It is currently 11 Dec 2017, 12:14

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135256 [0], given: 12679

If x<0,y>0, and |x|>|y|, which of the following must be true? [#permalink]

Show Tags

New post 06 Feb 2015, 07:38
Expert's post
6
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

74% (01:02) correct 26% (02:11) wrong based on 522 sessions

HideShow timer Statistics

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

A. x > y
B. y^2 > x^2
C. x^3 > y^2
D. –x < y
E. x < –y

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135256 [0], given: 12679

2 KUDOS received
Manager
Manager
User avatar
Joined: 04 Oct 2013
Posts: 176

Kudos [?]: 164 [2], given: 29

Concentration: Finance, Leadership
GMAT 1: 590 Q40 V30
GMAT 2: 730 Q49 V40
WE: Project Management (Entertainment and Sports)
Re: If x<0,y>0, and |x|>|y|, which of the following must be true? [#permalink]

Show Tags

New post 06 Feb 2015, 08:13
2
This post received
KUDOS
Bunuel wrote:
If x<0, y>0, and |x| > |y|, which of the following must be true?

A. x > y
B. y^2 > x^2
C. x^3 > y^2
D. –x < y
E. x < –y

Kudos for a correct solution.


say x=-6 and y=3; say x=-0,5 and y=0,3. Plug them into the answer choices and the only one that must be true is E.
_________________

learn the rules of the game, then play better than anyone else.

Kudos [?]: 164 [2], given: 29

1 KUDOS received
Manager
Manager
avatar
Joined: 02 May 2014
Posts: 116

Kudos [?]: 63 [1], given: 475

Schools: ESADE '16, HKU'16, SMU '16
GMAT 1: 620 Q46 V30
GMAT ToolKit User
Re: If x<0,y>0, and |x|>|y|, which of the following must be true? [#permalink]

Show Tags

New post 06 Feb 2015, 22:26
1
This post received
KUDOS
x<0, y>0, and |x| > |y|

The above statements mean that the magnitude of x is greater than the magnitude of y but x is negative.
So, if we make both of them -ve by changing the sign of y to -ve i.e. -y , then -y, which has a magnitude less than x, will be greater than x.
Hence (E).

U can also solve this problem fairly quickly if u plot x and y on a number line.
x will be at a greater distance from 0 on the left hand side than y on the right hand side.

Thanks!

Kudos [?]: 63 [1], given: 475

Expert Post
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5336

Kudos [?]: 6088 [0], given: 121

Re: If x<0,y>0, and |x|>|y|, which of the following must be true? [#permalink]

Show Tags

New post 07 Feb 2015, 05:21
the three inequalities tell us ..
x is -ive and y is +ive..
x is farther than y from 0 on a line..
so ans E
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6088 [0], given: 121

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 42544

Kudos [?]: 135256 [0], given: 12679

Re: If x<0,y>0, and |x|>|y|, which of the following must be true? [#permalink]

Show Tags

New post 09 Feb 2015, 06:00
Expert's post
3
This post was
BOOKMARKED
Bunuel wrote:
If x<0, y>0, and |x| > |y|, which of the following must be true?

A. x > y
B. y^2 > x^2
C. x^3 > y^2
D. –x < y
E. x < –y

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

Correct Answer: (E)

Let’s go through each answer choice: (A) can never be true, since no negative is greater than a positive. (B) doesn’t have to be true – consider what would happen if x = -2 and y = 1. (C) can never be true, as x^3 must be negative, and y^2 must be positive. (D) can never be true, since if x < 0, -x is the same thing as |x|, and |x| > y. (E) can be manipulated by multiplying both sides by -1, which gives us –x > y. Remember that x < 0, so –x = |x|, and y is positive, so |y| = y. Thus –x > y is the same statement as |x| > |y|, and (E) must be true.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Kudos [?]: 135256 [0], given: 12679

Intern
Intern
avatar
Joined: 30 Apr 2015
Posts: 3

Kudos [?]: 2 [0], given: 45

Re: If x<0,y>0, and |x|>|y|, which of the following must be true? [#permalink]

Show Tags

New post 13 Jun 2015, 11:00
First, I will put the variables in a tabular format. Then try to plug in values to the variables which satisfy all the given conditions . Match the answer choices . e.g.
X Y !X! !Y! -X -Y
-4 3 4 3 4 -3

From the answer choices, you can see that only option E matches. i.e. X<-Y

Kudos [?]: 2 [0], given: 45

Expert Post
2 KUDOS received
EMPOWERgmat Instructor
User avatar
P
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10351

Kudos [?]: 3669 [2], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If x<0,y>0, and |x|>|y|, which of the following must be true? [#permalink]

Show Tags

New post 13 Jun 2015, 16:14
2
This post received
KUDOS
Expert's post
Hi All,

This question involves Number Properties and can be solved by TESTing VALUES.

We're given three facts to work with:
1) X < 0
2) Y > 0
3) |X| > |Y|

We're asked "which of the following MUST be true", which is the same as asking "which of the following is ALWAYS TRUE no matter how many different examples we can come up with?" We can TEST VALUES to prove which of the answers is sometimes NOT true (and you'll likely find that the right pair of values can be used to eliminate MORE than one answer)....

Answer A: X > Y
IF...X = -3, Y = 2, then this answer is NOT true. Eliminate A.

Answer B: Y^2 > X^2
If...X = -3, Y = 2, then this answer is NOT true. Eliminate B.

Answer C: X^3 > Y^2
IF...X = -3, Y = 2, then this answer is NOT true. Eliminate C.

Answer D: -X < Y
If...X = -3, Y = 2, then this answer is NOT true. Eliminate D.

Since we've eliminated 4 answers, there only answer that's left must be the correct one.

Final Answer:
[Reveal] Spoiler:
E


GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3669 [2], given: 173

Intern
Intern
avatar
B
Joined: 19 Apr 2017
Posts: 19

Kudos [?]: 5 [0], given: 23

Location: India
WE: Management Consulting (Consulting)
Re: If x<0,y>0, and |x|>|y|, which of the following must be true? [#permalink]

Show Tags

New post 12 Nov 2017, 01:16
Used negation to get to E. Since x must be negative, A, B, C, and D are out.
But is the sign correct in option E? I understand that -(-x) > y is the same as |x| > |y|, but E says x < -y.
_________________

We are what we REPEATEDLY do. GREATNESS then is not ACT, but a HABIT.

Kudos [?]: 5 [0], given: 23

Expert Post
1 KUDOS received
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5336

Kudos [?]: 6088 [1], given: 121

Re: If x<0,y>0, and |x|>|y|, which of the following must be true? [#permalink]

Show Tags

New post 12 Nov 2017, 04:45
1
This post received
KUDOS
Expert's post
dumbodingo wrote:
Used negation to get to E. Since x must be negative, A, B, C, and D are out.
But is the sign correct in option E? I understand that -(-x) > y is the same as |x| > |y|, but E says x < -y.


Hi..
Whenever you multiply both sides of INEQUALITY by '-', you change the sign of INEQUALITY.
That is -x>y......-*-x.<-y....x<-y
Reason is the properties of number when NEGATIVE is OPPOSITE of when POSITIVE.
Larger the numeric value, larger the number 8>4
While when negative, larger the numeric value, smaller the number -8<-4

Example of -x>y
-2>-7.....-*-2<-*-7....2<7
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 6088 [1], given: 121

1 KUDOS received
VP
VP
avatar
P
Joined: 22 May 2016
Posts: 1106

Kudos [?]: 396 [1], given: 640

If x<0,y>0, and |x|>|y|, which of the following must be true? [#permalink]

Show Tags

New post 13 Nov 2017, 10:21
1
This post received
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:
If x<0, y>0, and |x| > |y|, which of the following must be true?

A. x > y
B. y^2 > x^2
C. x^3 > y^2
D. –x < y
E. x < –y

Kudos for a correct solution.

Translate:
x < 0 --> x is negative
y > 0 --> y is positive

|x| > |y| --> the "positive" value of x, -(-x), is greater than y. Magnitude of x > magnitude of y

Or, x is more negative than y is positive: on the number line, x's distance from 0, to the left, is farther than y's distance from 0, to the right.

Pick numbers and check answers.
x = -3, y = 2

Plug in
A. x > y: FALSE. -3 is not > 2

B. y^2 > x^2: FALSE. 4 is not > than 9

C. x^3 > y^2: FALSE. -27 is not greater than 4

D. –x < y. FALSE. -(-3) = 3. 3 is not less than 2

E. x < –y: TRUE. -3 is less than -2

Answer E

Assess signs x = -3, y = +2

A. x > y:
(-) > (+)?? NO

B. y^2 > x^2. Integers raised to even powers = positive.
Small (+) > Bigger (+)?? NO

C. x^3 > y^2: (-) raised to odd power = negative.
(-) > (+)?? NO

D. –x < y. For (x), the negative, or opposite (which is one thing the "-" sign means), of a negative is positive. So
bigger positive < smaller positive?? NO

E. x < –y. For y, the negative of a positive is negative.
More negative < less negative? YES.
<--[-3]---[-2]-------[0]-->
More to the left of zero = smaller

Answer E

Kudos [?]: 396 [1], given: 640

If x<0,y>0, and |x|>|y|, which of the following must be true?   [#permalink] 13 Nov 2017, 10:21
Display posts from previous: Sort by

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

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.