GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 16 Feb 2020, 10:54

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 and x < 0, then which of the following must be true?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 61189
If x > y and x < 0, then which of the following must be true?  [#permalink]

Show Tags

New post 02 Apr 2019, 02:59
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

62% (02:21) correct 38% (02:08) wrong based on 41 sessions

HideShow timer Statistics

GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 11 Sep 2015
Posts: 4318
Location: Canada
Re: If x > y and x < 0, then which of the following must be true?  [#permalink]

Show Tags

New post 02 Apr 2019, 05:38
1
Top Contributor
Bunuel wrote:
If \(x > y\) and \(x < 0\), then which of the following must be true?

I. \(\frac{1}{x} < \frac{1}{y}\)

II. \(\frac{1}{x−1} < \frac{1}{y−1}\)

III. \(\frac{1}{x+1} < \frac{1}{y+1}\)


(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only


We're told that x is NEGATIVE, and we're told that y < x, so y is also NEGATIVE

Take each statement and manipulate it (by applying the rules of inequalities) to see which one(s) obey the restriction that y < x

I. \(\frac{1}{x} < \frac{1}{y}\)

Multiply both sides by x to get: \(1 > \frac{x}{y}\) [since we multiplied by a NEGATIVE value, we REVERSED the inequality symbol]

Multiply both sides by y to get: \(y < x\) [since we multiplied by a NEGATIVE value, we REVERSED the inequality symbol]

PERFECT! This obeys the restriction that y < x

Statement I is true.
Check the answer choices . . . ELIMINATE B and C


II. \(\frac{1}{x−1} < \frac{1}{y−1}\)
NOTE: Since x is NEGATIVE, we know that x-1 is NEGATIVE
Likewise, since y is NEGATIVE, we know that y-1 is NEGATIVE

Multiply both sides by \(x-1\) to get: \(1 > \frac{x-1}{y−1}\) [since we multiplied by a NEGATIVE value, we REVERSED the inequality symbol]

Multiply both sides by \(y-1\) to get: \(y-1 < x-1\) [since we multiplied by a NEGATIVE value, we REVERSED the inequality symbol]

Add 1 to both sides to get: \(y < x\)

PERFECT! This obeys the restriction that y < x

Statement II is true.
Check the remaining answer choices . . . ELIMINATE A and E


By the process of elimination, the correct answer is D

RELATED VIDEO FROM MY COURSE

_________________
Test confidently with gmatprepnow.com
Image
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5898
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Reviews Badge CAT Tests
Re: If x > y and x < 0, then which of the following must be true?  [#permalink]

Show Tags

New post 03 Apr 2019, 02:46
Bunuel wrote:
If \(x > y\) and \(x < 0\), then which of the following must be true?

I. \(\frac{1}{x} < \frac{1}{y}\)

II. \(\frac{1}{x−1} < \frac{1}{y−1}\)

III. \(\frac{1}{x+1} < \frac{1}{y+1}\)


(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I and III only


given x<0 ; x is -ve so y has to be -ve as well
x=-1 and y=-2
test with options
only IMO E is correct
Manager
Manager
avatar
S
Joined: 18 Oct 2018
Posts: 91
Location: India
Concentration: Finance, International Business
GMAT 1: 710 Q50 V36
GPA: 4
WE: Business Development (Retail Banking)
Re: If x > y and x < 0, then which of the following must be true?  [#permalink]

Show Tags

New post 03 Apr 2019, 10:06
The 3rd statement won't stand for x=-1, y=-2
In this case, it will be 1/x= 1/(-1+1)= infinity
While, 1/y= 1/(-2+1)=-1

Hence answer should be D, statement 1 and 2 are true
GMAT Club Bot
Re: If x > y and x < 0, then which of the following must be true?   [#permalink] 03 Apr 2019, 10:06
Display posts from previous: Sort by

If x > y and x < 0, then 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