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

 It is currently 23 Jan 2019, 18:57

### 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

## Events & Promotions

###### Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• ### Key Strategies to Master GMAT SC

January 26, 2019

January 26, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn how to leverage Meaning and Logic to solve the most challenging Sentence Correction Questions.
• ### Free GMAT Number Properties Webinar

January 27, 2019

January 27, 2019

07:00 AM PST

09:00 AM PST

Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes.

# If x and y are non zero numbers less than 1 is (y^4 - x^4)>(y^3 - x^5)

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

### Hide Tags

Intern
Joined: 21 May 2016
Posts: 28
If x and y are non zero numbers less than 1 is (y^4 - x^4)>(y^3 - x^5)  [#permalink]

### Show Tags

Updated on: 14 Aug 2018, 03:16
8
00:00

Difficulty:

95% (hard)

Question Stats:

25% (01:38) correct 75% (01:41) wrong based on 91 sessions

### HideShow timer Statistics

If x and y are non zero numbers less than 1, is $$(y^4 - x^4) > (y^3 - x^5)$$ ?

(1) y > 0
(2) y > |x|

_________________

If you like my post press +1 Kudos

Originally posted by a70 on 03 Aug 2018, 10:15.
Last edited by a70 on 14 Aug 2018, 03:16, edited 2 times in total.
##### Most Helpful Community Reply
Intern
Joined: 22 Jul 2018
Posts: 6
Re: If x and y are non zero numbers less than 1 is (y^4 - x^4)>(y^3 - x^5)  [#permalink]

### Show Tags

04 Aug 2018, 07:51
3
2
Rearrange the terms
y^4 -y^3 > -x^5 + x^4
factor, so the question now is:
is y^3(y - 1) > - (x^4) (x - 1)?

1) y>0
so y is between 0 and 1
This means the LHS is negative (because (y-1) is negative, and y^3 is positive)
RHS is always positive (because (x-1) is always negative since x is less than 1, -(x^4) is always negative, so their product is always positive)
If LHS is always negative and RHS is always positive, this means that RHS>LHS, so statement 1 is sufficient to determine that the inequality is false.

2) y> |x|
This means y is positive i.e. y>0
The statement is therefore equivalent to statement 1, and we can use the same logic to determine that the inequality is false

Hence, the answer is D
##### General Discussion
Manager
Status: Studying SC
Joined: 04 Sep 2017
Posts: 120
GPA: 3.6
WE: Sales (Computer Software)
Re: If x and y are non zero numbers less than 1 is (y^4 - x^4)>(y^3 - x^5)  [#permalink]

### Show Tags

03 Aug 2018, 10:59
2
ankit7055 wrote:
If x and y are non zero numbers less than 1, is (y^4 - x^4) > (y^3 - x^5) ?

(1) y > 0
(2) y > |x|

1 > x
1 > y

(1) y > 0

make y= $$\frac{1}{2}$$

1 > y > 0

($$.5^4$$ - $$x^4$$) > ($$.5^3$$ - $$x^5$$) ---> ($$\frac{1}{16}$$ - $$x^4$$) > ($$\frac{1}{8}$$ - $$x^5$$)

Make x=-1 ---> ($$\frac{1}{16}$$ - 1) > ($$\frac{1}{8}$$ + 1) Answer is NO

make x=$$\frac{1}{2}$$ ---> ($$\frac{1}{16}$$ - $$\frac{1}{16}$$) > ($$\frac{1}{8}$$ - $$\frac{1}{32}$$) Answer is NO

Sufficient

(2) y > |x|

Same applies from statement 1.

NO. Sufficient.

Answer: D

PS - I got this wrong at first 700 level IMO.
_________________

Would I rather be feared or loved? Easy. Both. I want people to be afraid of how much they love me.

How to sort questions by Topic, Difficulty, and Source:
https://gmatclub.com/forum/search.php?view=search_tags

SVP
Joined: 26 Mar 2013
Posts: 2010
Re: If x and y are non zero numbers less than 1 is (y^4 - x^4)>(y^3 - x^5)  [#permalink]

### Show Tags

03 Aug 2018, 17:47
ankit7055 wrote:
If x and y are non zero numbers less than 1, is (y^4 - x^4) > (y^3 - x^5) ?

(1) y > 0
(2) y > |x|

Hi

What is the source if the question. It is really good.
Senior Manager
Joined: 22 Feb 2018
Posts: 416
Re: If x and y are non zero numbers less than 1 is (y^4 - x^4)>(y^3 - x^5)  [#permalink]

### Show Tags

04 Aug 2018, 09:21
2
1
ankit7055 wrote:
If x and y are non zero numbers less than 1, is (y^4 - x^4) > (y^3 - x^5) ?

(1) y > 0
(2) y > |x|

OA:D

Is $$(y^4 - x^4) > (y^3 - x^5)$$?
Is $$y^3(y-1)>x^4(1-x)$$?

Statement 1 : $$y > 0$$
$$0<y<1$$
L.H.S $$y^3(y-1)$$ would always be negative

For $$x$$, there can be 2 cases,
1) $$0<x<1$$
2) $$x<0$$
R.H.S will be always positive, as $$x^4$$ is +ve, $$(1-x)$$ would give +ve value in both of the cases
So There is definite answer to Is $$(y^4 - x^4) > (y^3 - x^5)$$? , That is No
Statement 1 alone is sufficient

Statement 2 : $$y > |x|$$
it means $$y$$ is positive, i,e $$y>0$$ same as statement 1
So There is definite answer to Is $$(y^4 - x^4) > (y^3 - x^5)$$? , That is No
Statement 2 alone is sufficient
_________________

Good, good Let the kudos flow through you

Re: If x and y are non zero numbers less than 1 is (y^4 - x^4)>(y^3 - x^5) &nbs [#permalink] 04 Aug 2018, 09:21
Display posts from previous: Sort by

# If x and y are non zero numbers less than 1 is (y^4 - x^4)>(y^3 - x^5)

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

 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®.