Carcass wrote:
If the product of \(\frac{ab}{c}\) and \(\frac{b}{cd}\) is negative, which two of the following variables must have a product that is less than zero?
Indicate two such variables.
A. a
B. b
C. c
D. d
GIVEN: (ab/c)(b/cd) = some negative number
Simplify to get: (ab²)/(c²d) = some negative number
Rewrite to get: (a/d)(b²/c²) = some negative number
Notice that
b²/c² must be
POSITIVESo, we can write: (a/d)(
POSITIVE) =
some NEGATIVE number Divide both sides by (
POSITIVE) to get: a/d = (
some NEGATIVE number)/(
some POSITIVE number)
Simplify to get: a/d = NEGATIVE
This means one value (a or d) must be POSITIVE and the other must be NEGATIVE
As such, we can be certain that ad is NEGATIVE
Answer: A & D