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10 Dec 2018, 00:36
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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:
35%
(medium)
Question Stats:
75% (02:13) correct
25%
(02:30)
wrong
based on 216
sessions
History
Date
Time
Result
Not Attempted Yet
If \(x^{-2} - 2 = -1.96\), \(y^{\frac{1}{3}} - 5 = -2\), and xy > 0, then what is the value of xy ?
A. 5
B. 27
C. 32
D. 135
E. 165
A. 5
B. 27
C. 32
D. 135
E. 165
10 Dec 2018, 00:52
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Let us rearrange to simplify.
\(x^{-2} - 2 = -1.96\) ...( multiply this by -1)
\(2 - x^{-2}= 1.96\)
\(x^{-2} = 0.04\)
\(x^{2} = \frac{1}{0.04}\)
\(x^{2} = 25\)
x = +- 5
\(y^{\frac{1}{3}} - 5 = -2\)
\(y^{\frac{1}{3}} = 3\)
\(y = 27\)
xy > 0 and y > 0 means x will also be > 0
Hence x = 5 and y = 27
xy = 135
Hence Option (D) is correct.
Best,
Gladi
\(x^{-2} - 2 = -1.96\) ...( multiply this by -1)
\(2 - x^{-2}= 1.96\)
\(x^{-2} = 0.04\)
\(x^{2} = \frac{1}{0.04}\)
\(x^{2} = 25\)
x = +- 5
\(y^{\frac{1}{3}} - 5 = -2\)
\(y^{\frac{1}{3}} = 3\)
\(y = 27\)
xy > 0 and y > 0 means x will also be > 0
Hence x = 5 and y = 27
xy = 135
Hence Option (D) is correct.
Best,
Gladi
Bunuel
10 Dec 2018, 03:53
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Bunuel
Solve for
\(x^{-2} - 2 = -1.96\),
we get x = 5
and solve for
\(y^{\frac{1}{3}} - 5 = -2\)
we get y = 27
x*y = 27*5= 135 IMO D
