imply, for example, that the total sum `a+b+c+d` would also be positive, but that's not the same as saying `(A), a+b+c gt 0`. If `a=3, b=-2, c=-4`, and d = 5, then (A) is not true. Nor is (B). (C ) is true for this set of numbers and for any possible set of numbers because `a^(2)+b^(2)` will be greater than zero as long as a and b are not both zero.