It is currently 20 Jan 2018, 19:09

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# If x>y>0, which of the following must be true:

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139611 [1], given: 12794

If x>y>0, which of the following must be true: [#permalink]

### Show Tags

11 Feb 2015, 05:40
1
KUDOS
Expert's post
7
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

78% (00:43) correct 22% (00:56) wrong based on 592 sessions

### HideShow timer Statistics

If x>y>0, which of the following must be true:

I. x^2>y^2
II. x^3 > y^3
III. |x|>y

A. I only
B. II only
C. III only
D. II and III
E. I, II and III

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

Kudos [?]: 139611 [1], given: 12794

Manager
Joined: 04 Oct 2013
Posts: 176

Kudos [?]: 169 [0], given: 29

GMAT 1: 590 Q40 V30
GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)
Re: If x>y>0, which of the following must be true: [#permalink]

### Show Tags

11 Feb 2015, 06:21
Bunuel wrote:
If x>y>0, which of the following must be true:

I. x^2>y^2
II. x^3 > y^3
III. |x|>y

A. I only
B. II only
C. III only
D. II and III
E. I, II and III

I would go wih E here

I. the issue is to check whether proper fractions can disprove this statement. Pick y=0,1 and pick x=0,101 $$x^2$$ is going to be greater than $$y^2$$ try with x= √0,6 and y= √0,5 $$x^2$$ is greater than $$y^2$$.

II. We don't have to worry about even/odd powers since our values are greater than zero. Thus our considerations on I. hold on II.

III. We don't have to worry about the modulus. |x| is x when x>0 this is our case. x>y thus |x| is greater than y.

_________________

learn the rules of the game, then play better than anyone else.

Kudos [?]: 169 [0], given: 29

Manager
Joined: 24 Jun 2014
Posts: 52

Kudos [?]: 25 [1], given: 97

Concentration: Social Entrepreneurship, Nonprofit
Re: If x>y>0, which of the following must be true: [#permalink]

### Show Tags

12 Feb 2015, 00:19
1
KUDOS
Assuming x and y to be integers
X=3,Y=2
X^2=3^2=9
Y^2=2^2=4
So I is true

Now lets look at option III because if option 3 is true E is the answer or else A
As per question X>Y>0 Hence |X| >Y

So OA=E

Kudos [?]: 25 [1], given: 97

Manager
Joined: 14 Jul 2014
Posts: 97

Kudos [?]: 34 [1], given: 49

Re: If x>y>0, which of the following must be true: [#permalink]

### Show Tags

12 Feb 2015, 21:27
1
KUDOS
Ans - E

Since given both X & Y are +ve,

Stmnt 1 - Quickly plugged in decimals ( x = 0.2, y = 0.1) and (x = 1.2 and y = 1.1) and integers

Stmnt 2 - No need for any computation
Infact , irrespective of the sign , whenever given that X > Y, any odd power will always hold true
i.e. x^3 > y^3, x^5 > y^5, x^7 > y^7,
x^1/3 > y^1/3 (cube root)...etc

Stmnt 3 - No need for any computation - Modulas does not matter as the constraint in the Q is that both X & Y are +ve

Kudos [?]: 34 [1], given: 49

Intern
Joined: 22 Aug 2014
Posts: 42

Kudos [?]: 24 [1], given: 6

Re: If x>y>0, which of the following must be true: [#permalink]

### Show Tags

12 Feb 2015, 21:54
1
KUDOS
When two positive integers x & y are compared by the given condition x>y, then the only case when y>x will be when the power is -ve. So it satisfies all the options i, ii & iii.

Therefore option e

Kudos [?]: 24 [1], given: 6

Math Expert
Joined: 02 Sep 2009
Posts: 43334

Kudos [?]: 139611 [0], given: 12794

Re: If x>y>0, which of the following must be true: [#permalink]

### Show Tags

16 Feb 2015, 05:00
Expert's post
3
This post was
BOOKMARKED
Bunuel wrote:
If x>y>0, which of the following must be true:

I. x^2>y^2
II. x^3 > y^3
III. |x|>y

A. I only
B. II only
C. III only
D. II and III
E. I, II and III

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

Solution: E.

The "trick" here is that you are apt to expect a trick. Clearly all three statements hold for integers (if x = 2 and y = 1, then x^2 = 4 and y^2 = 1, and x^3 = 8 and y^3 = 1). But you may expect for fractions to be different - if you square, say, 1/2, then it gets smaller (1/4). But, still, the larger fraction will remain larger when squared or cubed. Take for example 1/2 and 1/3 each squared. 1/2 --> 1/4, and 1/3 --> 1/9. The smaller fraction becomes even smaller. Statement III is true simply by definition - the absolute value of a positive number is just that number.
_________________

Kudos [?]: 139611 [0], given: 12794

Manager
Joined: 03 Dec 2014
Posts: 120

Kudos [?]: 62 [1], given: 391

Location: India
GMAT 1: 620 Q48 V27
GPA: 1.9
WE: Engineering (Energy and Utilities)
Re: If x>y>0, which of the following must be true: [#permalink]

### Show Tags

05 Dec 2015, 21:10
1
KUDOS
Bunuel wrote:
Bunuel wrote:
If x>y>0, which of the following must be true:

I. x^2>y^2
II. x^3 > y^3
III. |x|>y

A. I only
B. II only
C. III only
D. II and III
E. I, II and III

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

Solution: E.

The "trick" here is that you are apt to expect a trick. Clearly all three statements hold for integers (if x = 2 and y = 1, then x^2 = 4 and y^2 = 1, and x^3 = 8 and y^3 = 1). But you may expect for fractions to be different - if you square, say, 1/2, then it gets smaller (1/4). But, still, the larger fraction will remain larger when squared or cubed. Take for example 1/2 and 1/3 each squared. 1/2 --> 1/4, and 1/3 --> 1/9. The smaller fraction becomes even smaller. Statement III is true simply by definition - the absolute value of a positive number is just that number.

if I consider X= 1/3 and y=1/2 , then, X square is not greater that y Square. and same is true for cube power. In my view only o'ption three holds must be true. please clarify. thanks in advance.

Kudos [?]: 62 [1], given: 391

Current Student
Joined: 20 Mar 2014
Posts: 2685

Kudos [?]: 1848 [0], given: 800

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If x>y>0, which of the following must be true: [#permalink]

### Show Tags

05 Dec 2015, 21:16
robu wrote:
if I consider X= 1/3 and y=1/2 , then, X square is not greater that y Square. and same is true for cube power. In my view only o'ption three holds must be true. please clarify. thanks in advance.

You can not consider x=1/3 and y=1/2 as this will make y>x but per the given condition x>y

Hope this helps.

Kudos [?]: 1848 [0], given: 800

Senior Manager
Joined: 17 Jun 2015
Posts: 259

Kudos [?]: 45 [0], given: 165

GMAT 1: 540 Q39 V26
GMAT 2: 680 Q46 V37
Re: If x>y>0, which of the following must be true: [#permalink]

### Show Tags

28 Dec 2015, 12:28
Plug values

For any two numbers x and y such that x>y>0 the squares and cubes are also in the same inequality. However, x^2 is smaller than x in case of 0<x<1; so is the cube.

Also |x| = x for x>0 or -x for x <0. Given that x>0, this too is positive and so is the result.

Hence all options are true.
E
_________________

Fais de ta vie un rêve et d'un rêve une réalité

Kudos [?]: 45 [0], given: 165

Retired Moderator
Joined: 12 Aug 2015
Posts: 2340

Kudos [?]: 1000 [0], given: 682

GRE 1: 323 Q169 V154
Re: If x>y>0, which of the following must be true: [#permalink]

### Show Tags

10 Mar 2016, 10:04
We just need to remember here that if x and y are both greater than zero => and x>y => x^n>y^n is true
_________________

Give me a hell yeah ...!!!!!

Kudos [?]: 1000 [0], given: 682

Retired Moderator
Status: I Declare War!!!
Joined: 02 Apr 2014
Posts: 255

Kudos [?]: 98 [0], given: 546

Location: United States
Concentration: Finance, Economics
GMAT Date: 03-18-2015
WE: Asset Management (Investment Banking)
Re: If x>y>0, which of the following must be true: [#permalink]

### Show Tags

17 Jul 2016, 13:52
Bunuel wrote:
Bunuel wrote:
If x>y>0, which of the following must be true:

I. x^2>y^2
II. x^3 > y^3
III. |x|>y

A. I only
B. II only
C. III only
D. II and III
E. I, II and III

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

Solution: E.

The "trick" here is that you are apt to expect a trick. Clearly all three statements hold for integers (if x = 2 and y = 1, then x^2 = 4 and y^2 = 1, and x^3 = 8 and y^3 = 1). But you may expect for fractions to be different - if you square, say, 1/2, then it gets smaller (1/4). But, still, the larger fraction will remain larger when squared or cubed. Take for example 1/2 and 1/3 each squared. 1/2 --> 1/4, and 1/3 --> 1/9. The smaller fraction becomes even smaller. Statement III is true simply by definition - the absolute value of a positive number is just that number.

plz correct me if i am wrong, it means this is good for integers as well as for fractions too.. (provided positive)
thanks

Kudos [?]: 98 [0], given: 546

Non-Human User
Joined: 09 Sep 2013
Posts: 14211

Kudos [?]: 291 [0], given: 0

Re: If x>y>0, which of the following must be true: [#permalink]

### Show Tags

01 Jan 2018, 05:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Kudos [?]: 291 [0], given: 0

Re: If x>y>0, which of the following must be true:   [#permalink] 01 Jan 2018, 05:05
Display posts from previous: Sort by