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If y ≠ 0, what is the value of 6^(x-y)^2/6^(x+3)(x-3)?
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If y ≠ 0, what is the value of 6^(x-y)^2/6^(x+3)(x-3)? [#permalink] New post  22 Feb 2020, 08:41
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If \(y ≠ 0\), what is the value of \(\frac{6^{(x-y)^2}}{6^{(x+3)(x-3)}}\)?

(1) \(y = 2x\).

(2) \(y = 2\).
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Re: If y ≠ 0, what is the value of 6^(x-y)^2/6^(x+3)(x-3)? [#permalink] New post  22 Feb 2020, 12:08
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If \(y ≠ 0\), what is the value of \(\frac{6^{(x-y)^2}}{6^{(x+3)(x-3)}}\)?

\(\frac{6^{(x-y)^2}}{6^{(x+3)(x-3)}}=6^{(x-y)^2-(x+3)(x-3)}=6^{x^2-2xy+y^2-x^2+9}=6^{y^2-2xy+9}\)


(1) \(y = 2x\). The expression above becomes: \(6^{y^2-2xy+9}=6^{4x^2-4x^2+9}=6^9\). Sufficient.

(2) \(y = 2\). The expression above becomes: \(6^{y^2-2xy+9}=6^{4-4x+9}\). No info about x. Not sufficient.


Answer: A.
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Re: If y ≠ 0, what is the value of 6^(x-y)^2/6^(x+3)(x-3)? [#permalink] New post  24 Feb 2020, 02:04
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Asad wrote:
If \(y ≠ 0\), what is the value of \(\frac{6^{(x-y)^2}}{6^{(x+3)(x-3)}}\)?

(1) \(y = 2x\).

(2) \(y = 2\).


Solution


Step 1: Analyse Question Stem


    • \(y≠0\)
    • We need to find the value of \(\frac{6^{(x-y)^2}}{6^{(x+3)(x-3)}}\)
      o Or, \(\frac{6^{(x-y)^2}}{6^{(x+3)(x-3)}} = \frac{6^{(x^2+y^2–2xy)}}{6^{(x^2 – 9)}}= \frac{6^{x^2} *6^{y^2}*6^9}{6^{x^2}*6^{2xy}}= \frac{6^{y^2} *6^9}{6^{2xy}}\)
So, we need to find the value of \(\frac{6^{y^2} *6^9}{6^{2xy}}\)

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE


Statement 1: \(y = 2x\)
• \(\frac{6^{y^2}*6^9}{6^{2xy}} = \frac{6^{4*x^2}*6^9}{6^{4x^2}} = 6^9\).
Hence, statement 1 is sufficient and we can eliminate answer options B, C and E
Statement 2: \(y = 2\).
• Here, \(\frac{6^{y^2}*6^9}{6^{2xy} }= \frac{6^{2^2}*6^9}{6^{4x}}\)
• However, we don’t know the value of x.
Hence, statement 2 is NOT sufficient.
Thus, the correct answer is Option A.
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Re: If y ≠ 0, what is the value of 6^(x-y)^2/6^(x+3)(x-3)? [#permalink]
24 Feb 2020, 02:04
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