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

It is currently 21 Nov 2019, 09:54

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If Z is a positive integer such that (Z/81)^(1/3) = Y^4 - 7. What is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59229
If Z is a positive integer such that (Z/81)^(1/3) = Y^4 - 7. What is  [#permalink]

Show Tags

New post 07 Nov 2019, 02:56
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

32% (02:08) correct 68% (02:28) wrong based on 56 sessions

HideShow timer Statistics

Senior Manager
Senior Manager
avatar
G
Joined: 25 Jul 2018
Posts: 349
If Z is a positive integer such that (Z/81)^(1/3) = Y^4 - 7. What is  [#permalink]

Show Tags

New post 07 Nov 2019, 03:19
1
If Z is a positive integer such that \((Z/81)^{1/3} = Y^{4} —7\)

What is the value of Y?

(Statement1): \(Z^{5/2} = 3^{25}\)
—> \(Z = 3^{25*(2/5)}= 3^{10}\)

\((3^{10}/ 81)^{1/3}= Y^{4} —7\)
\(3^{2} = Y^{4} —7\)
\(Y^{4}= 16\)

Y= 2, Y= —2
Insufficient

( Statement2)
—4 < Y—1< 4
—3< Y< 5
Clearly insufficient

Taken together 1&2,
Y=—2 and Y= 2
—3 < Y < 5
Insuffient

The answer is E

Posted from my mobile device
Intern
Intern
avatar
Joined: 07 Nov 2019
Posts: 1
Re: If Z is a positive integer such that (Z/81)^(1/3) = Y^4 - 7. What is  [#permalink]

Show Tags

New post 08 Nov 2019, 09:29
But the question says if z is a positive integer!!
So statement 1 will be sufficient?

Posted from my mobile device
Intern
Intern
avatar
S
Joined: 24 May 2016
Posts: 46
Premium Member CAT Tests
Re: If Z is a positive integer such that (Z/81)^(1/3) = Y^4 - 7. What is  [#permalink]

Show Tags

New post 11 Nov 2019, 11:16
[wrapimg=][/wrapimg]
Islam2468 wrote:
But the question says if z is a positive integer!!
So statement 1 will be sufficient?

Posted from my mobile device


The question says that Z is a positive number, not Y.
Manhattan Prep Instructor
User avatar
G
Joined: 04 Dec 2015
Posts: 851
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: If Z is a positive integer such that (Z/81)^(1/3) = Y^4 - 7. What is  [#permalink]

Show Tags

New post 11 Nov 2019, 14:16
Bunuel wrote:
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) \(|Y−1|< 4\)


Are You Up For the Challenge: 700 Level Questions


The first thing that stands out is that I don't really see a way to simplify the info from the question stem. I could add 7 to both sides, but then I'd need to take a fourth root of both sides to get Y by itself, and that seems to make things more complicated, not less complicated. I could also cube both sides to get rid of the cube root, but that would make the right side really complicated. So, I'll just leave it for now.

The second thing that stands out is that z is a positive integer. However, it never says that y is a positive integer! It also doesn't say that y is an integer at all. I bet that's a trap: the problem writer wants me to assume that y is a positive integer, but there may be negative or non-integer results for y that also work.

Finally, the second statement looks way easier than the first one. So, I'll start there, with the intention of bailing out afterwards if this problem starts to take too long.

Statement 2: |y - 1| < 4. Normally, I would want to call this one insufficient immediately, and keep moving. However, I remember the constraint that says that z has to be a positive integer, and I'm a little bit suspicious. Is it possible that there's only one value of z that even gives us a value of y in this range? If we have time, let's do a little more work with this one.

|y - 1| < 4 means that y is within 4 units of 1 on the number line. In other words, -3 < y < 5.

Are there multiple valid values of y in this range? Or is there perhaps only one? Let's try a few things.

If z = 81, then the equation would simplify like this:

\(\sqrt[3]{\frac{81}{81}} =Y^4−7\)

\(1 =Y^4−7\)

\(Y^4 = 8\)

I don't know exactly what value of Y solves this. However, I'm confident of two things. First, it's definitely between -3 and 5. (It's somewhere between 1 and 2, actually.) Second, there are two different values of Y in that range that solve this equation, because Y can be either positive or negative.

Therefore, Y can have two different values, so the statement is insufficient. Eliminate B and D.

This is more work than we technically needed to do, by the way. On test day, it's probably better to just conclude that it's insufficient without actually proving it with math!

Statement 1: This lets us calculate the exact value of z. However, it doesn't let us calculate the exact value of y. That's because, just like with the other statement, y will have both a positive value and a negative value, due to the 4th power. So, this one is insufficient as well. Eliminate A.

Statements 1 and 2 together:

It's possible that they're sufficient together, but it seems unlikely. On test day, I'd probably just pick E and keep moving.

One way to check would be to figure out the actual two values of y that you get from Statement 1. Then, if both of those values are within the range given in statement 2, then you know the two statements are insufficient put together. That's because you'd have two values of y that work with both statements. Otherwise, we'd need to do a ton more math to find different values, so I'm going to try that before I do anything else...

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

\(Z^{5}=3^{50}\)

\(Z = 3^{10}\)

\(\sqrt[3]{\frac{3^{10}}{81}} =Y^4−7\)

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

\(\sqrt[3]{3^6} =Y^4−7\)

\(3^2 = Y^4 - 7\)

\(Y^4 = 16\)

Y = 2, Y = -2

Okay, there are two values of Y that fit both statements: 2, and -2. Therefore, the statements are insufficient together and the answer is E! (Interestingly, if the question instead said "What is the value of Y^2?", we'd have more work to do...
_________________
Image

Chelsey Cooley | Manhattan Prep | Seattle and Online

My latest GMAT blog posts | Suggestions for blog articles are always welcome!
GMAT Club Bot
Re: If Z is a positive integer such that (Z/81)^(1/3) = Y^4 - 7. What is   [#permalink] 11 Nov 2019, 14:16
Display posts from previous: Sort by

If Z is a positive integer such that (Z/81)^(1/3) = Y^4 - 7. What is

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne