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Re: If a > 0 and b > 0, is a/b > b/a ?
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22 Aug 2016, 05:01
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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 < a Since 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 < a Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT
Re: If a > 0 and b > 0, is a/b > b/a ?
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15 Sep 2018, 06:24
I tried with fractions and integers-- the question doesn't expressly say its not an integer. 1) St 1; if with integers, a = 8, b = 10 - 2 --> 8/10 < 5/4 A is suff, with a = 1/4 , b = 9/4 A suff 2) a = 4/5 b, which is suff for both integers and fractions
Re: If a > 0 and b > 0, is a/b > b/a ?
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06 Oct 2020, 02:47
Expert Reply
Bunuel wrote:
If a > 0 and b > 0, is a/b > b/a ?
(1) a = b - 2 (2) a/(4b) =1/5
Solution:
Since both a and b are positive, a/b is greater than b/a if a > b and a/b is not greater than b/a if a ≤ b.
Statement One Only:
a = b - 2
Since a = b - 2, then a < b and therefore, a/b is not greater than b/a. Statement one alone is sufficient.
Statement Two Only:
a/(4b) = 1/5
Simplifying, we have a = 4b/5. Since both a and b are positive, this means a < b, and therefore, a/b is not greater than b/a. Statement two alone is sufficient.
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