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605-655 (Medium)|   Algebra|      
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Bunuel
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What is the value of 36x^2 - 108xy + 81y^2? 10 Aug 2018, 03:50
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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45% (medium)

Question Stats:

67% (01:48) correct 33% (02:16) wrong based on 368 sessions

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What is the value of \(36x^2 - 108xy + 81y^2\)?


(1) \(3y−2x=−4\)

(2) \(x=\frac{5}{y}\)
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A
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What is the value of 36x^2 - 108xy + 81y^2? Updated on: 10 Aug 2018, 05:03
Originally posted by sandman13 on 10 Aug 2018, 04:14.
Last edited by sandman13 on 10 Aug 2018, 05:03, edited 1 time in total.
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We need (6x-9y)^2 = 9(2x - 3y)^2

S1: Sufficient

S2: x = 5/y
x = 1, y = 5 --> 2x - 3y = -13
y = 1, x = 5 --> 2x - 3y = 7
Clearly, not sufficient.

Answer: A
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What is the value of 36x^2 - 108xy + 81y^2? 10 Aug 2018, 05:00
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Bunuel
What is the value of \(36x^2 - 108xy + 81y^2\)?


(1) \(3y−2x=−4\)

(2) \(x=\frac{5}{y}\)
Show more

\(36x^2 - 108xy + 81y^2\)=\(9(4x^2 - 12xy + 9y^2)\)=\(9(3y-2x)^2\)

Re-phrased question stem:- \(9(3y-2x)^2\)=?

St1:- \(3y−2x=−4\)
Sufficient.(substitute the value of 3y-2x in rephrased question stem)

St2:- \(x=\frac{5}{y}\)
Insufficient. (Either value x or y is required)

Ans. (A)
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What is the value of 36x^2 - 108xy + 81y^2? 13 Aug 2018, 07:45
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Solution


Given:
    • An expression, \(36x^2 – 108xy + 81y^2\)

To find:
    • The value of the given expression, \(36x^2 – 108xy + 81y^2\)

Analysing Statement 1
“3y – 2x = -4”
    • Squaring on both sides, we get,
      o \(4x^2 – 12xy + 9y^2 = 16\)
    • Multiplying this equation by 9, we get
      o \(36x^2 – 108xy + 81y^2 = 144\)

Therefore, Statement (1) ALONE is sufficient to answer this question

Analysing Statement 2
“x = 5/y”
    • Substituting this in the required expression, we get,
      o \(180/y^2 – 540 + 81y^2\)
      o We cannot find the value of this expression as we do not have any further information about y.

Therefore, Statement (2) ALONE is not sufficient to answer this question

Hence, the correct answer is option A.

Answer: A

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What is the value of 36x^2 - 108xy + 81y^2? 23 Apr 2020, 11:56
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Bunuel
What is the value of \(36x^2 - 108xy + 81y^2\)?


(1) \(3y−2x=−4\)

(2) \(x=\frac{5}{y}\)

\(36x^2 - 108xy + 81y^2\)=\(9(4x^2 - 12xy + 9y^2)\)=\(9(3y-2x)^2\)

Re-phrased question stem:- \(9(3y-2x)^2\)=?

St1:- \(3y−2x=−4\)
Sufficient.(substitute the value of 3y-2x in rephrased question stem)

St2:- \(x=\frac{5}{y}\)
Insufficient. (Either value x or y is required)

Ans. (A)
Show more

Hello, would you kindly demonstrate the process of factoring the equation from
This
\(9(4x^2 - 12xy + 9y^2)\)

To this?
[m]9(3y-2x)^2[/m

Thank you!
Chris
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What is the value of 36x^2 - 108xy + 81y^2? 04 Feb 2025, 21:07
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Same. If i knew i could factor ir like that tis would be a much easier question.
Clycos
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Bunuel
What is the value of \(36x^2 - 108xy + 81y^2\)?


(1) \(3y−2x=−4\)

(2) \(x=\frac{5}{y}\)

\(36x^2 - 108xy + 81y^2\)=\(9(4x^2 - 12xy + 9y^2)\)=\(9(3y-2x)^2\)

Re-phrased question stem:- \(9(3y-2x)^2\)=?

St1:- \(3y−2x=−4\)
Sufficient.(substitute the value of 3y-2x in rephrased question stem)

St2:- \(x=\frac{5}{y}\)
Insufficient. (Either value x or y is required)

Ans. (A)

Hello, would you kindly demonstrate the process of factoring the equation from
This
\(9(4x^2 - 12xy + 9y^2)\)

To this?
[m]9(3y-2x)^2[/m

Thank you!
Chris
Show more
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What is the value of 36x^2 - 108xy + 81y^2? 05 Feb 2025, 00:14
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spuntamb
Same. If i knew i could factor ir like that tis would be a much easier question.
Clycos
PKN
What is the value of \(36x^2 - 108xy + 81y^2\)?


(1) \(3y−2x=−4\)

(2) \(x=\frac{5}{y}\)


\(36x^2 - 108xy + 81y^2\)=\(9(4x^2 - 12xy + 9y^2)\)=\(9(3y-2x)^2\)

Re-phrased question stem:- \(9(3y-2x)^2\)=?

St1:- \(3y−2x=−4\)
Sufficient.(substitute the value of 3y-2x in rephrased question stem)

St2:- \(x=\frac{5}{y}\)
Insufficient. (Either value x or y is required)

Ans. (A)

Hello, would you kindly demonstrate the process of factoring the equation from
This
\(9(4x^2 - 12xy + 9y^2)\)

To this?
[m]9(3y-2x)^2[/m

Thank you!
Chris
Show more

To factor 9(4x^2 - 12xy + 9y^2) into 9(3y - 2x)^2, follow these steps:

Recognize that 4x^2 - 12xy + 9y^2 is a perfect square in the form (a - b)^2 = a^2 - 2ab + b^2.

Identify the square terms:

  • 4x^2 is (2x)^2.
  • 9y^2 is (3y)^2.
  • -12xy is -2(2x)(3y), which matches the middle term in the perfect square formula.

This confirms that 4x^2 - 12xy + 9y^2 can be rewritten as (3y - 2x)^2.
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