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

It is currently 22 Oct 2019, 08:04

Close

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If x < y < 0, which of the following must be true?

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 58428
If x < y < 0, which of the following must be true?  [#permalink]

Show Tags

New post 21 Jan 2019, 02:31
1
2
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

68% (01:20) correct 32% (01:30) wrong based on 190 sessions

HideShow timer Statistics

Intern
Intern
avatar
B
Joined: 30 Dec 2018
Posts: 34
Concentration: International Business, Marketing
Re: If x < y < 0, which of the following must be true?  [#permalink]

Show Tags

New post 21 Jan 2019, 03:08
Answer is A only

As x and y are negative with Mode of X always greater than Mode of Y

Second and third condition are may be true or may not bw

Posted from my mobile device
Veritas Prep GMAT Instructor
User avatar
V
Joined: 16 Oct 2010
Posts: 9701
Location: Pune, India
If x < y < 0, which of the following must be true?  [#permalink]

Show Tags

New post 21 Jan 2019, 04:37
1
1
Bunuel wrote:
If x < y < 0, which of the following must be true?

I. |x| > |y|
II. x/y > 1
III. x^y < 0

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


x and y are both negative numbers. Imagine the number line: y is to the left of 0 and x is to the left of y.
e.g. x = -2 and y = -1
or
x = -1/2 and y = -1/3
and so on.
The absolute value of x will be greater than absolute value of y to make x "more negative".

Since x and y are both negative, x/y is positive. Since absolute value of x is greater than absolute value of y, x/y > 1

So both I and II will hold.

III may not hold if y is even. e.g. x = -3, y = -2 so x^y = (-3)^(-2) = 1/9 (not negative)

Answer (D)


You can prove I and II algebraically too.

x and y are negative.

x < y
Multiply both sides by -1 to get -x > -y
Since x and y are negative, |x| = -x and |y| = -y
So |x| > |y|

x < y
Divide both sides by y (which is negative) to get
x/y > 1 (the inequality sign flips)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Director
Director
avatar
G
Joined: 09 Mar 2018
Posts: 994
Location: India
If x < y < 0, which of the following must be true?  [#permalink]

Show Tags

New post 21 Jan 2019, 05:22
Bunuel wrote:
If x < y < 0, which of the following must be true?

I. |x| > |y|
II. x/y > 1
III. x^y < 0

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


Given x<y< 0

x and y are -ive.

I. |x| > |y|, will always be true, just plug in these values -2 < -1 < 0 or - 0.50 < - 0.25 < 0

II. x/y > 1, in this case, y will always be less than x, -4/-2 > 1, -0.1/ - 0.05 > 1, -6/-5 > 1

At this stage, we can just mark D and go ahead.

Still, III. x^y < 0,
if y is an even power, the relationship will become +ive which wont be < 0
if y is an odd power, the relationship will become -ive which is < 0

Answer D
_________________
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.
GMAT Club Legend
GMAT Club Legend
User avatar
D
Joined: 18 Aug 2017
Posts: 5031
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member
Re: If x < y < 0, which of the following must be true?  [#permalink]

Show Tags

New post 21 Jan 2019, 09:44
Bunuel wrote:
If x < y < 0, which of the following must be true?

I. |x| > |y|
II. x/y > 1
III. x^y < 0

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


from given relation we can say that whether x & y are fractions or integers they would both be -ve values since <0 is mentioned

test the relations with x = -2 and y = -3 and fractions y= -1/3 and x = -1/2

upon reviewing the options we can conclude that options 1 & 2 would stand correct
IMO D
GMAT Club Bot
Re: If x < y < 0, which of the following must be true?   [#permalink] 21 Jan 2019, 09:44
Display posts from previous: Sort by

If x < y < 0, which of the following must be true?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne