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

It is currently 18 Jul 2018, 03:57

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 and y are integers, is |xy|/y>0?

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

Hide Tags

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6230
If x and y are integers, is |xy|/y>0? [#permalink]

Show Tags

New post 17 Nov 2017, 09:29
2
3
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

23% (01:09) correct 77% (01:48) wrong based on 74 sessions

HideShow timer Statistics

If x and y are integers, is \(\frac{|xy|}{y}\geq{0}\) ?

(1) \(y^3<|y|\)
(2) \(|xy|>|y|\)


self made - a tricky one

_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

1 KUDOS received
DS Forum Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1280
Location: India
Premium Member
Re: If x and y are integers, is |xy|/y>0? [#permalink]

Show Tags

New post 17 Nov 2017, 11:20
1
We know that |xy| will always be >=0, so the expression |xy|/y will be >=0 if y > 0 and it will be < 0 if y < 0 (we cannot take y=0 as that would make the question undefined).

(1) y^3 < |y|
This expression will be true for ALL negative values of y. Thats because |y| will be positive but y^3 will be negative.
Now this will also be true for 0<y<1. If y lies between 0 and 1, y^3 will be less than y or |y|. BUT the catch here is that we are given y is an integer. So it cannot lie between 0 and 1.
So from this statement we can safely say that y can only be negative. So |xy|/y will be negative. We got NO as our answer. Sufficient.

(2) |xy| > |y|
LHS can also be written as |x|*|y|. So |x|*|y| > |y| or |x| > |y|/|y| or |x| > 1. So either x > 1 or x < -1.
But this doesnt tell us anything about whether y is positive or negative. Insufficient.

Hence A answer.
Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 6230
Re: If x and y are integers, is |xy|/y>0? [#permalink]

Show Tags

New post 18 Nov 2017, 20:22
1
1
chetan2u wrote:
If x and y are integers, is \(\frac{|xy|}{y}\geq{0}\) ?

(1) \(y^3<|y|\)
(2) \(|xy|>|y|\)


self made



Hi amanvermagmat,

your thinking has been correct but you have neglected the role of second variable x..

lets solve it..
\(\frac{|xy|}{y}\geq{0}\)
the numerator will be 0 if x is 0 OR it will be POSITIVE as the value is in MOD

(1) \(y^3<|y|\)
since y is an integer, y will be a negative integer..
BUT we have x too..
if x is 0, \(\frac{|xy|}{y}={0}\), and ans is YES
If x is an integer, \(\frac{|xy|}{y}<{0}\)... ans is NO
insuff

(2) \(|xy|>|y|\)
square both sides...
\((xy)^2>y^2......y^2(x^2-1)>0\)
although it does not give anything to solve but tells us that both x and y are non zero
insuff

combined-
y is negative and x is non zero
so \(\frac{|xy|}{y}\geq{0}\) is always NO.

C
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

DS Forum Moderator
avatar
P
Joined: 22 Aug 2013
Posts: 1280
Location: India
Premium Member
Re: If x and y are integers, is |xy|/y>0? [#permalink]

Show Tags

New post 18 Nov 2017, 22:26
chetan2u wrote:
chetan2u wrote:
If x and y are integers, is \(\frac{|xy|}{y}\geq{0}\) ?

(1) \(y^3<|y|\)
(2) \(|xy|>|y|\)


self made



Hi amanvermagmat,

your thinking has been correct but you have neglected the role of second variable x..

lets solve it..
\(\frac{|xy|}{y}\geq{0}\)
the numerator will be 0 if x is 0 OR it will be POSITIVE as the value is in MOD

(1) \(y^3<|y|\)
since y is an integer, y will be a negative integer..
BUT we have x too..
if x is 0, \(\frac{|xy|}{y}={0}\), and ans is YES
If x is an integer, \(\frac{|xy|}{y}<{0}\)... ans is NO
insuff

(2) \(|xy|>|y|\)
square both sides...
\((xy)^2>y^2......y^2(x^2-1)>0\)
although it does not give anything to solve but tells us that both x and y are non zero
insuff

combined-
y is negative and x is non zero
so \(\frac{|xy|}{y}\geq{0}\) is always NO.

C


oh ok! Thanks so much. Kudos!
Re: If x and y are integers, is |xy|/y>0?   [#permalink] 18 Nov 2017, 22:26
Display posts from previous: Sort by

If x and y are integers, is |xy|/y>0?

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

Events & Promotions

PREV
NEXT


cron

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.