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19 Jan 2022, 10:00
Kudos
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
56% (01:13) correct
44%
(01:15)
wrong
based on 45
sessions
History
Date
Time
Result
Not Attempted Yet
If x > y, then what is the value of \(\frac{3^x}{3^y}\) ?
(1) \(2^{3x -3y} = 64\)
(2) x and y are consecutive odd numbers.
(1) \(2^{3x -3y} = 64\)
(2) x and y are consecutive odd numbers.
19 Jan 2022, 10:30
Kudos
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Bunuel
Given: x > y
Target question: What is the value of \(\frac{3^x}{3^y}\)?
This is a good candidate for rephrasing the target question.
\(\frac{3^x}{3^y} = 3^{x-y}\)
To determine the value of \(3^{x-y}\), we need only determine the value of \(x - y\)
REPHRASED target question: What is the value of \(x-y\) ?
Statement 1: \(2^{3x -3y} = 64\)
Rewrite as follows: \(2^{3x -3y} = 2^6\)
Since the bases are equal, the exponents must be equal: \(3x-3y=6\)
Divide both sides of the equation by 3 to get: \(x-y = 2\)
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: x and y are consecutive ODD numbers
We know that consecutive odd integers differ by 2.
Since it's given that x > y, we know that \(x-y = 2\)
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT
Answer: D
VIDEO ON REPHRASING THE TARGET QUESTION:
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