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

 It is currently 14 Oct 2019, 06:09

### 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

# Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4

Author Message
TAGS:

### Hide Tags

VP
Joined: 23 Feb 2015
Posts: 1253
Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4  [#permalink]

### Show Tags

Updated on: 26 Mar 2019, 03:59
3
00:00

Difficulty:

95% (hard)

Question Stats:

37% (01:59) correct 63% (02:04) wrong based on 54 sessions

### HideShow timer Statistics

Is $$\frac{|x|}{|y|} < |x|*|y|$$?

(1) $$x^3>y^3$$

(2) $$y^5>y^4$$

_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”

Do you need official questions for Quant?
3700 Unique Official GMAT Quant Questions
------
SEARCH FOR ALL TAGS
GMAT Club Tests

Originally posted by Asad on 11 Mar 2019, 08:28.
Last edited by Bunuel on 26 Mar 2019, 03:59, edited 1 time in total.
Edited the OA.
Retired Moderator
Joined: 27 Oct 2017
Posts: 1256
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4  [#permalink]

### Show Tags

11 Mar 2019, 09:26
2
1
Is |x|/ |y| < |x|*|y| ?
Squaring both sides and cross multiplying, we get
or, x^2 < x^2 *y^4
or, x^2 (1-y^4)<0

This would be true if x is not equal to 0, and y >1 or y <-1
So, the question reduces to " Is x is not equal to 0, and y >1 or y <-1" ?

Statement 1: x^3 > y^3
Here x can be zero, and y any negative number. for which the answer can be NO
(x,y) can be (2,3), Answer is YES

NOT SUFFICIENT

Statement 2:
y^5 > y^4
or y^4(y-1) >0

here y >1, but x can be zero or non zero.
if y >1, x =0 , answer is NO
if y >1, x is non zero, ans is YES

NOT SUFFICIENT

Combing Both statements , we get y >1
and x^3 > y^3 , Hence x is NON zero,

So, We have y >1 ans X is NON ZERO.

Hence SUFFICIENT.

Is $$\frac{|x|}{|y|} < |x|*|y|$$?

(1) $$x^3>y^3$$

(2) $$y^5>y^4$$

_________________
##### General Discussion
Manager
Joined: 07 Oct 2018
Posts: 57
Re: Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4  [#permalink]

### Show Tags

11 Mar 2019, 10:05
If i wanted to solve this question with the help of numbers how can I solve it? Can anyone help me?
Manager
Joined: 11 Feb 2013
Posts: 149
GMAT 1: 490 Q44 V15
GMAT 2: 690 Q47 V38
GPA: 3.05
WE: Analyst (Commercial Banking)
Re: Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4  [#permalink]

### Show Tags

11 Mar 2019, 12:32
1
I would go for C.

Statement 1: insufficient
Case 1: X=0 & y=-1 (thus, both sides are equal in main question. So, NO to main question)

Case 2: x=2 & y=3 (yes to main question)

Statement 2: insufficient
Case 1: X=0 & y=2 (thus, both sides are equal in main question. So, NO to main question)

Case 2: x=2 & y=3 (yes to main question)

Combining
From statement 2, it is clear that y is positive and greater than 1.
So in statement 1, x must be positive.

In such situation, multiplication of same direction two number is greater than division of same numbers.

I.e. x=3 & y=2

Posted from my mobile device
Intern
Joined: 24 Mar 2019
Posts: 5
Location: United Kingdom
GMAT 1: 730 Q47 V42
Re: Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4  [#permalink]

### Show Tags

Updated on: 26 Mar 2019, 03:33
Can people make sure that their answers are correct when posting questions? Makes it a lot harder to study when you are trying to work out whether the answer is actually the answer or not

Originally posted by strawberryjelly on 25 Mar 2019, 14:38.
Last edited by strawberryjelly on 26 Mar 2019, 03:33, edited 1 time in total.
VP
Joined: 23 Feb 2015
Posts: 1253
Re: Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4  [#permalink]

### Show Tags

26 Mar 2019, 02:57
Is $$\frac{|x|}{|y|} < |x|×|y|$$?

(1) $$x^3>y^3$$

(2) $$y^5>y^4$$

Hi Bunuel and IanStewart,
Can I rearrange the question stem in the following way?
$$\frac{|x|}{|y|} < |x|×|y|$$?
==> $$\frac{x^2}{y^2}<x^2 × y^2?$$
==> $$x^2<x^2 × y^4$$? [dividing by $$x^2$$ in both side as $$x^2$$ is positive]
==> $$y^4>1?$$
_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”

Do you need official questions for Quant?
3700 Unique Official GMAT Quant Questions
------
SEARCH FOR ALL TAGS
GMAT Club Tests
Math Expert
Joined: 02 Sep 2009
Posts: 58312
Re: Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4  [#permalink]

### Show Tags

26 Mar 2019, 03:14
Is $$\frac{|x|}{|y|} < |x|×|y|$$?

(1) $$x^3>y^3$$

(2) $$y^5>y^4$$

Hi Bunuel and IanStewart,
Can I rearrange the question stem in the following way?
$$\frac{|x|}{|y|} < |x|×|y|$$?
==> $$\frac{x^2}{y^2}<x^2 × y^2?$$
==> $$x^2<x^2 × y^4$$? [dividing by $$x^2$$ in both side as $$x^2$$ is positive]
==> $$y^4>1?$$

Yes. You could reduce by |x| directly (provided x is not 0). $$\frac{1}{|y|} < |y|$$ --> |y|^2 > 1 --> y < -1 or y > 1.

BTW, the correct answer is C, not B. (2) give y > 1. If x ≠ 0, then $$\frac{|x|}{|y|} > |x|×|y|$$ (answer YES) but if x = 0, then $$\frac{|x|}{|y|} = |x|×|y|$$ (answer NO).

What is the source of the question?
_________________
VP
Joined: 23 Feb 2015
Posts: 1253
Re: Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4  [#permalink]

### Show Tags

26 Mar 2019, 03:54
Bunuel wrote:
Is $$\frac{|x|}{|y|} < |x|×|y|$$?

(1) $$x^3>y^3$$

(2) $$y^5>y^4$$

Hi Bunuel and IanStewart,
Can I rearrange the question stem in the following way?
$$\frac{|x|}{|y|} < |x|×|y|$$?
==> $$\frac{x^2}{y^2}<x^2 × y^2?$$
==> $$x^2<x^2 × y^4$$? [dividing by $$x^2$$ in both side as $$x^2$$ is positive]
==> $$y^4>1?$$

Yes. You could reduce by |x| directly (provided x is not 0). $$\frac{1}{|y|} < |y|$$ --> |y|^2 > 1 --> y < -1 or y > 1.

BTW, the correct answer is C, not B. (2) give y > 1. If x ≠ 0, then $$\frac{|x|}{|y|} > |x|×|y|$$ (answer YES) but if x = 0, then $$\frac{|x|}{|y|} = |x|×|y|$$ (answer NO).

What is the source of the question?

Source: Wizako
In this question, if we can determine that $$y^2>1$$ then the data is sufficient.
Conversely, if we can determine that $$y^2≤1$$ then the data is also sufficient.
Isn't it?
Statement 2 says:
(2) $$y^5>y^4$$
Here, y^4 is positive, so we can divide both part by $$y^4$$. We get from statement 2:
==> $$y>1$$
==> $$y^2>1$$ [multiplying by both side]
So, why not B sufficient?
_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”

Do you need official questions for Quant?
3700 Unique Official GMAT Quant Questions
------
SEARCH FOR ALL TAGS
GMAT Club Tests
Math Expert
Joined: 02 Sep 2009
Posts: 58312
Re: Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4  [#permalink]

### Show Tags

26 Mar 2019, 03:59
1
Bunuel wrote:
Hi Bunuel and IanStewart,
Can I rearrange the question stem in the following way?
$$\frac{|x|}{|y|} < |x|×|y|$$?
==> $$\frac{x^2}{y^2}<x^2 × y^2?$$
==> $$x^2<x^2 × y^4$$? [dividing by $$x^2$$ in both side as $$x^2$$ is positive]
==> $$y^4>1?$$

Yes. You could reduce by |x| directly (provided x is not 0). $$\frac{1}{|y|} < |y|$$ --> |y|^2 > 1 --> y < -1 or y > 1.

BTW, the correct answer is C, not B. (2) give y > 1. If x ≠ 0, then $$\frac{|x|}{|y|} > |x|×|y|$$ (answer YES) but if x = 0, then $$\frac{|x|}{|y|} = |x|×|y|$$ (answer NO).

What is the source of the question?

Source: Wizako
In this question, if we can determine that $$y^2>1$$ then the data is sufficient.
Conversely, if we can determine that $$y^2≤1$$ then the data is also sufficient.
Isn't it?
Statement 2 says:
(2) $$y^5>y^4$$
Here, y^4 is positive, so we can divide both part by $$y^4$$. We get from statement 2:
==> $$y>1$$
==> $$y^2>1$$ [multiplying by both side]
So, why not B sufficient?

Because we have one more variable in the question:|x|/|y|[/fraction] < |x|*|y|. From (2) we know that y > 1 but know nothing about x. If x ≠ 0, then $$\frac{|x|}{|y|} > |x|×|y|$$ (answer YES) but if x = 0, then $$\frac{|x|}{|y|} = |x|×|y|$$ (answer NO).
_________________
VP
Joined: 23 Feb 2015
Posts: 1253
Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4  [#permalink]

### Show Tags

26 Mar 2019, 04:08
Can I rearrange the question stem in the following way?
$$\frac{|x|}{|y|} < |x|×|y|$$?
==> $$\frac{x^2}{y^2}<x^2 × y^2?$$
==> $$x^2<x^2 × y^4$$? [dividing by $$x^2$$ in both side as $$x^2$$ is positive]
==> $$y^4>1?$$

Bunuel wrote:
Because we have one more variable in the question:|x|/|y|[/fraction] < |x|*|y|. From (2) we know that y > 1 but know nothing about x. If x ≠ 0, then $$\frac{|x|}{|y|} > |x|×|y|$$ (answer YES) but if x = 0, then $$\frac{|x|}{|y|} = |x|×|y|$$ (answer NO).

But i've deduced the question stem as $$y^4>1$$ where there is no existence of x.
Thanks__
_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”

Do you need official questions for Quant?
3700 Unique Official GMAT Quant Questions
------
SEARCH FOR ALL TAGS
GMAT Club Tests
Math Expert
Joined: 02 Sep 2009
Posts: 58312
Re: Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4  [#permalink]

### Show Tags

26 Mar 2019, 04:11
1
Can I rearrange the question stem in the following way?
$$\frac{|x|}{|y|} < |x|×|y|$$?
==> $$\frac{x^2}{y^2}<x^2 × y^2?$$
==> $$x^2<x^2 × y^4$$? [dividing by $$x^2$$ in both side as $$x^2$$ is positive]
==> $$y^4>1?$$

Bunuel wrote:
Because we have one more variable in the question:|x|/|y|[/fraction] < |x|*|y|. From (2) we know that y > 1 but know nothing about x. If x ≠ 0, then $$\frac{|x|}{|y|} > |x|×|y|$$ (answer YES) but if x = 0, then $$\frac{|x|}{|y|} = |x|×|y|$$ (answer NO).

But i've deduced the question stem as $$y^4>1$$ where there is no existence of x.
Thanks__

Check my post above: You could reduce by |x| directly (provided x is not 0). If x = 0, then we cannot reduce and thus only y^5 > y^4 will not be sufficient.
_________________
VP
Joined: 23 Feb 2015
Posts: 1253
Re: Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4  [#permalink]

### Show Tags

26 Mar 2019, 04:16
Bunuel wrote:
Can I rearrange the question stem in the following way?
$$\frac{|x|}{|y|} < |x|×|y|$$?
==> $$\frac{x^2}{y^2}<x^2 × y^2?$$
==> $$x^2<x^2 × y^4$$? [dividing by $$x^2$$ in both side as $$x^2$$ is positive]
==> $$y^4>1?$$

Bunuel wrote:
Because we have one more variable in the question:|x|/|y|[/fraction] < |x|*|y|. From (2) we know that y > 1 but know nothing about x. If x ≠ 0, then $$\frac{|x|}{|y|} > |x|×|y|$$ (answer YES) but if x = 0, then $$\frac{|x|}{|y|} = |x|×|y|$$ (answer NO).

But i've deduced the question stem as $$y^4>1$$ where there is no existence of x.
Thanks__

Check my post above: You could reduce by |x| directly (provided x is not 0). If x = 0, then we cannot reduce and thus only y^5 > y^4 will not be sufficient.

Thank you so much. Better if you edit the OA.
_________________
“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.”

Do you need official questions for Quant?
3700 Unique Official GMAT Quant Questions
------
SEARCH FOR ALL TAGS
GMAT Club Tests
Senior Manager
Joined: 04 Aug 2010
Posts: 474
Schools: Dartmouth College
Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4  [#permalink]

### Show Tags

26 Mar 2019, 11:22
1
Since division by 0 is not allowed, the prompt should indicate that $$y≠0$$:

If $$y≠0$$, is $$\frac{|x|}{|y|} < |x|*|y|$$?

(1) $$x^3>y^3$$

(2) $$y^5>y^4$$

Since an absolute value cannot be negative. we can simplify the question stem by multiplying both sides by |y|:
$$\frac{|x|}{|y|}|y| < |x||y||y|$$
$$|x| < |x|y^2$$?

If $$x=0$$, the answer to the question stem is NO.
If $$x≠0$$, we can divide both sides by $$|x|$$:
$$\frac{|x|}{|x|} < \frac{|x|y^2}{|x|}$$
$$1 < y^2$$?
Here, the answer will be YES if $$y>1$$ or $$y<-1$$.

Question stem, rephrased:
Is it true that $$x≠0$$ and that $$y>1$$ or $$y<-1$$?

Statement 1:
Case 1: x=3 and y=2
Since $$x≠0$$ and $$y>1$$, the answer to the question stem is YES.
Case 2: x=2 and y=1
Since $$y=1$$, the answer to the question stem is NO.
INSUFFICIENT.

Statement 2:
Since the inequality implies that $$y≠0$$, we can safely divide both sides by $$y^4$$, which must be positive:
$$\frac{y^5}{y^4}>\frac{y^4}{y^4}$$
$$y > 1$$
No information about $$x$$.
INSUFFICIENT.

Statements combined:
$$y>1$$ implies that $$y^3>1$$.
Thus:
$$x^3 > y^3 > 1$$
$$x^3 > 1$$
$$x > 1$$
Since $$x≠0$$ and $$y>1$$, the answer to the question stem is YES.
SUFFICIENT.

.
_________________
GMAT and GRE Tutor
Over 1800 followers
GMATGuruNY@gmail.com
New York, NY
If you find one of my posts helpful, please take a moment to click on the "Kudos" icon.
Available for tutoring in NYC and long-distance.
Is |x|/|y| < |x||y|? (1) x^3 > y^3 (2) y^5 > y^4   [#permalink] 26 Mar 2019, 11:22
Display posts from previous: Sort by