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03 Apr 2020, 08:20
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
62% (02:50) correct
38%
(03:01)
wrong
based on 248
sessions
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Date
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Result
Not Attempted Yet
Given that \(x^{2018} y^{2017} = \frac{1}{2}\) and \(x^{2016} y^{2019} = 8\), what is the value of \(x^2 + y^3\) ?
A. 37/4
B. 35/4
C. 33/4
D. 31/4
E. 29/4
Are You Up For the Challenge: 700 Level Questions
A. 37/4
B. 35/4
C. 33/4
D. 31/4
E. 29/4
Are You Up For the Challenge: 700 Level Questions
03 Apr 2020, 12:56
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Given that \(x^{2018}y^{2017}=\frac{1}{2}\) and \(x^{2016}y^{2019}=8\), what is the value of \(x^2+y^3\) ?
--> Since nothing tells us about what x and y are, the number picking approach is best way to get the value of it:
\(x= \frac{1}{2}\) and \(y =2\)
--> \(\frac{1}{2^{2018}}* 2^{2017} = \frac{1}{2}\)
--> \(\frac{1}{2^{2016}}* 2^{2019} = 2^3 =8\)
well, \(x^{2}+ y^{3}= (\frac{1}{2})^{2} + 2^{3}= \frac{1}{4}+ 8 = \frac{33}{4} \)
Answer (C).
--> Since nothing tells us about what x and y are, the number picking approach is best way to get the value of it:
\(x= \frac{1}{2}\) and \(y =2\)
--> \(\frac{1}{2^{2018}}* 2^{2017} = \frac{1}{2}\)
--> \(\frac{1}{2^{2016}}* 2^{2019} = 2^3 =8\)
well, \(x^{2}+ y^{3}= (\frac{1}{2})^{2} + 2^{3}= \frac{1}{4}+ 8 = \frac{33}{4} \)
Answer (C).
yashikaaggarwal
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03 Apr 2020, 08:46
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X^2018*Y^2017=1/2------(1)
X^2016*Y^2019=8--------(2)
Divide equation 1 by 2
(X^2018*Y^2017)/(X^2016*Y^2019)=(1/2)/8
X^2/Y^2=1/16
X^2*16=Y^2
By taking square root
4X = Y ------(3)
Putting value in equation 1
X^2018*Y^2017=1/2
X^2018*(4X)^2017=1/2
X^2018*x^2017*4^2017=1/2
X^4035*2^4034=1/2
X^4035=1/2*2^4034
X^4035=(1/2)^4035
X=1/2
And Y = 4*1/2
Y=2
Therefore, Value of X^2+Y^3 is
(1/2)^2+2^3=33/4
So OA is C
Posted from my mobile device
X^2016*Y^2019=8--------(2)
Divide equation 1 by 2
(X^2018*Y^2017)/(X^2016*Y^2019)=(1/2)/8
X^2/Y^2=1/16
X^2*16=Y^2
By taking square root
4X = Y ------(3)
Putting value in equation 1
X^2018*Y^2017=1/2
X^2018*(4X)^2017=1/2
X^2018*x^2017*4^2017=1/2
X^4035*2^4034=1/2
X^4035=1/2*2^4034
X^4035=(1/2)^4035
X=1/2
And Y = 4*1/2
Y=2
Therefore, Value of X^2+Y^3 is
(1/2)^2+2^3=33/4
So OA is C
Posted from my mobile device
