MathRevolution wrote:
Is \(\frac{1}{x}>\frac{1}{y}?\)
\(1) x < y\)
\(2) x > 0\)
Target question: Is 1/x > 1/y?This is a good candidate for
rephrasing the target question.
Take:
1/x > 1/ySubtract 1/y from both sides to get:
1/x - 1/y > 0Rewrite with common denominators:
y/xy - x/xy > 0Combine:
(y - x)/xy > 0REPHRASED target question: Is (y - x)/xy positive? Statement 1: x < y Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 1 and y = 2. In this case, (y - x)/xy = 1/2. So, the answer to the REPHRASED target question is
YES, (y - x)/xy IS positive Case b: x = -1 and y = 2. In this case, (y - x)/xy = 3/-2 = -3/2. So, the answer to the REPHRASED target question is
NO, (y - x)/xy is NOT positive Since we cannot answer the
REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x > 0Since we have not information about y there's no way to answer the REPHRASED target question with certainty.
Statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined Statement 1 tells us that x < y
Statement 2 tells us that 0 < x
When we combine the statements, we get: 0 < x < y
If x < y, then y - x > 0. In other words, (y - x) is POSITIVE
Also, if x and y are both greater than 0, we know that the product xy is POSITIVE
So, (y - x)/xy = POSITIVE/POSITIVE = POSITIVE
So, the answer to the REPHRASED target question is
YES, (y - x)/xy IS positive Since we can answer the
REPHRASED target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
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