Bunuel wrote:
Is \((\frac{a}{d})(\frac{b}{e})(\frac{c}{f}) > (\frac{b}{d})(\frac{c}{e})\) ?
(1) \(bc > de\)
(2) \(a > f\)
When seeing
inequalities and variables, the following thoughts go through my head:
- I have to consider that variables can be zero, positive, or negative.
- I cannot cross multiply or multiply/divide by a variable without knowing if the variable is zero, positive, or negative.
I want to rewrite the question to the following:
Is \((\frac{a}{f})(\frac{bc}{de})>(\frac{bc}{de})\)?If you can 100 % determine which side of the inequality sign is biggest, you can answer the question.
Statement 1:This statement does NOT mean that \((\frac{bc}{de})\) must be more than 1. It is true that \(bc\) can be \(5\) while \(de\) is \(2\), but it can also be true that \(bc\) is \(2\) and \(de\) is \(-5\). Though, it cannot be between 0 and 1, since \(bc\) cannot be less than \(de\) if both are positive.
So we get that \((\frac{bc}{de})>1\) or \((\frac{bc}{de})\leq{0}\).
We do not know if the RHS (right-hand-side) is positive or negative, and we do not know how \(\frac{a}{f}\) affects the LHS (left-hand-side).
INSUFFICIENTStatement 2:From this information we can make the same inferences, only with \(\frac{a}{f}\).
Too little information to say which side of the inequality sign is biggest.
INSUFFICIENTStatement 1 and 2 together:Too much is still unknown...
Let us say that \((\frac{bc}{de})\) is equal to \(3\). Then \(\frac{a}{f}\) could be \(2\), making the answer to the question YES.
Let us say that \((\frac{bc}{de})\) is equal to \(3\). Then \(\frac{a}{f}\) could be \(-2\), making the answer to the question NO.
INSUFFICIENT
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