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If Z is a positive integer such that

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If Z is a positive integer such that [#permalink]

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New post 21 May 2017, 23:36
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E

Difficulty:

  75% (hard)

Question Stats:

49% (01:44) correct 51% (02:14) wrong based on 59 sessions

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If Z is a positive integer such that\(\sqrt[3]{\frac{Z}{81}} =Y^4−7\). What is the value of Y?

(1) \(Z^{\frac{5}{2}}=3^{25}\)

(2) |Y−1|< 4
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If Z is a positive integer such that [#permalink]

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New post 22 May 2017, 00:19
If Z is a positive integer such that\(\sqrt[3]\frac{Z}{81}\) =\(Y^4−7\), What is the value of Y?

(1) \(Z^\frac{5}{2}=3^{25}\)

We can take fifth root for both sides

\(Z^\frac{1}{2}=3^{5}\)

Square both sides

\(Z =3^{10}\)

Apply in equation above:

\(\sqrt[3]\frac{3^{10}}{3^{4}}\) =\(Y^4−7\)

\(\sqrt[3]3^{6}\) =\(Y^4−7\)

\(3^{2}\) =\(Y^4−7\)

Y ^ 4 =16

Y = 2 or -2

Insufficient

(2) |Y−1|< 4

-4 < Y−1< 4

-3 < Y < 5

No certain value.

Insufficient

Combine 1 & 2

-2 & 2 are in the range -3 < Y < 5.....No clear value

Insufficient

Answer: E
If Z is a positive integer such that   [#permalink] 22 May 2017, 00:19
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