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Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
27 Jun 2018, 21:41
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
71% (00:50) correct
29%
(01:09)
wrong
based on 176
sessions
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Which of the following equals the reciprocal of \(x - \frac{1}{y}\), where \(x - \frac{1}{y}\) different from zero ?
(A) \(\frac{1}{x} - y\)
(B) \(\frac{-y}{x}\)
(C) \(\frac{y}{x - 1}\)
(D) \(\frac{x}{xy - 1}\)
(E) \(\frac{y}{xy - 1}\)
(A) \(\frac{1}{x} - y\)
(B) \(\frac{-y}{x}\)
(C) \(\frac{y}{x - 1}\)
(D) \(\frac{x}{xy - 1}\)
(E) \(\frac{y}{xy - 1}\)
27 Jun 2018, 22:39
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Solution
To find:
- • What is the value of the reciprocal of \(x – \frac{1}{y}\), if \(x – \frac{1}{y}\) is not equal to 0
Approach and Working:
We can simplify the given expression first in the following manner:
- • \(x – \frac{1}{y}\) = \(\frac{xy – 1}{y}\)
Therefore, the reciprocal = \(\frac{y}{xy – 1}\)
Hence, the correct answer is option E.
Answer: E
28 Jun 2018, 19:41
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Bunuel
To take the reciprocal of a rational expression with fractions, first simplify the expression to get a consolidated fraction, then flip the fraction over.
(1) Simplify \(x -\frac{1}{y}\)
\((x -\frac{1}{y})=\\
(\frac{x}{1} -\frac{1}{y})=\)
\(((\frac{y}{y}*\frac{x}{1})-\frac{1}{y})=\)
\((\frac{xy}{y}-\frac{1}{y})=\frac{xy-1}{y}\)
(2) Invert the fraction \(\frac{xy-1}{y}\)
\(\frac{y}{xy - 1}\)
Answer E
* To find the reciprocal of a real number, divide 1 by the number. Thus the reciprocal of \(\frac{xy-1}{y}\) is
\(\frac{1}{(\frac{xy-1}{y})}\). As with any division by a fraction, invert the divisor fraction and multiply:
\(\frac{1}{(\frac{xy-1}{y})}=(1*\frac{y}{xy-1})=\frac{y}{xy-1}\)
Instead of going through that process to find the reciprocal of a factional expression, once the expression is simplified, just invert the fraction.
