GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Oct 2018, 09:38

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# If Z is a positive integer such that

Author Message
TAGS:

### Hide Tags

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]

### Show Tags

21 May 2017, 23:36
1
00:00

Difficulty:

75% (hard)

Question Stats:

49% (02:39) correct 51% (02:43) wrong based on 61 sessions

### HideShow timer Statistics

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
SVP
Joined: 26 Mar 2013
Posts: 1836
If Z is a positive integer such that  [#permalink]

### Show Tags

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
Display posts from previous: Sort by