Bunuel wrote:
If a > 0 and b > 0, is a/b > b/a ?
(1) a = b - 2
(2) a/(4b) =1/5
Target question: Is a/b > b/a ? Given: a > 0 and b > 0 This is a great candidate for REPHRASING the target question:
Is a/b > b/a ?Since a and b are both POSITIVE, we can multiply both sides of the inequality by ab to get:
Is a² > b²?Nice Rules: If 0 < b < a, then and b² < a²
Conversely, if a and b are positive AND b² < a², then we can be certain that b < a
This allows us to REPHRASE our target question once more to get...
REPHRASED target question: Is b < a? Once we're rephrased the target question like this, the statements are pretty easy to analyze.
Statement 1: a = b - 2 In other words, a is 2 less than b
So, we can be certain that a < b
In other words,
it is definitely NOT the case that b < aSince we can answer the
REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: a/(4b) =1/5 Multiply both sides by 4b to get: a = (4/5)b
In other words, a is equal to 4/5 of b
Since it's given that a and b are positive, we can be certain that a < b
In other words,
it is definitely NOT the case that b < aSince we can answer the
REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer:
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