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# If Z is a positive integer such that

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Manager
Joined: 14 Sep 2015
Posts: 65
Location: India
GMAT 1: 700 Q45 V40
GPA: 3.41
If Z is a positive integer such that  [#permalink]

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21 May 2017, 23:36
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Difficulty:

75% (hard)

Question Stats:

49% (02:39) correct 51% (02:43) wrong based on 61 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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Joined: 26 Mar 2013
Posts: 1836
If Z is a positive integer such that  [#permalink]

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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

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

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