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

It is currently 17 Jul 2018, 10:42

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 x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of

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

Hide Tags

2 KUDOS received
Manager
Manager
avatar
Joined: 09 Feb 2013
Posts: 120
If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of [#permalink]

Show Tags

New post Updated on: 16 Apr 2013, 06:11
2
10
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

41% (01:54) correct 59% (01:58) wrong based on 222 sessions

HideShow timer Statistics

If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of the following is true?

(A) x > y > z
(B) y > x > z
(C) y > z > x
(D) z > y > x
(E) z > x > y

_________________

Kudos will encourage many others, like me.
Good Questions also deserve few KUDOS.


Originally posted by emmak on 16 Apr 2013, 06:07.
Last edited by Bunuel on 16 Apr 2013, 06:11, edited 1 time in total.
Edited the question.
Most Helpful Community Reply
5 KUDOS received
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 619
Premium Member
Re: If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of [#permalink]

Show Tags

New post 16 Apr 2013, 06:53
5
5
emmak wrote:
If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of the following is true?

(A) x > y > z
(B) y > x > z
(C) y > z > x
(D) z > y > x
(E) z > x > y


Given that x = \(5^{2/3}, y = 2^{3/2}.\) As xy>0, they both have the same sign and also as odd power of x is positive, thus x>0--> Both x,y>0.'

Now lets assume that x>y, thus as both the sides are positive, we can safely raise to the power of 6. Thus, we assume that \(5^{4}>2^{9}\)

or 625>512; this is infact correct. Thus eliminate all the options wherein x<y. Thus we are left with A and E.

Now \(z = 2^{3/5}*3^{3/5}\). We again start with the assumption that z>y[We take y and z as there is a common factor of 2]. Again, as the odd power of z is positive, thus z is also positive. Raising the inequality z>y to the 10th power, we have \(2^{6}*3^{6}>2^{15}\)

or \(3^6>2^9\)

or 729>512, which is again correct. Thus the order is : z>x>y

E.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

General Discussion
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 701
Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of [#permalink]

Show Tags

New post 27 Dec 2013, 03:09
emmak wrote:
If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of the following is true?

(A) x > y > z
(B) y > x > z
(C) y > z > x
(D) z > y > x
(E) z > x > y


Mau5 method is better. I have a little more crued way but it gets you by...

here it

We know x= Cuberoot 25 (or 5^2)
y= 4th root of 64 (or 2^6) and
z= 5th root of 216 (or 2^3 *3^3)

Note that x>0 so y also is greater then 0 (because xy>0)
Consider x and y at first,
y can be written as 2*4th root of 4 and 4th root of 1 is 1 so 4th root of 4 will be ~ close to 1 so value of y will be close to 2*(Something close to 1) = 2

For x we have Cube root of 25...if we divide and multiply by 5 so x = 5/ (cuberoot of 5)....Now Cube root of 1 is 1 so cube root of 5 will be value less than 2 but more than 1.....less than 2 because cube root of 8 is 2 and hence possible values x will be between 5 and 2.5 but more close to 2.5

So x>y


Coming to z ie 5th root of 216....Can be written as 5th root of (2^3*3^3). Now multiply and divide by 36(2^2*3^2) in the numerator and denominator, we get 6/ (5th root of 36).....Now 2^5 = 32 or 2 = 5th root of 32 and 3^5 =243 or 3=5th root of 216......so 5th root of 216 will be between 2 and 3 and hence value of z will be close to 2.(Something) and therefore z little less than 3


Therefore z>x>y
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

1 KUDOS received
Manager
Manager
avatar
Joined: 17 Jul 2013
Posts: 87
Premium Member
Re: If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of [#permalink]

Show Tags

New post 20 Jun 2014, 01:43
1
1
I approached this ques with approximation .. though I like mau's above mentioned method :
x cube = 25 this means x<3 bcoz cube 3 = 27
y raise to power 4 = 64 will result in 2.8 or -2.8 since its given x and y has similar signs hence consider only 2.8
z raise to power 5 = 216 which is cube 6 ... 3*3*3*4*2 which will be closer to 3 but greater than x. reason being the 4*2 =8 just one digit less to be perfect root 5, but 25 is 2 digits less than perfect cube root.

hence the desired order will be
z>x>y
Intern
Intern
User avatar
Joined: 22 Dec 2014
Posts: 39
GMAT ToolKit User
If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of [#permalink]

Show Tags

New post 12 Jul 2015, 10:32
emmak wrote:
If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of the following is true?

(A) x > y > z
(B) y > x > z
(C) y > z > x
(D) z > y > x
(E) z > x > y


\(3^{3}=27\) --> x is approaching 3
\(8^{2}=4^{3}=2^{4}=64\) --> \(y =2\)
\(3^{5}=243\) ---> z is approaching 3

--> y is the smallest number. Among the options, E offers y as the smallest number. --> Answer: E
Senior Manager
Senior Manager
avatar
S
Joined: 15 Jan 2017
Posts: 362
CAT Tests
Re: If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of [#permalink]

Show Tags

New post 06 Dec 2017, 16:39
Was really flummoxed for the first 30 seconds.
Then:
X, y we know will be fractions,though positive. And, x>y (root x = basically more than 3, y is 2)
z is also positive, but with highest value --> z^5 = 216 --> but root z value is approaching 6, greater than 5)

Hence E --> z> x> y
Expert Post
EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 11979
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of [#permalink]

Show Tags

New post 16 Mar 2018, 10:57
Hi All,

This is something of a convoluted, layered "math" question, and you're not likely to see it on Test Day. It can be solved with comparative math though - instead of calculating the exact values of X, Y and Z, you can deduce which is bigger or smaller by pattern comparison.

First, let's do a quick estimation…

3^3 = 27
3^4 = 81
3^5 = 243

X^3 = 25, so X is a little less than 3
Y^4 = 64, so Y is a little less than 3 (or a little bigger than -3)
Z^5 = 216, so Z is a little less than 3

We're told that XY > 0, so we're forced to consider only the positive value of Y.

X, Y and Z are all pretty close to one another, so we have to look for something that will differentiate them (and help us to figure out which is bigger when we look at any 2 of them)

X^3 = (X)(X)(X) = 25
Y^4 = (Y)(Y)(Y)(Y) = 64

Since the values of X and Y are pretty close, multiplying by the "extra" Y is what turns 25 into 64…..

64/25 = about 2.5

This does NOT mean that Y = 2.5, but it DOES mean that Y MUST be farther away from 3 than X is.

So X > Y

Y^4 = (Y)(Y)(Y)(Y) = 64
Z^5 = (Z)(Z)(Z)(Z)(Z) = 216

The values of Y and Z are also pretty close, so multiplying by the "extra" Z is what turns 64 into 216….

216/64 = more than 3

This does NOT mean that Z is greater than 3, but it DOES mean that Z MUST be closer to 3 than Y is.

So Z > Y

From here, the answer choices provide us with a great way "out" of this question. Since Y is smaller than both X and Z, the only answer that makes sense is….

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Re: If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of   [#permalink] 16 Mar 2018, 10:57
Display posts from previous: Sort by

If x^3 = 25, y^4 = 64, and z^5 = 216, and xy > 0, which of

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

Events & Promotions

PREV
NEXT


cron

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.