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

 It is currently 19 Nov 2019, 05:21

### 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

# If x and y are non-zero numbers and the value of (y)10x5 is -1, which

Author Message
TAGS:

### Hide Tags

Manager
Joined: 14 Sep 2015
Posts: 64
Location: India
GMAT 1: 700 Q45 V40
GPA: 3.41
If x and y are non-zero numbers and the value of (y)10x5 is -1, which  [#permalink]

### Show Tags

Updated on: 29 May 2017, 12:21
4
33
00:00

Difficulty:

95% (hard)

Question Stats:

31% (02:17) correct 69% (02:31) wrong based on 388 sessions

### HideShow timer Statistics

If x and y are non-zero numbers and the value of $$\frac{(\sqrt{y})^{10}}{x^5}$$ is -1, which of the following expressions must be true?

I. |y-1| > |x-1|

II. y|y| > x|x|

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

A. I only
B. II only
C. III only
D. I, II and III
E. None of I, II and III

Originally posted by niteshwaghray on 29 May 2017, 10:28.
Last edited by Bunuel on 29 May 2017, 12:21, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 59147
Re: If x and y are non-zero numbers and the value of (y)10x5 is -1, which  [#permalink]

### Show Tags

29 May 2017, 12:34
4
3
niteshwaghray wrote:
If x and y are non-zero numbers and the value of $$\frac{(\sqrt{y})^{10}}{x^5}$$ is -1, which of the following expressions must be true?

I. |y-1| > |x-1|

II. y|y| > x|x|

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

A. I only
B. II only
C. III only
D. I, II and III
E. None of I, II and III

First of all notice for $$\sqrt{y}$$ to be defined y must be positive (the square root from a negative number is not defined for the GMAT + we are told that y is non-zero therefore y is positive).

$$\frac{(\sqrt{y})^{10}}{x^5}=-1$$;

$$\frac{y^5}{x^5}=-1$$;

$$\frac{y}{x}=-1$$;

$$y = -x$$.

Since y is positive the x is negative.

I. |y-1| > |x-1|. If y = 1 and x = -1, this won't be true. Discard.

II. y|y| > x|x|

y*y > (-y)|-y|

y^2 > -y^2.

y^2 + y^2 > 0.

Since y is non-zero, then this must be true,

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

$$\sqrt{−y|-y|}=\sqrt{−(-y)y}$$

$$\sqrt{−y^2}=\sqrt{y^2}$$

-y^2 will be negative, so the left hand side won't be defined. Thus, this also cannot be true.

P.S. Also, not very nice question.
_________________
##### General Discussion
Intern
Joined: 28 Sep 2016
Posts: 18
Re: If x and y are non-zero numbers and the value of (y)10x5 is -1, which  [#permalink]

### Show Tags

01 Jun 2017, 01:20
1
Bunuel wrote:
niteshwaghray wrote:
If x and y are non-zero numbers and the value of $$\frac{(\sqrt{y})^{10}}{x^5}$$ is -1, which of the following expressions must be true?

I. |y-1| > |x-1|

II. y|y| > x|x|

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

A. I only
B. II only
C. III only
D. I, II and III
E. None of I, II and III

First of all notice for $$\sqrt{y}$$ to be defined y must be positive (the square root from a negative number is not defined for the GMAT + we are told that y is non-zero therefore y is positive).

$$\frac{(\sqrt{y})^{10}}{x^5}=-1$$;

$$\frac{y^5}{x^5}=-1$$;

$$\frac{y}{x}=-1$$;

$$y = -x$$.

Since y is positive the x is negative.

I. |y-1| > |x-1|. If y = 1 and x = -1, this won't be true. Discard.

II. y|y| > x|x|

y*y > (-y)|-y|

y^2 > -y^2.

y^2 + y^2 > 0.

Since y is non-zero, then this must be true,

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

$$\sqrt{−y|-y|}=\sqrt{−(-y)y}$$

$$\sqrt{−y^2}=\sqrt{y^2}$$

-y^2 will be negative, so the left hand side won't be defined. Thus, this also cannot be true.

P.S. Also, not very nice question.

Thanks Bunuel for the Solution.

But How did you do this

$$\frac{y^5}{x^5}=-1$$;

$$\frac{y}{x}=-1$$;

To cancel the powers the bases should be equal?
Math Expert
Joined: 02 Sep 2009
Posts: 59147
Re: If x and y are non-zero numbers and the value of (y)10x5 is -1, which  [#permalink]

### Show Tags

01 Jun 2017, 01:43
1
joepc wrote:
Bunuel wrote:
niteshwaghray wrote:
If x and y are non-zero numbers and the value of $$\frac{(\sqrt{y})^{10}}{x^5}$$ is -1, which of the following expressions must be true?

I. |y-1| > |x-1|

II. y|y| > x|x|

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

A. I only
B. II only
C. III only
D. I, II and III
E. None of I, II and III

First of all notice for $$\sqrt{y}$$ to be defined y must be positive (the square root from a negative number is not defined for the GMAT + we are told that y is non-zero therefore y is positive).

$$\frac{(\sqrt{y})^{10}}{x^5}=-1$$;

$$\frac{y^5}{x^5}=-1$$;

$$\frac{y}{x}=-1$$;

$$y = -x$$.

Since y is positive the x is negative.

I. |y-1| > |x-1|. If y = 1 and x = -1, this won't be true. Discard.

II. y|y| > x|x|

y*y > (-y)|-y|

y^2 > -y^2.

y^2 + y^2 > 0.

Since y is non-zero, then this must be true,

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

$$\sqrt{−y|-y|}=\sqrt{−(-y)y}$$

$$\sqrt{−y^2}=\sqrt{y^2}$$

-y^2 will be negative, so the left hand side won't be defined. Thus, this also cannot be true.

P.S. Also, not very nice question.

Thanks Bunuel for the Solution.

But How did you do this

$$\frac{y^5}{x^5}=-1$$;

$$\frac{y}{x}=-1$$;

To cancel the powers the bases should be equal?

$$(\frac{y}{x})^5=-1$$;

Take the fifths root from both sides: $$\frac{y}{x}=\sqrt[5]{(-1)}=-1$$.

Hope it's clear.
_________________
SVP
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1701
Location: India
GPA: 3.01
WE: Engineering (Real Estate)
Re: If x and y are non-zero numbers and the value of (y)10x5 is -1, which  [#permalink]

### Show Tags

01 Jun 2017, 03:11
Bunuel wrote:
niteshwaghray wrote:
If x and y are non-zero numbers and the value of $$\frac{(\sqrt{y})^{10}}{x^5}$$ is -1, which of the following expressions must be true?

I. |y-1| > |x-1|

II. y|y| > x|x|

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

A. I only
B. II only
C. III only
D. I, II and III
E. None of I, II and III

First of all notice for $$\sqrt{y}$$ to be defined y must be positive (the square root from a negative number is not defined for the GMAT + we are told that y is non-zero therefore y is positive).

$$\frac{(\sqrt{y})^{10}}{x^5}=-1$$;

$$\frac{y^5}{x^5}=-1$$;

$$\frac{y}{x}=-1$$;

$$y = -x$$.

Since y is positive the x is negative.

I. |y-1| > |x-1|. If y = 1 and x = -1, this won't be true. Discard.

II. y|y| > x|x|

y*y > (-y)|-y|

y^2 > -y^2.

y^2 + y^2 > 0.

Since y is non-zero, then this must be true,

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

$$\sqrt{−y|-y|}=\sqrt{−(-y)y}$$

$$\sqrt{−y^2}=\sqrt{y^2}$$

-y^2 will be negative, so the left hand side won't be defined. Thus, this also cannot be true.

P.S. Also, not very nice question.

Bunuel, Is it too tough or is it not a GMAT type question?
_________________
"Do not watch clock; Do what it does. KEEP GOING."
Math Expert
Joined: 02 Sep 2009
Posts: 59147
Re: If x and y are non-zero numbers and the value of (y)10x5 is -1, which  [#permalink]

### Show Tags

01 Jun 2017, 06:32
understandZERO wrote:
Bunuel wrote:
niteshwaghray wrote:
If x and y are non-zero numbers and the value of $$\frac{(\sqrt{y})^{10}}{x^5}$$ is -1, which of the following expressions must be true?

I. |y-1| > |x-1|

II. y|y| > x|x|

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

A. I only
B. II only
C. III only
D. I, II and III
E. None of I, II and III

First of all notice for $$\sqrt{y}$$ to be defined y must be positive (the square root from a negative number is not defined for the GMAT + we are told that y is non-zero therefore y is positive).

$$\frac{(\sqrt{y})^{10}}{x^5}=-1$$;

$$\frac{y^5}{x^5}=-1$$;

$$\frac{y}{x}=-1$$;

$$y = -x$$.

Since y is positive the x is negative.

I. |y-1| > |x-1|. If y = 1 and x = -1, this won't be true. Discard.

II. y|y| > x|x|

y*y > (-y)|-y|

y^2 > -y^2.

y^2 + y^2 > 0.

Since y is non-zero, then this must be true,

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

$$\sqrt{−y|-y|}=\sqrt{−(-y)y}$$

$$\sqrt{−y^2}=\sqrt{y^2}$$

-y^2 will be negative, so the left hand side won't be defined. Thus, this also cannot be true.

P.S. Also, not very nice question.

Bunuel, Is it too tough or is it not a GMAT type question?

Not that tough but I don't like III option. It gives undefined value for LHS, don't remember seeing such thing in official questions.
_________________
Current Student
Status: Preparing for GMAT!!
Joined: 11 Oct 2015
Posts: 126
Location: India
GMAT 1: 660 Q47 V34
GMAT 2: 700 Q48 V38
GPA: 3.1
WE: General Management (Entertainment and Sports)

### Show Tags

02 Jun 2017, 23:37
Bunuel

Can we say that, for a negative number, ODD ROOT is defined but EVEN ROOT isn't.

5THROOT(-1)=-1
SQRT(-Y^2)=NOT DEFINED.

Thank you.

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 59147
Re: If x and y are non-zero numbers and the value of (y)10x5 is -1, which  [#permalink]

### Show Tags

03 Jun 2017, 17:49
Sirakri wrote:
Bunuel

Can we say that, for a negative number, ODD ROOT is defined but EVEN ROOT isn't.

5THROOT(-1)=-1
SQRT(-Y^2)=NOT DEFINED.

Thank you.

Posted from my mobile device

Yes.

When the GMAT provides the square root sign for an even root, such as $$\sqrt{x}$$ or $$\sqrt[4]{x}$$, then the only accepted answer is the positive root. That is, $$\sqrt{16}=4$$, NOT +4 or -4. Even roots have only a positive value on the GMAT.

$$\sqrt{negative}=undefined$$

In contrast, the equation $$x^2=16$$ has TWO solutions, +4 and -4.

Odd roots have the same sign as the base of the root. For example, $$\sqrt[3]{125} =5$$ and $$\sqrt[3]{-64} =-4$$.
_________________
Manager
Joined: 05 Dec 2015
Posts: 99
Re: If x and y are non-zero numbers and the value of (y)10x5 is -1, which  [#permalink]

### Show Tags

12 Jun 2017, 21:57
for II doesn't y=-1 and x=1 work and thus it must not be true? becomes -1>1 which is not correct, or am i missing something easy?

Bunuel wrote:
niteshwaghray wrote:
If x and y are non-zero numbers and the value of $$\frac{(\sqrt{y})^{10}}{x^5}$$ is -1, which of the following expressions must be true?

I. |y-1| > |x-1|

II. y|y| > x|x|

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

A. I only
B. II only
C. III only
D. I, II and III
E. None of I, II and III

First of all notice for $$\sqrt{y}$$ to be defined y must be positive (the square root from a negative number is not defined for the GMAT + we are told that y is non-zero therefore y is positive).

$$\frac{(\sqrt{y})^{10}}{x^5}=-1$$;

$$\frac{y^5}{x^5}=-1$$;

$$\frac{y}{x}=-1$$;

$$y = -x$$.

Since y is positive the x is negative.

I. |y-1| > |x-1|. If y = 1 and x = -1, this won't be true. Discard.

II. y|y| > x|x|

y*y > (-y)|-y|

y^2 > -y^2.

y^2 + y^2 > 0.

Since y is non-zero, then this must be true,

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

$$\sqrt{−y|-y|}=\sqrt{−(-y)y}$$

$$\sqrt{−y^2}=\sqrt{y^2}$$

-y^2 will be negative, so the left hand side won't be defined. Thus, this also cannot be true.

P.S. Also, not very nice question.
Math Expert
Joined: 02 Sep 2009
Posts: 59147
Re: If x and y are non-zero numbers and the value of (y)10x5 is -1, which  [#permalink]

### Show Tags

12 Jun 2017, 22:23
1
mdacosta wrote:
for II doesn't y=-1 and x=1 work and thus it must not be true? becomes -1>1 which is not correct, or am i missing something easy?

Bunuel wrote:
niteshwaghray wrote:
If x and y are non-zero numbers and the value of $$\frac{(\sqrt{y})^{10}}{x^5}$$ is -1, which of the following expressions must be true?

I. |y-1| > |x-1|

II. y|y| > x|x|

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

A. I only
B. II only
C. III only
D. I, II and III
E. None of I, II and III

First of all notice for $$\sqrt{y}$$ to be defined y must be positive (the square root from a negative number is not defined for the GMAT + we are told that y is non-zero therefore y is positive).

$$\frac{(\sqrt{y})^{10}}{x^5}=-1$$;

$$\frac{y^5}{x^5}=-1$$;

$$\frac{y}{x}=-1$$;

$$y = -x$$.

Since y is positive the x is negative.

I. |y-1| > |x-1|. If y = 1 and x = -1, this won't be true. Discard.

II. y|y| > x|x|

y*y > (-y)|-y|

y^2 > -y^2.

y^2 + y^2 > 0.

Since y is non-zero, then this must be true,

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

$$\sqrt{−y|-y|}=\sqrt{−(-y)y}$$

$$\sqrt{−y^2}=\sqrt{y^2}$$

-y^2 will be negative, so the left hand side won't be defined. Thus, this also cannot be true.

P.S. Also, not very nice question.

_________________
Intern
Joined: 11 Aug 2013
Posts: 24
Location: India
Concentration: Finance, General Management
GMAT 1: 620 Q47 V28
GPA: 3.23
WE: Information Technology (Investment Banking)
Re: If x and y are non-zero numbers and the value of (y)10x5 is -1, which  [#permalink]

### Show Tags

13 Jun 2017, 16:24
Before we start point to remember is root of negative number is not defined. ---(a)
Now Numerator(N) is (root y)^10 and denominator(D) is x^5.
since N/D =-1 and N has root y ,Therefore root y is positive (from (a)) =>(root y )^10 is +ve =>y^5 is +ve ---(b)
Since N>0 ,therefore D will be <0 and D=-N =>x^5<0 =>x<0 ---(C)
also from (b) and (c) |X|=|Y| ---(d)

now lets check the options
1> |y-1|>|x-1| ; from (d) we know|x|=|y| and from (c) we know x<0 => |y-1|<|x-1| (substitute some random values for x and y and verify for better understanding) .... NOT POSSIBLE
2>y|y| > x|x| ; again from (c) and (d)
since y>x and |y|=|x| therefore y|y|> 0 and x|x| <0 hence this is correct OPTION

Looking into the options.
We have only one option (B) where we do not have 1 but have 2. Hence it will be only (B) no need to verify option 3
_________________
Thanks
----------------
Click +1 Kudos if my post helped...
Current Student
Joined: 22 Sep 2016
Posts: 156
Location: India
GMAT 1: 710 Q50 V35
GPA: 4
Re: If x and y are non-zero numbers and the value of (y)10x5 is -1, which  [#permalink]

### Show Tags

12 Jul 2017, 18:05
Bunuel wrote:
niteshwaghray wrote:
If x and y are non-zero numbers and the value of $$\frac{(\sqrt{y})^{10}}{x^5}$$ is -1, which of the following expressions must be true?

I. |y-1| > |x-1|

II. y|y| > x|x|

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

A. I only
B. II only
C. III only
D. I, II and III
E. None of I, II and III

First of all notice for $$\sqrt{y}$$ to be defined y must be positive (the square root from a negative number is not defined for the GMAT + we are told that y is non-zero therefore y is positive).

$$\frac{(\sqrt{y})^{10}}{x^5}=-1$$;

$$\frac{y^5}{x^5}=-1$$;

$$\frac{y}{x}=-1$$;

$$y = -x$$.

Since y is positive the x is negative.

I. |y-1| > |x-1|. If y = 1 and x = -1, this won't be true. Discard.

II. y|y| > x|x|

y*y > (-y)|-y|

y^2 > -y^2.

y^2 + y^2 > 0.

Since y is non-zero, then this must be true,

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

$$\sqrt{−y|-y|}=\sqrt{−(-y)y}$$

$$\sqrt{−y^2}=\sqrt{y^2}$$

-y^2 will be negative, so the left hand side won't be defined. Thus, this also cannot be true.

P.S. Also, not very nice question.

I'm confused.

(-5)^2 =25
So what if y = 25? Then, the root of y can be either 5 or -5.
Correct me if I'm wrong.
_________________
Desperately need 'KUDOS' !!
Intern
Joined: 25 Jul 2018
Posts: 2
Re: If x and y are non-zero numbers and the value of (y)10x5 is -1, which  [#permalink]

### Show Tags

12 Aug 2018, 07:41
Bunuel wrote:
niteshwaghray wrote:
If x and y are non-zero numbers and the value of $$\frac{(\sqrt{y})^{10}}{x^5}$$ is -1, which of the following expressions must be true?

I. |y-1| > |x-1|

II. y|y| > x|x|

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

A. I only
B. II only
C. III only
D. I, II and III
E. None of I, II and III

First of all notice for $$\sqrt{y}$$ to be defined y must be positive (the square root from a negative number is not defined for the GMAT + we are told that y is non-zero therefore y is positive).

$$\frac{(\sqrt{y})^{10}}{x^5}=-1$$;

$$\frac{y^5}{x^5}=-1$$;

$$\frac{y}{x}=-1$$;

$$y = -x$$.

Since y is positive the x is negative.

I. |y-1| > |x-1|. If y = 1 and x = -1, this won't be true. Discard.

II. y|y| > x|x|

y*y > (-y)|-y|

y^2 > -y^2.

y^2 + y^2 > 0.

Since y is non-zero, then this must be true,

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

$$\sqrt{−y|-y|}=\sqrt{−(-y)y}$$

$$\sqrt{−y^2}=\sqrt{y^2}$$

-y^2 will be negative, so the left hand side won't be defined. Thus, this also cannot be true.

P.S. Also, not very nice question.
SVP
Joined: 03 Jun 2019
Posts: 1849
Location: India
Re: If x and y are non-zero numbers and the value of (y)10x5 is -1, which  [#permalink]

### Show Tags

12 Oct 2019, 11:56
niteshwaghray wrote:
If x and y are non-zero numbers and the value of $$\frac{(\sqrt{y})^{10}}{x^5}$$ is -1, which of the following expressions must be true?

I. |y-1| > |x-1|

II. y|y| > x|x|

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

A. I only
B. II only
C. III only
D. I, II and III
E. None of I, II and III

Asked: If x and y are non-zero numbers and the value of $$\frac{(\sqrt{y})^{10}}{x^5}$$ is -1, which of the following expressions must be true?

I. |y-1| > |x-1|
When y=1; x=-1; NOT TRUE

II. y|y| > x|x|
y>0; x=-y;
y|y|>(-y)|-y|
y^2>-y^2
MUST BE TRUE

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$
-y|x|<0
NOT TRUE

IMO B

Posted from my mobile device
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts."

Please provide kudos if you like my post. Kudos encourage active discussions.

My GMAT Resources: -

Efficient Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
Manager
Joined: 04 Jun 2010
Posts: 87
Location: India
GMAT 1: 660 Q49 V31
GPA: 3.22
Re: If x and y are non-zero numbers and the value of (y)10x5 is -1, which  [#permalink]

### Show Tags

14 Oct 2019, 02:29
Bunuel wrote:
niteshwaghray wrote:
If x and y are non-zero numbers and the value of $$\frac{(\sqrt{y})^{10}}{x^5}$$ is -1, which of the following expressions must be true?

I. |y-1| > |x-1|

II. y|y| > x|x|

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

A. I only
B. II only
C. III only
D. I, II and III
E. None of I, II and III

First of all notice for $$\sqrt{y}$$ to be defined y must be positive (the square root from a negative number is not defined for the GMAT + we are told that y is non-zero therefore y is positive).

$$\frac{(\sqrt{y})^{10}}{x^5}=-1$$;

$$\frac{y^5}{x^5}=-1$$;

$$\frac{y}{x}=-1$$;

$$y = -x$$.

Since y is positive the x is negative.

I. |y-1| > |x-1|. If y = 1 and x = -1, this won't be true. Discard.

II. y|y| > x|x|

y*y > (-y)|-y|

y^2 > -y^2.

y^2 + y^2 > 0.

Since y is non-zero, then this must be true,

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

$$\sqrt{−y|-y|}=\sqrt{−(-y)y}$$

$$\sqrt{−y^2}=\sqrt{y^2}$$

-y^2 will be negative, so the left hand side won't be defined. Thus, this also cannot be true.

P.S. Also, not very nice question.

Dear Sir,

thank You for the elegant solution......

However, would you please clear my doubt...

Condition is x and y are non-zero numbers .... so for statement II......I AM FREE TO CHOOSE Y=(-1)................for which , it does not hold ......
Math Expert
Joined: 02 Sep 2009
Posts: 59147
Re: If x and y are non-zero numbers and the value of (y)10x5 is -1, which  [#permalink]

### Show Tags

14 Oct 2019, 02:37
1
avikroy wrote:
Bunuel wrote:
niteshwaghray wrote:
If x and y are non-zero numbers and the value of $$\frac{(\sqrt{y})^{10}}{x^5}$$ is -1, which of the following expressions must be true?

I. |y-1| > |x-1|

II. y|y| > x|x|

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

A. I only
B. II only
C. III only
D. I, II and III
E. None of I, II and III

First of all notice for $$\sqrt{y}$$ to be defined y must be positive (the square root from a negative number is not defined for the GMAT + we are told that y is non-zero therefore y is positive).

$$\frac{(\sqrt{y})^{10}}{x^5}=-1$$;

$$\frac{y^5}{x^5}=-1$$;

$$\frac{y}{x}=-1$$;

$$y = -x$$.

Since y is positive the x is negative.

I. |y-1| > |x-1|. If y = 1 and x = -1, this won't be true. Discard.

II. y|y| > x|x|

y*y > (-y)|-y|

y^2 > -y^2.

y^2 + y^2 > 0.

Since y is non-zero, then this must be true,

III. $$\sqrt{−y|x|}=\sqrt{−xy}$$

$$\sqrt{−y|-y|}=\sqrt{−(-y)y}$$

$$\sqrt{−y^2}=\sqrt{y^2}$$

-y^2 will be negative, so the left hand side won't be defined. Thus, this also cannot be true.

P.S. Also, not very nice question.

Dear Sir,

thank You for the elegant solution......

However, would you please clear my doubt...

Condition is x and y are non-zero numbers .... so for statement II......I AM FREE TO CHOOSE Y=(-1)................for which , it does not hold ......

y cannot be -1, because even roots (such as the square root) of negative numbers are not defined on the GMAT so if y = -1, then $$\sqrt{y}=\sqrt{-1}=undefined$$, and $$\frac{(\sqrt{y})^{10}}{x^5}$$ will not equal to -1, as we are given in the stem.
_________________
Re: If x and y are non-zero numbers and the value of (y)10x5 is -1, which   [#permalink] 14 Oct 2019, 02:37
Display posts from previous: Sort by