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If x = 2 and y = –2, then x^4 - y^5/x^4y^5 =

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Bunuel
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If x = 2 and y = –2, then x^4 - y^5/x^4y^5 = [#permalink] New post   17 Oct 2020, 12:16
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If \(x = 2\) and \(y = –2\), then \(\frac{x^4 - y^5}{x^4y^5} =\)

(A) -3/32
(B) 0
(C) 1/32
(D) 1/16
(E) 1
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If x = 2 and y = –2, then x^4 - y^5/x^4y^5 = [#permalink] New post   17 Oct 2020, 12:21
=>\( \frac{X^4-Y^5 }{ X^4*Y^5}\)
=> \(\frac{(2)^4-(-2)^5 }{ (2)^4*(-2)^5}\)
=> \(\frac{16-(-32) }{ 16*(-32)}\)
=> \(\frac{48}{16*(-32)}\)
=>\( \frac{-3}{32}\)

=> Answer is A

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Re: If x = 2 and y = –2, then x^4 - y^5/x^4y^5 = [#permalink] New post   19 Oct 2020, 07:16
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\(\frac{x^4 \space - \space y^5}{x^4 \space y^5}\)


= \(\frac{x^4}{x^4 \space y^5} - \frac{y^5}{x^4 \space y^5}\)

= \(\frac{1}{y^5} - \frac{1}{x^4}\)

= \(\frac{1}{(-2)^5} - \frac{1}{2^4}\)

= \(-\frac{1}{16} - \frac{1}{32}\)

= \(\frac{-2 - 1}{32}\)

= \(-\frac{3}{32}\)


Option A

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Re: If x = 2 and y = –2, then x^4 - y^5/x^4y^5 = [#permalink] New post   19 Oct 2020, 17:03
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Bunuel wrote:
If \(x = 2\) and \(y = –2\), then \(\frac{x^4 - y^5}{x^4y^5} =\)

(A) -3/32
(B) 0
(C) 1/32
(D) 1/16
(E) 1


From the values we are given \(x = -y\), so we may use that to simplify the problem a bit. Plug in \(y^5 = -x^5\),

\(\frac{x^4 - y^5}{x^4y^5} = \frac{x^4 + x^5 }{ {-x^9}}\). Since x is positive, this result is negative and the only answer with a negative result is A, we may choose A from elimination.

Ans: A
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gmatclubot
Re: If x = 2 and y = –2, then x^4 - y^5/x^4y^5 = [#permalink]
19 Oct 2020, 17:03
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