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

 It is currently 20 Feb 2019, 12:24

### 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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Prep Hour

February 20, 2019

February 20, 2019

08:00 PM EST

09:00 PM EST

Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST
• ### Online GMAT boot camp for FREE

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

# Is x² - y > 1/y² where y is non-zero?

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

### Hide Tags

Intern
Joined: 28 May 2018
Posts: 48
Location: India
Schools: Tuck '21, ISB '20, NTU '20
GMAT 1: 640 Q45 V35
GMAT 2: 670 Q45 V37
Is x² - y > 1/y² where y is non-zero?  [#permalink]

### Show Tags

19 Oct 2018, 01:49
2
00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:18) correct 45% (02:35) wrong based on 73 sessions

### HideShow timer Statistics

Is x² - y > 1/y² where y is non-zero?

(1) x < y
(2) x² < y²

_________________

Please +1 KUDO if my post helps. Thank you.

Intern
Joined: 28 May 2018
Posts: 48
Location: India
Schools: Tuck '21, ISB '20, NTU '20
GMAT 1: 640 Q45 V35
GMAT 2: 670 Q45 V37
Re: Is x² - y > 1/y² where y is non-zero?  [#permalink]

### Show Tags

19 Oct 2018, 02:10
This is the solution that I found. I do not find this explanation satisfactory.

Can any of the experts please explain the solution better? Thanks in advance

Let's start by simplifying the original by multiplying both sides by y² (we can safely do so because we know that y² is positive):
Is $$x^2y^3$$ - $$y^3$$ > 1?
(1) x < y
If x and y are big positive numbers, $$y^3$$ will dominate x²y² and the left side will be negative; if x and y are big negative numbers, x²y² and (-$$y^3$$) will both be positive and the left side will be a big positive number: insufficient.
(2) x² < y²
Tells us that |x| < |y|, but nothing about the signs of x and y. If we pick really big values with different signs we can generate both "yes" and "no" answers.
Together: combining doesn't help us at all, since we have the same generalizations from both: choose E.
_________________

Please +1 KUDO if my post helps. Thank you.

Manager
Joined: 17 Jun 2018
Posts: 52
Location: India
Schools: IMD '20
GPA: 2.84
WE: Engineering (Consulting)
Re: Is x² - y > 1/y² where y is non-zero?  [#permalink]

### Show Tags

31 Jan 2019, 10:27
chetan2u please help with this question.
I guessed the answer right but not sure about the approach.
VP
Joined: 09 Mar 2018
Posts: 1001
Location: India
Re: Is x² - y > 1/y² where y is non-zero?  [#permalink]

### Show Tags

31 Jan 2019, 11:21
PriyankaPalit7 wrote:
Is x² - y > 1/y² where y is non-zero?

(1) x < y
(2) x² < y²

$$x^2$$ - y > 1/$$y^2$$

$$x^2$$ - y - 1/$$y^2$$ > 0

Lets try 2 first
(2) x² < y² or y^2 > x^2,
9 > 4, y can be -3 or 3 and x can be -2 or 2
1/4 > 1/16, y can be 1/2 or -1/2 and x can be 1/4 or -1/4

4 +3 - 1/9 > 0, This answers a yes to the question
1/16 - 1/2 - 1/4 < 0, This answers a no to the question

from 1)
x < y or y>x, here y & x can be again a fraction, integer or a number
1/2 > 1/4 or 3 > 2
1/16 - 1/2 - 1/4 < 0, This answers a no to the question
4 -3 - 1/9 > 0, This answers a yes to the question

The same test cases can be used again to show that after combining the 2, we wont get an unique answer

E
_________________

If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.

Math Expert
Joined: 02 Aug 2009
Posts: 7334
Is x² - y > 1/y² where y is non-zero?  [#permalink]

### Show Tags

31 Jan 2019, 17:39
PriyankaPalit7 wrote:
Is x² - y > 1/y² where y is non-zero?

(1) x < y
(2) x² < y²

Hi arpitkansal,

What $$x^2<y^2$$ means is $$|x|<|y|$$..
X<y and |x|<|y| when combined mean y>x and y>0..
By looking at the equation, $$x^2-y>\frac{1}{y^2}$$, we should realise that $$\frac{1}{y^2}$$ will be positive.
We have to see if x^2-y can be both negative and positive.
1) x=2 and y=3
So $$2^2-3>\frac{1}{3^2}....4-3>\frac{1}{9}...1>\frac{1}{9}....$$yes
2) x=1 and y=4
$$1^2-4>\frac{1}{4^2}.....1-4>\frac{1}{16}.....-3>\frac{1}{16}...$$.no

Thus no definite answer..

E
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Director
Joined: 31 Jul 2017
Posts: 518
Location: Malaysia
Schools: INSEAD Jan '19
GMAT 1: 700 Q50 V33
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: Is x² - y > 1/y² where y is non-zero?  [#permalink]

### Show Tags

31 Jan 2019, 20:08
PriyankaPalit7 wrote:
Is x² - y > 1/y² where y is non-zero?

(1) x < y
(2) x² < y²

Take (x,y) = (0,1) & (0,-1).

We get E.
_________________

If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!

Math Expert
Joined: 02 Aug 2009
Posts: 7334
Re: Is x² - y > 1/y² where y is non-zero?  [#permalink]

### Show Tags

31 Jan 2019, 20:27
rahul16singh28 wrote:
PriyankaPalit7 wrote:
Is x² - y > 1/y² where y is non-zero?

(1) x < y
(2) x² < y²

Take (x,y) = (0,1) & (0,-1).

We get E.

Hi Rahul, be careful with numbers you pick up..
(o, -1) does not fit into statement 1, which is x<y.. as 0>-1, meaning x>y
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

GMAT Expert

Chat Moderator
Joined: 07 Mar 2016
Posts: 51
Is x² - y > 1/y² where y is non-zero?  [#permalink]

### Show Tags

01 Feb 2019, 07:47
1
Here's how I solved, feel free to critique!

Is $$x^{2}$$ - y > $$\frac{1}{y^{2}}$$? If $$y\neq{0}$$.

I simplified the expression as follows:

Because $$y^{2}$$ is always positive I multiplied both sides by $$y^{2}$$ to get $$x^{2}y^{2}$$ - $$y^{3}$$ > 1.

From here I factored out $$y^{2}$$ to get $$y^{2}$$($$x^{2}$$ - y) > 1.

The question is now:

Is $$y^{2}$$($$x^{2}$$ - y) > 1? If Y $$x\neq{0}$$.

Statement 1: x < y

I picked x as -1 and y as 1. Plugging these values into the question the result is 0 > 1.

I then picked x as -3 and y as -2. Plugging these values into the question the result is 44 > 1.

Clearly insufficient.

Statement 2: $$x^{3}$$ < $$y^{3}$$

I picked x as -1 and y as 1. Since they are raised to an odd power the signs remain the same for x and y (1 and -1, respectively).
Plugging these values into the question the result is 0 > 1.

I then picked x as -3 and y as -2. Since they are raised to an odd power the signs remain the same for x and y (-3 and -2, respectively).
Plugging these values into the question the result is 44 > 1.

Clearly insufficient.

Statement 1&2

Clearly insufficient.

Therefore, the answer is E.
_________________

...once in a while you get shown the light, in the strangest of places if you look at it right...

Manager
Joined: 16 Oct 2011
Posts: 61
GMAT 1: 620 Q37 V38
GMAT 2: 640 Q36 V41
GMAT 3: 650 Q42 V38
GMAT 4: 650 Q44 V36
GMAT 5: 570 Q31 V38
Re: Is x² - y > 1/y² where y is non-zero?  [#permalink]

### Show Tags

01 Feb 2019, 09:00
1
PriyankaPalit7 wrote:
Is x² - y > 1/y² where y is non-zero?

(1) x < y
(2) x² < y²

(1) x < y Let x = -3, y =-2. Then we have (-3)^2 --2 > 1/(-2)^2 --> is 9 -2 > 1/4? Yes

Let x =-1/2 let y =-1/4 is (-1/2)^2 --1/4 > 1/(-1/4)^2 ? is 1/4 - 1/4 >4 NO NS

(2) x^2 <y^2 This is equivalent to |x| <|y| Let x =-2 y =-3

Is (-2)^2 --3 > 1/(-3)^2 ? is 4+3 > 1/9? Yes

let x = 3 y =4 is (3)^2 -4 > 1/4^2? is 9-4 > 1/16 No

NS

(1) and (2) x < y and |x|<|y| so values like x = -4, y =-3 won't work Let x=0 y =1 is 0^2 -1 >1/1^2 No

Let x =3, y=4 is 3^2 -4 > 1/4^2 ? is 9-4 >1/4^2 Yes

NS Answer is E.
Re: Is x² - y > 1/y² where y is non-zero?   [#permalink] 01 Feb 2019, 09:00
Display posts from previous: Sort by

# Is x² - y > 1/y² where y is non-zero?

 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®.