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If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y?

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KAS1
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If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y? [#permalink] New post   Updated on: 22 May 2020, 09:30
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If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y?

A. -14
B. -2
C. 3
D. 6
E. 18

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I understand how they came to the answer. But I'm confused as to why I can't replace 2y in the first equation with 4 to get x^2 = 64. That would give the equation x^2 + y, value of 66. Please tell me what am I missing? Attaching the screenshot of the question and answer. This is from the GMAC software.

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E

Originally posted by KAS1 on 24 Aug 2012, 13:36.
Last edited by Bunuel on 22 May 2020, 09:30, edited 2 times in total.
Edited the question.
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Re: If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y? [#permalink] New post   24 Aug 2021, 06:50
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KAS1 wrote:
If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y?

A. -14
B. -2
C. 3
D. 6
E. 18


Since we're told 2y = 4, we can conclude that y = 2

Now take the equation x^2 = 2y^3, and replace y with 2 to get: x^2 = 2(2^3)
Simplify: x^2 = 16

So, x^2 + y = 16 + 2 = 18

Answer: E
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Re: If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y? [#permalink] New post   24 Aug 2012, 13:49
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KAS1 wrote:
If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y?

    A. -14
    B. -2
    C. 3
    D. 6
    E. 18

I understand how they came to the answer. But I'm confused as to why I can't replace 2y in the first equation with 4 to get x^2 = 64. That would give the equation x^2 + y, value of 66. Please tell me what am I missing? Attaching the screenshot of the question and answer. This is from the GMAC software.


In the equation it is \(2y^3\) and not \((2y)^3.\) Therefore \(2y^3=2*2^3=16,\) because from \(2y=4,\)we obtain \(y=2.\)
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Re: If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y? [#permalink] New post   24 Aug 2012, 19:04
Wow!
Thanks so much. I have to pay attention to these little things on the exam.
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Re: If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y? [#permalink] New post   12 Feb 2019, 10:05
if x^2=2y^3 and 2y=4
X^2= 2(2)^3 [y=2]
X^2=2*8
X^2=16
X=4
Equation:- x^2+y
=(4)^2+2
=16+2
=18
Answer:- E

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Re: If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y? [#permalink] New post   24 Aug 2021, 08:15
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2y=4
so , y = 4/2 =2.


\(x^2 = 2 y^3\)

\(x^2 = 2* 2^3\)
\(x^2 = 16\)

Then \(x^2 +y \) = 16 + 2 = 18

Option E is the answer.

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Clifin J Francis,
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Re: If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y? [#permalink] New post   31 Aug 2021, 02:49
Expert Reply

Solution



Given
• \(x^2\) = 2\(y^3\)
• 2y = 4

To find
• The value of \(x^2\) + y

Approach and Working out
• 2y = 4
    o y = 2
    o So, 2\(y^3\) = 2(8) = 16

• Now, \( x^2\) = 2\(y^3\) = 16
    o Thus, \(x^2\) = 16

Finally, \(x^2\) + y = 16 + 2 = 18

Correct Answer: Option E
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Re: If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y? [#permalink] New post   15 Jan 2023, 04:20
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Given that \(x² = 2y³\) and 2y = 4 and we need to find the value of \(x² + y\)

2y = 4
=> y = \(\frac{4}{2}\) = 2

\(x² = 2y³\) = 2 * \(2^3\) = 2 * 8 = 16

=> \(x² + y\) = 16 + 2 = 18

So, Answer will be E
Hope it helps!

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Re: If x^2 = 2y^3 and 2y = 4, what is the value of x^2 + y? [#permalink]
15 Jan 2023, 04:20
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