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

 It is currently 22 Feb 2019, 18:48

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 February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• Free GMAT RC Webinar

February 23, 2019

February 23, 2019

07:00 AM PST

09:00 AM PST

Learn reading strategies that can help even non-voracious reader to master GMAT RC. Saturday, February 23rd at 7 AM PT
• FREE Quant Workshop by e-GMAT!

February 24, 2019

February 24, 2019

07:00 AM PST

09:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.

If X*Y ≠ 0 and X^3*Y = X*Y^3, then which of the following must be true

Author Message
TAGS:

Hide Tags

Director
Joined: 08 Jun 2013
Posts: 556
Location: France
GMAT 1: 200 Q1 V1
GPA: 3.82
WE: Consulting (Other)
If X*Y ≠ 0 and X^3*Y = X*Y^3, then which of the following must be true  [#permalink]

Show Tags

23 Jan 2019, 07:48
1
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:14) correct 25% (01:31) wrong based on 83 sessions

HideShow timer Statistics

If $$XY ≠ 0$$ and $$X^3Y = XY^3$$, then which of the following must be true?

I) $$|X| = -|Y|$$
II) $$|X| = |Y|$$
III) $$X = Y = 1$$

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

_________________

Everything will fall into place…

There is perfect timing for
everything and everyone.
Never doubt, But Work on
improving yourself,
Keep the faith and
It will all make sense.

VP
Joined: 09 Mar 2018
Posts: 1002
Location: India
If X*Y ≠ 0 and X^3*Y = X*Y^3, then which of the following must be true  [#permalink]

Show Tags

Updated on: 24 Jan 2019, 23:21
1
Helium wrote:
If $$XY ≠ 0$$ and $$X^3Y = XY^3$$, then which of the following must be true?

I) $$|X| = -|Y|$$
II) $$|X| = |Y|$$
III) $$X = Y = 1$$

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

$$X^3Y = XY^3$$
$$X^3Y - XY^3 = 0$$
$$XY (X^2 - Y^2) = 0$$
$$XY (X - Y) (X+Y) = 0$$

Now XY != 0(given) so X^2 = Y^2

I) $$|X| = -|Y|$$
Now this inequality can show 4 cases, We can't say anything about XY(This can be +ive or -ive), i wont go with this. Not sufficient
X= - Y, X= -(-Y), -X = -Y and -X = - (-Y)

II) $$|X| = |Y|$$
This is always true, square root of X^2 = Y^2 => |X| = |Y|

III) $$X = Y = 1$$
Not necessary, what if the value is different

_________________

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.

Originally posted by KanishkM on 23 Jan 2019, 08:15.
Last edited by KanishkM on 24 Jan 2019, 23:21, edited 2 times in total.
Intern
Joined: 15 Nov 2018
Posts: 25
Re: If X*Y ≠ 0 and X^3*Y = X*Y^3, then which of the following must be true  [#permalink]

Show Tags

23 Jan 2019, 08:35
If XY≠0XY≠0 and X3Y=XY3X3Y=XY3, then which of the following must be true?

I) |X|=−|Y||X|=−|Y|
II) |X|=|Y||X|=|Y|
III) X=Y=1X=Y=1

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

IMO B
1- |X| = -|Y|
Not sufficient coz modulus never gives a negative value ,

2- |X| = |Y|
4 cases but it will always end up in 2 saying x=Y or x= -Y
Upon simplifying the original equation we will get
Xy= 0 - not possible
X= Y or x= -y
Sufficient

3- x=Y=1
Not sufficient coz x and u could 2 and 2 or 3 and 3 or 2 and -2
Not sufficient

Posted from my mobile device
Manager
Joined: 02 Aug 2015
Posts: 152
Re: If X*Y ≠ 0 and X^3*Y = X*Y^3, then which of the following must be true  [#permalink]

Show Tags

23 Jan 2019, 09:31
Helium wrote:
If $$XY ≠ 0$$ and $$X^3Y = XY^3$$, then which of the following must be true?

I) $$|X| = -|Y|$$
II) $$|X| = |Y|$$
III) $$X = Y = 1$$

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

$$X^3Y = XY^3$$

$$X^3Y - XY^3$$ = 0

XY($$X^2 -Y^2$$) = 0

Given $$XY ≠ 0$$

So $$X^2 -Y^2$$ = 0

$$X^2 = Y^2$$

Options II and III satisfy the above condition.

Also in I) $$|X| = -|Y|$$,

|X| is always positive, how can it be equal to a negative value? The case is only possible when X=Y=0 but questions says $$XY ≠ 0$$.

Are the given options correct or am I missing something?

Cheers!
Intern
Joined: 24 Jun 2018
Posts: 12
Re: If X*Y ≠ 0 and X^3*Y = X*Y^3, then which of the following must be true  [#permalink]

Show Tags

23 Jan 2019, 12:56
KanishkM

If C must be true ie X=Y=1 that means X & Y cant hold any other value, other than 1.

However, X=Y=2 or X=Y=3 also achieves the condition mentioned in the question.
Re: If X*Y ≠ 0 and X^3*Y = X*Y^3, then which of the following must be true   [#permalink] 23 Jan 2019, 12:56
Display posts from previous: Sort by