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Find the value of y given that
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18 Apr 2021, 11:31
18 Apr 2021, 11:31
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66% (01:40) correct
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Find the value of y given that \(\frac{4^{y^2}}{64}=2^{-y}\) and \(y < |y|\)
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Show: :: OA
-2
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Find the value of y given that
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18 Apr 2021, 21:53
18 Apr 2021, 21:53
1
To solve for y, we need to equate powers.
\(\frac{4^{y^2} }{ 64} = 2^ {-y}\)
\(\frac{2^{2y^2} }{ 2^6 * 2^{-y}} = 1\) (Any number to the power 0 is 1)
\(2^{2y^2 - 6 + y} = 2^0\)
Equating powers,
\(2y^2 - 6 + y = 0\)
We will have to factorise this expression.
\(2y^2 + 4y - 3y - 6 = 0\)
\(2y (y + 2) - 3(y + 2) = 0\)
\((2y - 3) (y + 2) = 0\)
y = 3/2, -2
Since y<|y|, only -2 can satisfy this.
Hence, -2 is the answer.
\(\frac{4^{y^2} }{ 64} = 2^ {-y}\)
\(\frac{2^{2y^2} }{ 2^6 * 2^{-y}} = 1\) (Any number to the power 0 is 1)
\(2^{2y^2 - 6 + y} = 2^0\)
Equating powers,
\(2y^2 - 6 + y = 0\)
We will have to factorise this expression.
\(2y^2 + 4y - 3y - 6 = 0\)
\(2y (y + 2) - 3(y + 2) = 0\)
\((2y - 3) (y + 2) = 0\)
y = 3/2, -2
Since y<|y|, only -2 can satisfy this.
Hence, -2 is the answer.
General Discussion
Re: Find the value of y given that
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07 Jan 2025, 01:45
07 Jan 2025, 01:45
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Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
