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If (2x)^3(3x)^2 = 6xy, then which of the following expresses y in term

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Bunuel
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If (2x)^3(3x)^2 = 6xy, then which of the following expresses y in term [#permalink] New post   23 Jun 2017, 02:00
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If \((2x)^3(3x)^2 = 6xy\), then which of the following expresses y in terms of x?

A. \(6^4*x^4\)

B. \(2^2*3*x^4\)

C. \(2^3*3^2*x^4\)

D. \(x^5\)

E. \(x^4\)
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B
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Re: If (2x)^3(3x)^2 = 6xy, then which of the following expresses y in term [#permalink] New post   23 Jun 2017, 02:15
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\((2x)^3(3x)^2=6xy\)
\(2^3*3^2*x^5=2*3xy\)
\(2^2*3*x^4=y\)
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If (2x)^3(3x)^2 = 6xy, then which of the following expresses y in term [#permalink] New post   23 Jun 2017, 02:35
Given : \((2x)^3(3x)^2 = 6xy\)

Since we need the expression for y in terms of x,

The expression \(6xy = (2x)^3(3x)^2\) becomes \(y = \frac{((2x)^3(3x)^2)}{6x}\)

Assume x=1, we get y = \(2^2 * 3\)
Of the available options, Option B will give you the same value when x=1.
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Re: If (2x)^3(3x)^2 = 6xy, then which of the following expresses y in term [#permalink] New post   23 Jun 2017, 02:39
Bunuel wrote:
If \((2x)^3(3x)^2 = 6xy\), then which of the following expresses y in terms of x?

A. \(6^4*x^4\)

B. \(2^2*3*x^4\)

C. \(2^3*3^2*x^4\)

D. \(x^5\)

E. \(x^4\)


\((2x)^3(3x)^2 = 6xy\)

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

\(2^3*3^2*x^5 = 2*3xy\)

Cancelling common term from both sides, we get;

\(y = 2^2*3*x^4.\) Answer (B)...
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Re: If (2x)^3(3x)^2 = 6xy, then which of the following expresses y in term [#permalink] New post   23 Jun 2017, 06:15
Bunuel wrote:
If \((2x)^3(3x)^2 = 6xy\), then which of the following expresses y in terms of x?

A. \(6^4*x^4\)

B. \(2^2*3*x^4\)

C. \(2^3*3^2*x^4\)

D. \(x^5\)

E. \(x^4\)



\((2x)^3(3x)^2 = 6xy\)
2^3 * 3^2 *x^5 = 2 * 3* x *y
y = 2^2 * 3 * x^4
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Re: If (2x)^3(3x)^2 = 6xy, then which of the following expresses y in term [#permalink] New post   23 Jun 2017, 08:03
Bunuel wrote:
If \((2x)^3(3x)^2 = 6xy\), then which of the following expresses y in terms of x?

A. \(6^4*x^4\)

B. \(2^2*3*x^4\)

C. \(2^3*3^2*x^4\)

D. \(x^5\)

E. \(x^4\)


\((2x)^3(3x)^2 = 6xy\)

Or, \(8x^3*9x^2 = 6xy\)

Or, \(72x^5 = 6xy\)

Or, \(y = 12x^4\)

Or, \(y = 2^2*3*x^4\)

Thus, answer must be (B)
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Re: If (2x)^3(3x)^2 = 6xy, then which of the following expresses y in term [#permalink] New post   23 Jun 2017, 10:39
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Bunuel wrote:
If \((2x)^3(3x)^2 = 6xy\), then which of the following expresses y in terms of x?

A. \(6^4*x^4\)

B. \(2^2*3*x^4\)

C. \(2^3*3^2*x^4\)

D. \(x^5\)

E. \(x^4\)


y = \(2^3x^3*3^2x^2 / 2*3*x\) = \(2^2x^2*3*x^2\) = \(2*2*3*x^4\)

Correct Option: B
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Re: If (2x)^3(3x)^2 = 6xy, then which of the following expresses y in term [#permalink] New post   24 Jun 2017, 14:19
\((2x)^3(3x)^2 = 6xy\)

\(8 * {x^3} * 9 * {x^2} = 6 * x * y\)

Simplify both the sides

\(y = 12 * {x^4}\)

or we can also write it as

\(2^2*3*x^4\)

Hence, Answer is B
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Re: If (2x)^3(3x)^2 = 6xy, then which of the following expresses y in term [#permalink] New post   26 Jun 2017, 17:58
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Bunuel wrote:
If \((2x)^3(3x)^2 = 6xy\), then which of the following expresses y in terms of x?

A. \(6^4*x^4\)

B. \(2^2*3*x^4\)

C. \(2^3*3^2*x^4\)

D. \(x^5\)

E. \(x^4\)



Let’s simplify the given equation:

(2^3)(x^3)(3^2)(x^2) = 6xy

(2^3)(3^2)(x^5) = 6xy

(2^3)(3^2)(x^5)/[(x)(2)(3)] = y

(2^2)(3)(x^4) = y

Answer: B
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Re: If (2x)^3(3x)^2 = 6xy, then which of the following expresses y in term [#permalink]
26 Jun 2017, 17:58
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