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Math Revolution GMAT Instructor
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If 2x+y=3 and 4x^24xy+y^2=1, what is the value of xy?
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01 Jan 2019, 06:52
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[ Math Revolution GMAT math practice question] If \(2x+y=3\) and \(4x^24xy+y^2=1\), what is the value of \(xy\)? \(A. \frac{1}{8}\) \(B. \frac{1}{2}\) \(C. 1\) \(D. 2\) \(E. 4\)
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Re: If 2x+y=3 and 4x^24xy+y^2=1, what is the value of xy?
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01 Jan 2019, 07:01
\(2x+y = 3\), \(y = 32x\) \(4x^24xy+y^2=1\)...............(1) Substituting the value of y in equation 1, we get \(16x^224x+8 = 0\) \(2x^23x+1 = 0\) \(2x^22xx+1 = 0\) \(2x(x1)1(x1) = 0\) \(x = 1 or 1/2\) Then, y becomes 1 when x is 1 or 2 when x is 1/2 xy becomes 1 C is the answer.
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Re: If 2x+y=3 and 4x^24xy+y^2=1, what is the value of xy?
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01 Jan 2019, 07:07
MathRevolution wrote: [ Math Revolution GMAT math practice question] If \(2x+y=3\) and \(4x^24xy+y^2=1\), what is the value of \(xy\)? \(A. \frac{1}{8}\) \(B. \frac{1}{2}\) \(C. 1\) \(D. 2\) \(E. 4\) Square the first equation, we have  \(4x^2+4xy+y^2=9\) and \(4x^24xy+y^2=1\).... Subtracting we get  xy = 1
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Re: If 2x+y=3 and 4x^24xy+y^2=1, what is the value of xy?
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01 Jan 2019, 09:37
MathRevolution wrote: [ Math Revolution GMAT math practice question] If 2x + y = 3 and 4x²  4xy + y² = 1, what is the value of xy? \(A. \frac{1}{8}\) \(B. \frac{1}{2}\) \(C. 1\) \(D. 2\) \(E. 4\) This question becomes a lot easier if we recognize that ( 2x + y)² = 4x² + 4xy + y² (which is VERY similar to 4x²  4xy + y²) Here's what I mean: Take 2x + y = 3 and square both sides to get: (2x + y)² = 3²Simplify both sides to get: 4x² + 4xy + y²= 9We now have two (quite similar) equations: 4x² + 4xy + y²= 94x²  4xy + y² = 1Subtract the bottom equation from the top equation to get: 8xy = 8 Divide both sides by 8 to get: xy = 1 Answer: C Cheers, Brent
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Re: If 2x+y=3 and 4x^24xy+y^2=1, what is the value of xy?
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01 Jan 2019, 10:23
MathRevolution wrote: [ Math Revolution GMAT math practice question] If \(2x+y=3\) and \(4x^24xy+y^2=1\), what is the value of \(xy\)? \(A. \frac{1}{8}\) \(B. \frac{1}{2}\) \(C. 1\) \(D. 2\) \(E. 4\) \(4x^24xy+y^2=1\) => (2x+y)^2  4xy 4xy =1 => (2x+y)^2  8xy = 1 Given 2x+y = 3 => 9 8xy = 1 => 8xy =8 => xy =1 Hence ans. C)



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Re: If 2x+y=3 and 4x^24xy+y^2=1, what is the value of xy?
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01 Jan 2019, 11:29
MathRevolution wrote: [ Math Revolution GMAT math practice question] If \(2x+y=3\) and \(4x^24xy+y^2=1\), what is the value of \(xy\)? \(A. \frac{1}{8}\) \(B. \frac{1}{2}\) \(C. 1\) \(D. 2\) \(E. 4\) Given \(4x^24xy+y^2=1\), \((2x  y)^2 = 1\) 2x  y = 1. 2x + y = 3 2x  y = 1 ...................... 4x = 4 x = 1. and y = 1. xy = 1. C is the correct answer.



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Re: If 2x+y=3 and 4x^24xy+y^2=1, what is the value of xy?
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01 Jan 2019, 11:54
First substitute 4x^24xy+y^2=1 Since it is in the form of (ab)^2, the above equation can be written as (4xy)^2=1
Also, 2x+y=3, then y=32x. Substitute this in the above equation, we get (2x3)^2=1
Expand it we get 2x^26x+9=1
2x^26x+8=0 By solving the equation we get (x=4 or x=1)
Substituting x=1 in y=32x, we get x=1 and y=1.
Hence, xy=1, Answer is C.
Kindly let me know if my approach is wrong.



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Re: If 2x+y=3 and 4x^24xy+y^2=1, what is the value of xy?
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03 Jan 2019, 00:27
=> Since \(2x+y=3, (2x+y)^2 = 4x^2+4xy+y^2 =9.\) When we subtract \(4x^24xy+y^2=1\) from \(4x^2+4xy+y^2 =9\), we obtain \((4x^2+4xy+y^2)  (4x^24xy+y^2) = 8xy = 9  1 = 8.\) So, \(xy = 1.\) Therefore, the answer is C. Answer: C
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Re: If 2x+y=3 and 4x^24xy+y^2=1, what is the value of xy?
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03 Jan 2019, 11:01
We can test values for this question. One can quickly spot that x = 1 and y=1 works for both equations. Therefore xy = 1 (Answer choice C). It took less than 40 secs to solve MathRevolution wrote: [ Math Revolution GMAT math practice question] If \(2x+y=3\) and \(4x^24xy+y^2=1\), what is the value of \(xy\)? \(A. \frac{1}{8}\) \(B. \frac{1}{2}\) \(C. 1\) \(D. 2\) \(E. 4\)




Re: If 2x+y=3 and 4x^24xy+y^2=1, what is the value of xy?
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